Homework answers / question archive / Finance topics in the questions are based on: market risk/diversifiable risk, finding net present values, debt to equity ratio, find IRR, required return, beta, (after-tax) weighted average cost of capital, rate of return, cost id equity and perform a ratio analysis for the firm

Finance topics in the questions are based on: market risk/diversifiable risk, finding net present values, debt to equity ratio, find IRR, required return, beta, (after-tax) weighted average cost of capital, rate of return, cost id equity and perform a ratio analysis for the firm

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Finance topics in the questions are based on: market risk/diversifiable risk, finding net present values, debt to equity ratio, find IRR, required return, beta, (after-tax) weighted average cost of capital, rate of return, cost id equity and perform a ratio analysis for the firm.1) 2) 3) 4) Course: Finance 300, 320 - Principle of Corporate Finance Answer all questions. Total points: 150. No late turn-in or extension. No allowance and credit will be given to any late assignment. Provide clear statements and analyses. State your assumptions whenever you need them. Good Luck! 1. (10 points) Explain the ideas of Market Risk and Diversifiable Risk. What is the main difference of these two concepts? Will adding more assets in the portfolio help to reduce the diversifiable risk? Why or Why not? Explain your reasons. 2. (40 points) You are given with the following information of two projects planned by your company. Two projects are of the same initial costs with $3 millions. Project A B Year 1 -650 560 Table 1: (in thousands) Year 2 Year 3 Year 4 720 - 50 1000 1875 1600 Year 5 2800 Answer the following questions. a) Suppose the cost of capital is 12%. What are the Net Present Values for these two projects? b) Suppose the financial manager discovered that if we postponed the project B to two years later, the cost of capital could be 8% due to possible low future interest rates. However, the deferment may cost the firm additional $0.5 million to restart the facilities and the initial cost must be spent now, instead of two years later. Will you recommend waiting for additional 2 years to start? c) Let the corporate income tax rate be 30%, the cost of debts be 6%, the cost of equity be 25% and there is no preferred stock issued by the firm. What is the debt-to-equity ratio for your company? d) Find the IRR (Internal Rate of Return) for project A and project B. e) Suppose there is a 40% chance that the market may be bad and the cash flows for both projects will change to Project A B Year 1 -650 560 Year 2 720 1875 Year 3 - 50 -1500 Year 4 -100 Year 5 -500 That is to say, the original cash flows in Table 1 only have 60% chance to happen. What is your decision for each project? What is the present value of the “marginal value of choice” for each project? f) Suppose now these projects are about to invest in foreign countries. The projects are to finance locally. Let the local capital market offer the interest rate as 5% and the local tax rate is 15%, the “beta’s” for project A and B are 1.2 and 1.5 respectively, where the risk-free rate is 5% and market index rate of return is on average 16%, the debt-to-equity ratio is 1 to 4, what are the risk-adjusted Net Present Values for these two projects? 3. (20 points) You have the following information for the company Exxon. The “beta” coefficient for Exxon is .85 based on the past information. The 3-year average of 30-day T-bill rate is 2%, the average market return of (say, S&P 500 index) in the same period is 16%. Answer the following questions: a) What is the required return for Exxon? Why do we call it “required” return? b) Suppose that Exxon’s current dividend is $.60 per share with possible expected growth rate as 4% per year from now on, what is your assessment for the value of Exxon’s stock? c) Suppose the current market price for the Exxon’s stock is $9 per share. Let the capital market be efficient as ideally assumed. That is, the current stock price is equal to the stock fair value. What is the required return for this stock now if the information in (b) still applies? What is the “beta” associated with this stock now? d) Exxon has the following capital structure: the firm issued 6 million shares of common stock with the stock price in c), the firm also issued 1.5 million shares of preferred stock with $4.5 preferred dividend per share, currently, Exxon has $25 millions in debts with interest rate as 6.5%. Suppose the current preferred stock price is $6 per share and the current common stock price is as in question (c), and the corporate tax rate is 25%. What is the (after-tax) weighted average cost of capital for Exxon? e) Why is Exxon able to undertake so much in debts? Is this related with the industry or business risk? f) Will this firm undertake high operating leverage? Why or why not? 4. (20 points) Let the information on your portfolio be given as follows. You have three assets in the basket. The "beta's" among them are given as follows; ?1 = -0.45, ? 2 = 0.89 ? 3 = 1.2, Answer the following questions; a) Why do we need these "beta's" to construct the portfolio? b) If the risk-free rate is given as 3%, what are the required returns for asset 1 and asset 2 if the market rate of return is expected to have 10%? c) Is it possible to construct a risk-free (or zero-beta) portfolio by combining asset 1 and asset 2? If yes, what is the required return for this portfolio? If the transaction cost for this portfolio requires 4.5% of commission, will you do it? d) If you'd like to form a portfolio with these three assets that mimic the overall market, what are the weights of this portfolio? (Notice that there may be more than one answer for this problem). 5. (20 points) You are given with the following information of two proposal of financing programs for your home loan. Suppose the new house costs you $650,000 (sales taxes and others are included). One program is asking you to deposit a 20% down payment on the $650,000 and it provides you with 5.5% interest rate for 15-year monthly payments of the remaining balance, the other program is a 100% financing program which gives you a 2.5% for the first 5 year with the balloon payment as 600,000 plus the PMI (property mortgage insurance) as $200 per month and the rate increases to 6.75% afterward for a 30-year mortgage if no balloon payment for the remaining balance or refinancing is pursued. Let there be no prepayment penalty. That is, you may pay off the loan should you have some extra cash later on. The brokerage fees and commissions are already considered in all the numbers given. Answer the following questions. a) What is the monthly payment for each program in the first 5 years? Which one is more favorable to you if your monthly income is $6,000 before tax? (Notice that most lenders will require the borrower to have ratio between mortgage payment and monthly income no greater than 33%). b) Suppose 4 years later, the market price of your house is $800,000. The tax rate on gains/losses on house sales is 8%. Will you consider selling this house and buy a bigger one if your income has gained to $7000 per month? What is the annualized rate of return in your investment on housing? (Hint: you need to apply amortization of loan here first). c) Which way of financing the house originally gives you more rate of return if you in fact, sell the house? 6. (20 points) Company JJ gives you the following information for its operation. The expected profit (before tax) is $60 millions next year. Suppose there is a 35% corporate income tax imposed on the company. Company JJ has no debt originally. There are 8 million shares of common stocks outstanding. Let the current market price for the stock be $25 per share. Suppose that there is no expansion plan for the company to either spend on working capital vs. long-term investment or to apply the accumulated retained earning. Answer the following questions: a) Suppose that Company JJ also has issued some 5-year coupon bonds recently. The bond carries 6% coupon with $1,000 par value. Let the current bond price be $700 per bond, what is the yield to maturity for this bond? What are the assumptions you make here? Is there any limitation for this model? b) Let Company JJ’s total debts on coupon bond be $70 millions. How much will be the value of stockholders’ equities under Modigliani and Miller’s proposition? c) What is the cost of equity for Company JJ, if there’s no preferred stock issued for this company? d) What is the weighted average cost of capital after Company JJ has debts? e) Will the application of debts increase the “beta” of Company JJ’s common stock? Why or why not? (Note: You don’t need to calculate it. Just explain the reasons). 7. (20 points) You are given with the following information of a firm "JoJo Bear", assuming that the firm did not issue preferred stocks while the firm may have some foreign subsidiaries overseas. The firm is making perfumes and cosmetics for middle-income class of consumers. This industry tends to have high gross profit margin such as 25% and the setup costs are also high due to the production and technology. The R&D (Research and Development) costs are entirely reported as operating expenses according to the GAAP. Balance Sheet (in millions) 2017 2018 2019 1230 50 1420 260 210 200 1350 1578 1070 0 2200 1450 2873 0 5833 2205 430 5973 90 1329 6139 107 421 1685 75 147 20 1025 130 326 1792 198 120 15 1976 30 534 657 62 128 35 2450 2001 74 278 5833 1201 156 59 5973 1975 144 124 6139 Income Statement(in millions) 2017 2018 2019 Net Sales Cost of Goods Sold 5418 3109 6883 3310 Assets Cash Marketable securities Accounts Receivable Inventory Plant, Building, and Equipments (net) Investments in affiliates Total Assets Liabilities Short-term debts Advances from customers Accounts payable Interest payable Tax payable Other Accrued Expenses Bonds payable Stockholders' Equity Common stock Additional paid-in capital Retained earning Total liabilities and equities 4529 2215 Selling and General Expenses Depreciation Expense Interest Expense Income Tax Expense Net Income 771 213 97 175 1058 812 298 109 137 953 1059 284 621 154 1455 a) Perform the Ratio Analysis for the firm. (Need all the ratios that cover the activity analysis, liquidity analysis, solvency analysis to the profitability analysis) b) Given your result in a), what is your opinion on the firm's performance so far? What is the firm's strategy in raising capital? What are the firm's possible business and financial strategies in your opinions? Capital Structure and The Theory Usually, the firm would keep their financing of capital as the industry will do. Balance Sheet (in millions) 2013 2014 2015 Assets Cash Marketable securities Accounts Receivable Inventory Plant Building and Equipment Investments in affiliates Total Assets 230 50 1420 1260 2873 0 5833 210 100 1350 1578 1205 430 4873 970 0 1300 1450 990 1329 6039 Liabilities Short-term debts Advances from customers Accounts payable Interest payable Tax payable Other Accrued Expenses Bonds payable Common stock Additional paid-in capital Retained earning Total liabilities and equities 107 130 1030 421 326 534 685 792 657 75 98 62 147 120 128 20 15 35 3025 1976 1450 1001 1201 1875 74 156 144 278 59 124 5833 4873 6039 One can easily calculate the solvency analysis: • As the debt-to-equity ratio = 2.24 in 2013 • = 1.395 in 2014 • = 0.677 in 2015 • By which the firm is using the equity to replace the debts they had. Yet, the situation is that we have to compare it with the industry’s average or standard. • Even so, the industry’s average is not quite the standard for the firm’s finance of capital. Capital Structure Theory • M&M Proposition: • Given that there is a “frictionless” capital market, • The firm’s productivity or generation of future cash flows is independent of the financing decision, • No transaction cost, • The firm has no difficulty in reporting its value through the accounting procedures, • There is no tax in the market, • The investors can finance themselves equally efficient as the firm can do, • The capital market can be “efficient” in all the investors can get the information as they want, Assumptions (Cont’d) • The pay-out ratio is 100% • There’s no brokerage fee. • There is no arbitrage opportunity. “Arbitrage” means to create a zerofee transaction and have a “sure” profit. • There’s no classification for the shareholder’s equity. • Suppose the firm only has to pay the principal until the maturity of the debt, • The market value of the debt is equal to its book value M&M proposition 1: • If there’s no tax, the value of the firm is the same when the firm has debt or have no debt. • Intuitively, if the firm’s generation of future cash flows are independent of its financing, then the firm’s value was determined by its productivity and not by how it may form its capital structure. • See, if the firm’s productivity is unchanged, the firm can use any methods to form its financing, yet its productivity remains the same. • Example: Say we have firm Eddy which has the 100 million shares outstanding. Currently the firm’ stock pays $2.50 dividend per share with stock price currently as $20 per share. Suppose the firm wants to raise $300 millions debt with 5% interest rate, what is the possible expected rate of return of its stock after raising the debt? Example (Cont’d) • When looking at the firm’s productivity, we can get • $2.5*(100 million shares) = $250 million for its possible future cash flow • The rate of return before debt • Ru= 2.5/20= 12.5% • Now the firm is going to have $300 millions debt, according to M&M proposition 1, the firm will have the left-over cash flows as it pays the interest payment • $250 million – (0.05)*300 million = 250 – 15 = $235 millions • So according to the M&M proposition 1 • ?? = ?? • Where ?? stands for the value of firm before debt, ?? stands for the value of the firm after the debts. Example (cont’d) • That is, the shareholder’s equity for the firm after debt will be • $2000 millions – $300 millions = $1700 millions • Since there are 100 millions shares of common stock outstanding. • Hence, the possible stock price after debts is equal to $17 per share. Yet the dividend per share will become $2.35 per share. Hence, based on the perpetuity model we can find that the rate of return now becomes • 2.35/17= 13.823% > 12.5% originally • So raising debts will increase the rate of return for the stock since the application of debt reduced the profit-sharing of the shareholders. M&M Proposition 2: • Following the same set of assumptions, and allows there is corporate income tax then, • The M&M Proposition 2 says • ?? = ?? + ?? ? • Where ?? is the corporate income tax rate • The main idea is that even though debts are not favorable, the tax deductibility of interest payment is of use. Hence, the firm can undertake some debts. • Example: Let the “Eddy” has the same of information, except that we have the corporate income tax as 25% Example: • The value of the unleveraged firm as • $20*(100 millions shares) = $ 2000 millions Yet according to the M&M proposition 2 we have the value of the firm after debt becomes • $2000 millions + (.25)*300 millions = $2075 millions after debts • Given the accounting identity (total assets = total liabilities + total equity), the shareholder’s equity = 2075 -300 =1775 millions after having debts. So the stock price becomes $17.75 per share. Example (con’t) • To find the income for dividends we need to find the EBIT, that is, • $2.50*(100 millions shares) = (1 - .25)EBIT • Hence, EBIT = $250 millions/.75 = $ 333.33 millions • This gives the operating income of the firm. Now it remains the same after debt due to the independence of the firm’s productivity with its financing decision. Example (cont’d) • Hence, the income for dividends becomes • (1-.25)(333.33 – (.05)*(300)) since the interest payment is tax deductible. • Hence, income available for dividends is 239 million. • That is, the dividend per share is $2.39 • So the rate of return becomes 2.39/17.75 = 13.46% • Because there is corporate income tax, even the debt is not in favor of the shareholders, the tax deductibility of interest payment is preferred. Hence, the rate of return is higher than when there is no debt and lower than there is no tax. The Capital Asset Pricing Model (CAPM) • The model describes the “equilibrium” expected rate of return for a risky asset as • • ? ?? = ?? + ?? (?(?? ) − ?? ) • Where ?(?? ) is the expected rate of return for the market portfolio which is approximated by the market index’s average rate of return. That is, this is the bottom-line expected rate of return the asset deserts. • The term as ?(?? ) − ?? can be called the market premium which shows how the capital market rewards the investor is taking extra risk Diversification with the systematic risk Asset 1 has the ?1 =1.5 , asset 2 has ?2 = 0.5 and asset 3 has ?3 =0.9. The combinations of these assets will have the systematic risk as 1. We are going to have the portfolio as ?1 ?1 + ?2 ?2 + ?3 ?3 = 1 And ?1 + ?2 + ?3 = 1 Where ?1 , ?2 and ?3 are not always positive By the capital asset pricing model with ?? = 2%, ? ?? = 12% • we have ? ?1 = 17% • And ? ?2 = 7%, ? ?3 = 11% • Hence, we trying to obtain the • ??? ? ?? = ?1 ? ?1 + ?2 ? ?2 + ?3 ?(?3 ) • By the linearity and the “betas” are known, the • ? ?? = ?1 (?? + ?1 (?(?? ) − ?? )) + ?2 ( ?? + ?2 (?(?? ) − ?? )) • +?3 (?? + ?3 (?(?? ) − ?? )) = (?? + ?? (?(?? ) − ?? ) Since ?? = 1 • We can find that • • ? ?? = ?? + ?? (?(?? ) − ?? ) • = ?? + (?(?? ) − ?? ) • This implies that the systematic risk of the portfolio will be the linear combinations of the risky assets’ “beta’s” and so is the expected rate of return of the portfolio should be the linear combinations of the risky assets. One can see that the linearity guarantees that the combinations of asset has the systematic risk of the portfolio is simply the linear combinations of the assets’ “beta’s” and the expected rate of return for the portfolio is also the same liner combinations of the assets’ expected rate of return. That it, the same CAPM should also work for the portfolio. Several Characteristics of CAPM • 1. It determines the equilibrium rate of return when given the measure of systematic risk of the risky asset. Hence, it can be used to determine the bottomline rate of return for the equity. • 2. It’s a linear model with respect to systematic risk. • 3. The systematic risk of the risky asset can be determined by the sensitivity of the asset versus the entire capital market. • 4. It shows if the combination of different assets is efficient, the expected rate of return for the portfolio will be also on the same line. That is, the portfolio’s expected rate of return versus its systematic risk (of the portfolio) must be on the same line as CAPM Example • Now suppose we want to construct a portfolio with three assets together. Let the systematic risk for asset 1 is 0.8, for asset 2 is 1.2 and asset 3 is 0.9. The combinations for the assets are ( ½, , ¼ ,¼) to make the portfolio. Suppose the Tbill rate is 2%, and S&P 500 index return has the average rate as 12%. • 1) what is the expected rate of the portfolio (in equilibrium)? • Let the systematic risk of the portfolio be given as • ½*(0.8)+ ¼ *(1.2) + ¼*(0.9) = (0.4)+(0.3) +(0.225) = 0.925 • Hence, by the CAPM we have • E(R) = 2% + (0.925)(12%-2%) = 11.25% • 2) Suppose we want to create a zero-beta portfolio of asset one and asset two with the transaction cost as $5 for the trade. Would you do it? • Say, in this case, you can have the portfolio as (3, -2,0) and the portfolio will have the zero beta in the systematic risk. A negative number shows that the short sell is applicable in the portfolio. But would you do it? Apparently, you will not do it. • If you don’t do anything, simply buying the T-bill rate is 2%. Yet constructing the portfolio will end up with a zero beta, the CAPM will give the 2% rate of return, too. Doing the construction of the portfolio is simply the same as doing nothing. • And the transaction cost is additional $5 fee that you have to pay. Would you do it? Certainly not. • Constructing the portfolio is a good idea. Yet, if the portfolio does not give you the expected rate of return subject to the risk is taking, the portfolio is not good enough to hold. Example: some mutual funds may boast of their rates of return from the past history. Yet they never show you the risk they are taking. In fact, if compare to the risk they’re taking, the portfolios may not be good enough. So, in the earlier capital budgeting questions, we usually assume the given discount rate. • We now can use this model to determine the underlying bottom-line Weighted Average Cost of Capital as the following. Say suppose there is no preferred stock issued. And the debt ratio is given as ¼, the equity ratio is 3/4., the tax rate is 15%. The current interest rate of the debt is 8%. And we use the above portfolio for financing our equity, the WACC is found as • (1/4)*8%(1-15%)+(3/4)(12%) = 10.7% • We can then use this rate for our capital budgeting decision using NPV or IRR decision rules. Now suppose the firm Apple Bees originally was in the restaurant industry the firm originally has the WACC as 7.5%, • The firm is considering the investment project in the computer game industry. Let the typical firm in the computer game industry be given as Zebra who has the debt ratio as ¼ for the debt requires 5% interest rate and the equity ratio as ¾ and the “beta’ the systematic risk is as 1.5 with the S&P 500 index rate of return as 10% and the T-bill rate as 2%. The tax rate in that industry is 15%. • Now the WACC for the Apple Bees’ investment is not the same as the original as it was before. Instead, we should choose the Zebra’s WACC as the investment’s discount rate. That is, we need to get the expected rate of return for Zebra for the cost of equity of the forthcoming investment • That is, E(R) = 2% + 1.5(10%-2%) = 14% • WACC = ¼*5%(1-15%)+3/4(14%) = 11.56% • Hence, this rate should be used for the capital budgeting question later on. Now suppose the investment project involves the following expected cash flows. Year 1 Year 2 Year 3 Year 4 Project 1 200 300 300 400 Project 2 300 200 500 Both projects will have the initial outlay as 150. The net present values of these projects are shown as • ???1 = −150 + 200 1+11.56% + 300 1+11.56% 2 + 200 1+11.56% 2 + 300 1+11.56% 3 + 500 1+11.56% 3 • and • ???2 = −150 + 300 1+11.56% + 400 (11.56%)4 Compare to the NPV in using the original WACC of Apple Bees • ???1 = −150 + 200 1+7.5% • ???2 = −150 + 300 1+7.5% + 300 1+7.5% 2 + 200 1+7.5% 2 + 300 1+7.5% 3 + 500 1+7.5% 3 + 400 (1+7.5%)4 • The assessment in using the original WACC has overstated the effectiveness of the investment project. Hence, using the capital budgeting criterions should be considering the nature of the investment. One can not simply use the original WACC for the investment project in all cases. How to estimate the systematic risk and its relationship with systematic risk • the Capital Asset Pricing Model (CAPM): • the trade-off between the (required) expected rate of return and the socalled systematic risk. • 1) it is a simple linear model, • 2) it is feasible to calculate the expected rate of return once one can easily obtain the assessment that how sensitive the asset will be associated with the market as a whole The Capital Asset Pricing Model (CAPM) • The model describes the “equilibrium” expected rate of return for a risky asset as • • ? ?? = ?? + ?? (?(?? ) − ?? ) • Where ?(?? ) is the expected rate of return for the market portfolio which is approximated by the market index’s average rate of return. • The term as ?(?? ) − ?? can be called the market premium which shows how the capital market rewards the investor is taking extra risk. Example: • Suppose there is a stock with beta risk around 1.2 and the market index’s rate of return as 12% on the average. Let the basically T-bill rate be 2%, the required rate of return for this stock is • E(R) = 2% + 1.2(12% - 2%) = 14%, • This is the “required” rate of return as the capital market equilibrium. Hence, we can use the rate as the cost of equity for the stock. So, in the capital budgeting problem, this becomes the discount rate for the future cash flows if the firm is full-equity. If the firm is also financed with debt, then the weighted average cost of capital will become • W.A.C.C.= (debt ratio)*(cost of debt)(1-tax)+(equity ratio)*(cost of equity) Diversification with the systematic risk and applications in capital budgeting Asset 1 has the ?1 =1.5 , asset 2 has ?2 = 0.5 and asset 3 has ?3 =0.9. The combinations of these assets will have the systematic risk as 1. We are going to have the portfolio as ?1 ?1 + ?2 ?2 + ?3 ?3 = 1 And ?1 + ?2 + ?3 = 1 Where ?1 , ?2 and ?3 are not always positive By the capital asset pricing model with ?? = 2%, ? ?? = 12% • we have ? ?1 = 17% • And ? ?2 = 7%, ? ?3 = 11% • Hence, we trying to obtain the • ??? ? ?? = ?1 ? ?1 + ?2 ? ?2 + ?3 ?(?3 ) • By the linearity and the “betas” are known, the • ? ?? = ?1 (?? + ?1 (?(?? ) − ?? )) + ?2 ( ?? + ?2 (?(?? ) − ?? )) • +?3 (?? + ?3 (?(?? ) − ?? )) = (?? + ?? (?(?? ) − ?? ) Since ?? = 1 • We can find that • • ? ?? = ?? + ?? (?(?? ) − ?? ) • = ?? + (?(?? ) − ?? ) • This implies that in equilibrium, the expected rate of return for the portfolio simply follows the linear combination of the expected rates of return where each expected rate of return simply follows the capital asset pricing model. • Thus, if the firm’s stock follows with systematic risk as 1.2, we can get the expected rate of return as capital asset pricing model indicates that (assuming that the say, T-bill rate is 2% and the market index rate of return is 12%, the expected for the firm’s stock is • ?? + (1.2)(?(?? ) − ?? ) = 14% 1 3 Suppose the firm has the debt ratio as and there is no tax • We have the weighted average cost of capital as • 1 3 5% + 2 (14%) 3 = 11% • We can base on this rate for the net present value in the capital budgeting problem or the bottom-line rate of return in the IRR function of the same problem. • Now instead of basing on the given rate of return in the capital budgeting problem, the cost of capital now takes into account the way to determine the cost of equity by using the capital asset pricing model. Capital budgeting with Option • Capital Budgeting: So far, there are three things we assume • 1) The projects’ future cash flows are determined or assumed, • 2) The discount rate for the cash flows is given, • 3) The projects are continued until the projects are done. • Yet, in the real time, the projects can be deferred, stop, sell-off and abandoned. The example: Suppose the project follows the forecasted cash flows based on whether the years are good or bad. Let the cost of capital be given as 10%, the initial outlay for the projects for both cases are $150 (in thousands) There are two cases for the projects’ cash flows and they depend on whether the years are good or bad. The usual capital budgeting simply consider the expected cash flow from taking both chances into account and calculate the expected cash flows and determine the projects are doable or not. • The cash flows of the projects: • Project • 1 • 1 • • 2 2 Chance 60% 40% Year 1 250 100 Year 2 300 -100 Year 3 350 -200 60% 40% 300 120 350 -200 -450 -200 • It is not reasonable to consider the projects when the bad year hits. The firm may stop the projects when the expected cash flows turn negative. The usual analysis: • Obtain the expected cash flows in the projects together and consider whether it pays off. • The expected cash flows are • Year 1: for project 1 (.6)*(250)+(.4)*(100) = 190 • • Year 2: for project 1 (.6)*(300) + (.4)*(-100) = 140 • Year 3: for project 1 (.6)*(350) + (.4)*(-200) = 130 • Hence, the usual capital budgeting with net present value will give The net present value: •[ 190 1+10% + 140 1+10% 2 + 130 ]− 1+10% 3 150 = ???. ? > 0 • In the usual sense, this project is doable, and the firm would continue the project until the end. And if the firm considers the option to discontinue the project if the year is bad, the cash flows may look like the following: • Project • 1 • 1 Chance 60% 40% Year 1 250 100 Year 2 300 - • Hence, the net present value will become ? .6 350 ? 3 1+10% project. Year 3 350 - 190 1+10% + .6 ∗ 300 1+10% 2 + − 150 = ???. ? > 0 which there’s a marginal gain for stopping the Rate of Return and Risk So far, we assume the discount rate is given. Yet in reality, this is subject to estimation and assessment. Risk: Systematic Idiosyncratic Systematic: when the risk may affect all the risky securities in the capital market. Idiosyncratic: when the risk is confined to a certain securities, certain industries and certain sectors. How to estimate the systematic risk and its relationship with systematic risk • the Capital Asset Pricing Model (CAPM): • the trade-off between the (required) expected rate of return and the socalled systematic risk. • 1) it is a simple linear model, • 2) it is feasible to calculate the expected rate of return once one can easily obtain the assessment that how sensitive the asset will be associated with the market as a whole The Probability Space State of the World Probability Rate of Return Recession 1/4 Recovery 1/2 20% Boom 1/4 14% -10% The Statistics • The expected rate of return (according to the assessment from the probability distribution assessed perhaps subjectively) is • 1/4 ( -10% ) + 1/2 (20%)+ 1/4 ( 14% ) = 11%. • standard deviation as 1 (14% 4 1 (−10% 4 − 11%)2 + − 11%)2 as approximately as 12.37% 1 (20% 2 − 11%)2 + Suppose there are two assets of portfolio State of the world Probability R1 R2 Recession 1/4 -10% 4% Recovery 1/2 20% 12% Boom 1/4 14% 8% More statistics • It is easy to see that the asset-two's expected rate of return is • 1/ 4 ( 4% ) + 1/2 ( 12% ) + 1/4 ( 8% ) =9%. • And the variance of asset two is 44% 2 . • Namely, the co-variance of these two assets, • cov( R 1 , R 2 ) = 1/4 ( -10%-11% ) (4% - 9%)+ 1/2 ( 20%-11% ) (12% - 9%)+ 1/4 ( 14%-11% ) ( 8%-9% ) =156 %2 . • Remember that the co-variance is defined with “Two” arguments only. That is, the co-variance must explain the association between two arguments only. If one has more than two assets, one can not explain among all arguments in one co-variance alone. Mean Variance Analysis • For any risk-averse investor, suppose there are only two assets, the objective is to • ???? ? ?? subject to • ?1 + ?2 = 1, • ?? = ?1 ?1 + ?2 ?2 , • ??? ?? = ?12 ??? ?1 + ?22 ??? ?2 + 2?1 ?2 ???(?1 , ?2 ), • Where ? ?? = ?1 ? ?1 + ?2 ?(?2 ) Mean Variance Analysis • The problem is to maximize the expected rate of return and is subject to the constraints for the choice variables are the “weights” for each asset in the portfolio. • The problem depends heavily the estimates for the means, variances, and the covariance(s). Therefore, the problem centered on the statistics for the assets we choose. • Yet, the entire definition depends on the risk assessed as the “total risk” the assets may behave. • It shows the individual optimality only. No market equilibrium. The Systematic Risk • ?? = ???(?? ,?? ) , 2 ?? where ?? represents the rate of return for the market portfolio which can be approximated by the market index’s rate of 2 is the variance of the rate of return for the market portfolio. return, ?? It is easy to see that the numerator represents the co-respondence with the market altogether, while the denominator represents the volatility of the entire market. In other words, it shows how sensitive the rate of return for asset i with the market entirely. The Capital Asset Pricing Model (CAPM) • The model describes the “equilibrium” expected rate of return for a risky asset as • • ? ?? = ?? + ?? (?(?? ) − ?? ) • Where ?(?? ) is the expected rate of return for the market portfolio which is approximated by the market index’s average rate of return. • The term as ?(?? ) − ?? can be called the market premium which shows how the capital market rewards the investor is taking extra risk. Example: • Suppose there is a stock with beta risk around 1.2 and the market index’s rate of return as 12% on the average. Let the basically T-bill rate be 2%, the required rate of return for this stock is • E(R) = 2% + 1.2(12% - 2%) = 14%, • This is the “required” rate of return as the capital market equilibrium. Hence, we can use the rate as the cost of equity for the stock. So, in the capital budgeting problem, this becomes the discount rate for the future cash flows if the firm is full-equity. If the firm is also financed with debt, then the weighted average cost of capital will become • W.A.C.C.= (debt ratio)*(cost of debt)(1-tax rate)+(equity ratio)(14%) Another example: • Suppose the firm’s stock has the required rate of return as 12% and the T-bill rate as 2% and the market index’s rate of return as 10%, then we can find the firm’s stock is subject to the • ?? = (12% - 2%)/(10%-2%) = 1.25 • That is, the firm’s stock is somewhat more responsive than the market index in the impact from the systematic news. Capital Budgeting 2 Internal Rate of Return (IRR): The discount rate that sets the discounted cash flows of the project equal to the initial outlay. Or in other words, the discount rate that sets the Net Present Value of the project equal to zero. It’s a break-even rate of the project. Hence, it’s not the genuine rate of return of the project. It’s the worst-case scenario indicates the highest discount rate that the project can undertake. Decision Rule: • Choose the projects that the IRR exceed the actual financing cost. • Start with the project of the highest IRR. • Go to the second-best project if capital left-over • Go the rest if additional capital is available Example: • Suppose we have the projects to decide as follows . Project Initial Outlay Year 1 Year 2 Year 3 • 1. 150 60 80 180 • 2. 300 80 120 100 • 3. 100 70 90 100 • The equations can be written as •[ 60 1+???1 • 80 1+???2 • 70 1+???3 + 80 1+???1 2 + 120 1+???2 2 + 90 1+???3 2 + 180 ] 1+???1 3 + 100 1+???2 3 + 100 1+???3 3 Year 4 250 − 150 = 0 + 250 1+???2 4 − 100 = 0 − 300 = 0 Excel Applications • Go to Excel spreadsheet • Key in the associated cash flows for each project as • A B C • Project 1 Project 2 Project 3 • -150 -300 -100 • 60 80 70 • 80 120 90 • 180 100 100 • 250 Excel Example (continued) • Go to the function wizard • Ask for the “financial” function • Go to IRR function • The function will ask for the “Value”. • High-light the area for the project’s cash flows. Say for project 1. It’s • For column A and the second cell and on. So that’s A2..A5. Then, it will ask you for guess. (The reason is that the IRR may have multiple solutions.) You may ignore the question. • The IRR will give • ???1 = 39.68% • ???2 = 24.12% • ???3 = 62.92% Excel Applications (continued) • Suppose the actual cost for financing is 20% then, all the projects are doable. • The decision rule will be • 1) Try with project 3 first. • 2) Go to project 1 next if some capital is available • 3) Try with project 2 last. • The result is similar to the decision making with NPV. Limitation: • 1. The IRR is not the genuine rate of return for the project. Hence, it does not necessarily indicate the profitability of the investment. • 2. The IRR may have multiple solutions when the associated cash flows are of alternating signs. That is, the project may have some positive cash flows and some negative cash flows for a certain years. • IRR does not consider the possible the firm may change their decisions once the project begins. • All the cash flows expected are pre-determined. • Once the project is chosen, it will be continued as to the end. Limitation (continued) • The decisions based on NPV and IRR may not be the same. Hence, simply use one decision rule to determine the capital budgeting is dangerous. • For example, we have the following cash flows from the two projects. • Project Initial Outlay Year 1 Year 2 Year 3 • 1 250 350 -150 280 • 2 220 250 20 150 • If use the IRR decision rules, both will have the IRR as 50%. Yet if the actual discount rate of the projects is 10%, the NPV for project 1 is 140.53, white the second one has 124.09. Other decision rules • Payback Period: The time span needed that the forecasted future cash flows of the project may cover the initial outlay. That is, it’s a breakeven analysis. • Example: Based on the earlier case with three projects, we have • Payback Period for project 1 = 3 • Payback Period for project 2 = 3 • Payback Period for project 3 = 2 • Decision Rule: • 1. Choose projects that the payback periods are shorter than the preliminary cut-off time span. • 2. Choose the project that its payback period is minimal. Limitation: • 1. The decision rule emphasizes the time span needed to cover the resource spent and forget the profitability. • 2. All the future cash flows are not considered their time values of money. • 3. No alternative decision is considered, That is, the project once selected will continue until the end. Discounted Payback Period • The time span needed when the sum of discounted cash flows of the project break-even with its initial outlay. • Similar to the earlier example, suppose the discount rate is 12%, • Discounted Payback Period for project 1 = 3 • Discounted Payback Period for project 2 = 4 • Discounted Payback Period for project 3 = 3 • The decision: • 1. it is indifferent to try project 1 or 3. • 2. If there’s any capital left-over, then go to project 2. Limitation: • 1. It depends on the discount rate applied. • 2. The emphasis of decision rule is the break-even point for the investment, not profitability. • 3. It does not consider that the firm may have any alternatives when the project is chosen to do. No deferment, no stop or abandonment may be considered. Weighted Average Cost of Capital • So far, the analysis is to assume that the discount rate is given. In fact, the discount rate should consider that the rate should suffice to cover what the investor may want. • Weighted Average Cost of Capital (WACC) is the rate of financing the firm’s operation which represents the “minimum” requirement the investor may with respect to the portions of their contribution. • WACC is not the firm’s profitability index. It does not represent the firm’s rate of return. It is the minimal of what they should obtain. Calculation Format • • • • • WACC = (Debt Ratio)*Cost of Debt *(1-Tc) + (Equity Ratio)*Cost of Equity If the firm is financed with debt and equity only. Notice that in this case Debt Ratio + Equity Ratio = 1. Tc is the corporate tax rate. (because the debt payments are tax-deductible) • = (Debt Ratio)*Cost of Debt*(!-Tc) + (Common Equity Ratio)*(Cost of Common Equity) + (Preferred Equity Ratio)*(Cost of Preferred Equity) • If the firm has issued preferred stock. • The Format • The cost of debt and cost of equity are the required rates of return to return to the investors. “required” means minimal requirement to satisfy the said investors. • Hence, if the firm issued bonds, the required rate of return for the firm is the bond’s yield. (that is, the yield to maturity at least). • And the cost of equity represents the rate that makes the investors in equity would consider the rate is fair enough for them to investigate in the stocks. Example: • Suppose the firm has the following information – • The firm has issued 200,000 shares of common stock, no tax rate is given. • 50,000 shares of preferred stock, • $400,000 in bonds, • Common stock price = $25 • Preferred stock price = $15 • Cost of common stock = 25% • Cost of preferred stock = 10% • Cost of debt = 5% • Total Capital = (200,000*25)+(50,000)*15)+400,000 = 6,150.000 Calculation of WACC • WACC = • 5,000,000 6,150,000 × 25% 750,000 + 6,150,000 × 10% + 400,000 6,150,000 × 5% ≈ 21.87% • We can then, use this rate as the discount rate for the cash flows of each project to choose. • That is, this is the rate will on the average, cover the minimal expectations for different sources for the capital may obtain. • This is the rate that the firm may satisfy the requirement for the different sources of capital it finances. Perpetuity and Stock Valuation Present Value of StockInfinite Stream of Cash Flows: (Why?) ? PV= ? If there’s a constant growth rate for the cash flows ?(1 + ?) ?(1 + ?)2 ?(1 + ?) ?? = + +?= 2 1+? (1 + ?) ?−? Assumptions and applications for the model • 1. The cash flows are not necessarily the genuine payments. They are the forecasted cash flows. • 2. The discount rate is constant over time. • 3. There are so many periods involved. Hence, the infinite number of periods is a good approximation. • 4. No default is considered. • By the formula, it is feasible to say that •?= ?(1+?) ?? +? • That is, we can use the current information and the possible growth rate of the entity to forecast the rate of return in the investors. Some examples • Inferences from the market data • Suppose the current stock price is $20.00 per share • Expected growth rate of earning 5% • Current dividend is $2.00 per share • i = [2(1+5%))/20] +5% =15.5% • By the same token, if the discount rate is 15% • The expected stock price can be shown as • PV=(2(1+5%))/(15%-5%)=$21.00 Example 2 • Notice that this is for stock valuation, it is not for the stock price prediction. • Suppose the dividends will grow 5% annually for 5 years • And go down to 2% perpetually, • Suppose the current dividend is $ 2.00 per share • The discount rate is 15%, the valuation is • 2 1+5% [ 1+15% + 2(1+5%)2 1+15% 2 + 2 1+5% 5 ?+ ] 5 1+15% + 1 2 1+5% 5 (1+2%) (1+15%)5 (15%−2%) • The first part in the bracket is for the discount value of cash flows in the first 5 years, the second part is the present value of the discounted cash flow of the dividends that grow with 2% perpetually. Cautions: • 1. One should be careful about the time frame. • 2. The idea of “present value’ means the valuation on the time spot you’re standing. • 3. The formula for present value is for the time frame that was set as in the assumptions for cash flows shown. One can not simply apply the formula without checking the patterns of the cash flows. Bond Valuation • Assumptions: • 1. The pre-determined cash flows are given (that’s why the bond securities are usually called fixed-income securities) • 2. No default or prepayment penalties. • 3. The discount rates (usually called as yield) are constant. • 4.The interest rate for the face value (the denomination) is usually fixed and called coupon rate. Example • Suppose you are given the corporate bond as 5%-coupon with face value as $1000 for 10 years, paid semiannually and discount rate is as 5%=10%/2, • 25 (1 (5%) 1 −( )20 ) 1+5% + 1000 (1+5%)20 Why there is a $25 payment? Since it’s a semi-annual coupon payment, that is 5%*1000/2=$25. • The first part in the bracket is the annuity that we can figure out with the formula • The second part is the discounted cash flow (or present value of the face value (or the denomination) of the bond. Example • Now as before, we set the discount rate as 12% per year, then the bond’s valuation will be • 25 1 (1 − ( )20 ) (6%) 1+6% + 1000 (1+6%)20 • Now, one can see that if the discount rate is greater than the coupon rate, the bond’s value is less than the face value is called discount bond. • If the discount rate is equal to the coupon rate is called par bond. • If the discount rate is less than the coupon rate is called premium bond. Yield to Maturity • Expected return of the bond holders to hold the bond until maturity of the bond. • Or, it be called as the discount rate that makes the bond’s present value equal to its current bond price. That is, suppose you have a bond with 5% coupon rate in two years, paid semi-annually with face value as $1000, the current market price is $850, the yield to maturity of the bond can be calculated as • 850 = 25 1 4 (1 − ( ) ) ? 1+? 1000 + (1+?)4 • Notice that this is a complicated 4-degree polynomial. It is very complicated to solve it manually. Hence, we can solve it with the help of Excel • We can solve it as using the IRR function in Excel where • We set the initial outlay as $850, • Set the following cash flows as 25, 25, 25 and 1025 (face value +coupon), • It will give you 6.92%, which is 2*6.92%=13.84% annually. Excel Spreadsheet • 1. Go to Excel spreadsheet • Click the function wizard • Go to the “financial”. • Make the initial cost of bond as -850 (negative since it’s considered as cash outflow) • The coupon payments are 25 25, 25, 1025. Key in theses numbers. • Notice that since the bond is semi-annual, the coupon payment is 5%*1000/2=25. • The last payment is 1000+25=1025. • Go to a empty cell and click IRR function. The Excel Result • The result will indicate that the IRR is equal to 6.92%. • Since the bond is semi-annual, and all the interest rates are reported in the annual basis, the yield to maturity is reported as 2*6.92% = 13.84% • That is, the expected rate of return for the bond investor is around 13.84% Yield to Call • Not every bond will exist until the maturity, • The company or issuing entity can have the right to call back (or retire) the bond before the maturity if they have notified the bond buyers. • The Yield to Call is the discount rate of the bond if it’s called before the maturity • Example: If the earlier bond is called back in one year, and suppose the call price is $900 per bond then the problem becomes • 850 = 25 ? 1− 1 1+? 2 900 + (1+?)2 Notice that • The frequency that discounted is in the semi-annual basis • There is no default and pre-payment penalty • The solution can be done with the earlier fashion in Excel, • With IRR function, the solution is discount rate is 2*5.799%=11.598%. Why do we discount? 1. 2. 3. 4. 5. Time Preferences Financing Cost Opportunity Cost Risk The major difference between finance and accounting: Time Value of Money Discount Rate • The discount rate applied must contain the above reasons. • The Single Cash Flow • Suppose you have a single cash flow in the future, • The net worth of the cash flow must consider the Present Value • Present Value ? PV= (?+?) where C stands for the future cash flow. • And i represents the discount rate applied. The Future Value • It represents the amount of cash flow may be worth in terms of the value it may have in the future. • In the earlier notation, FV=PV(1+i). • However, these only represent a single period for the cash flow. If the cash flow requires several periods (say n periods) to get, then • ? PV= (1+?)? • And the future value is equal to • FV=PV(1 + ?)? • That is, the cash flow requires n periods of compounding. The Example for a bond valuation • Suppose you own a treasury bond that lasts for 30 years with 3% interest and face value $1,000. (face value means its denomination • amount) and paid semi-annual interest • PV=σ60 1 3%(1000) 2 3% (1+ 2 )? + 1000 (1+3%)30 • This is difficult to figure the terms one by one since it involves a stream of payments. • Hence, we introduce the following “Annuity” Annuity • Definition: A stream of (constant) payments for a finite number of periods of time. • Key feature: • 1. Some finite payments • 2. A finite number of periods of time. • 3. Assuming there’s no default. • 4. The discount rate for the stream of payments is identical Ordinary Annuity • Key Feature: Each payment is done at the end of each period. • The present value and future value • Present value of the ordinary annuity ? ? 1 )? ) (1+?) • PV= (1 − ( • where C is the cash flow per period and i is the discount rate. • ? FV= ((1 + ? ?)? − 1) Annuity due • The payments ae carried out at the beginning of each period. • The Present Value and Future Value • ?(1+?) PV= (1 ? − 1 ? ( ) ) 1+? • And the Future Value (at the end of the entire stream) • ? 1+? FV= ? ((1 + ?)? − 1) Excel Application • One can use the Excel spreadsheet to do the above problem without using the given formula • 1. Turn on the Excel spreadsheet • 2. use an open blank sheet • 3. Go click the function wizard ?? • 4. use the PV function in the list. The function may ask you several things. • “Rate” shows the discount rate per period (say monthly rate) • “NPER” shows how many periods are included. • “Pmt” asks you the payment per period. • The “Type” question is asking if it’s the begining or ending of each period. • The ”0” shows that it is at the end of each period, and “1” is at the beginning. Example: mortgage calculation Suppose you bought a house that costs $520,000 and you paid 20% down payment. Let the rest go to mortgage with 3% interest in 30 years. How much is the monthly payment? Go to the function wizard ?? Click the “PMT” function. This is the function that will figure out the payment amount per month. (that means there are $416,000 you need to finance) The payment function will be able to give you $1753.87 which is your monthly payment for the mortgage. Left-over Balance • Suppose you stay in the house for 10 years, you plan to sell it soon. How much is the bottom-line balance for the house? • Incorrect way to solve the problem; say 10 years of mortgage payments is 10*12*(1753.87)=210464.40 • So the balance is 416,000-210.464.40=205,535.6 • Why? • You forgot that each payment contains the payment for the principal and the interests. After 10 years, the monthly mortgage payment may be more toward the principal. The correct way for the balance • You have 30 years of loan. After 10 years of staying, you still have 20 years of mortgage payments owed. That is, • PV= Use the PMT function with Rate = 3%/12 • The “NPER” is 240 • “PMT” is 1753.87 • The balance is $316,241.90 • That means if you want to sell the house, you need to sell it more than 320,000 if you do not want to lose money. Amortization • This is an alternative method. That is, the balance let-over needs to take interest payment and payment for the principal into account. • For example, the balance is • Interest payment 416,000*(3%/12)=1040 • Monthly payment =1753.87 • Payment for the principal =713.87 • The balance of the mortgage after the first month • =416,000-713.87=415,286.13 Balance after the first month • Residual Balance = 415,286.13 • Interest Payment = (415,286.13)*(3%/12)=1038.22 • The Monthly mortgage payment = 1753.87 • Balance paid for the principal = 715.65 • Balance left-over after two months = 415,286.13-715.65=414,570.48 • This will keep on for the rest of payments • The process is called amortization. Excel application • The amortization schedule with manual calculation is tedious. Hence, we cam use the Excel spreadsheet to do so. • The details can be found in the amortization table sent to you separately Financial Ratio Analysis Activity Analysis (for sales-oriented firm) Sales-oriented firm 1. Account Receivable Turnover = Sales/Account Receivable 2. Inventory Turnover = Cost of Goods Sold/Inventory 3. Account Payable Turnover = Purchase/Account Payable Days of Operating Activity (for sales-oriented firm) • Days of account receivable still outstanding • = 365/account receivable turnover • Days of account payable still outstanding • = 365/account payable turnover • Days of inventory still unsold • = 365/inventory turnover Service-Oriented Industry (need to design differently) • For example, • Miles per Passenger (e.g. Airline Industry) • = Mileage per flight/Number of Passengers • Expense per flight = Cost/Number of Flights • Passengers per flight = Number of passengers/Number of flights Cycle of Business (sales-oriented industry) • Operating Cycle =Days of Account Receivable oustanding • +Days of Inventory Turnover • Cash Cycle = Operating Cycle –Days of Account Payable • For different industry, the ratios must be re-adjusted. Liquidity Analysis . 1. Current Ratio = Current Asset/Current Liabilities 2. Quick Ratio = (Current Asset – Inventory)/Current Liabilities 3. Cash Ratio =(Cash + Cash Equivalent)/Current Liabilities • These ratios work for all industries. Solvency Analysis • These ratios are for the firm’s capital structure • Debt Ratio = (Total Debt )/(Total Capitalization) • Equity Ratio = (Total Equity )/(Total Capitalization) • Debt-to-Equity Ratio = (Total Debt)/(Total Equity) • Interest Coverage Ratio • = (Earning before Interest and Tax)/(Interest Expense) Profitability Analysis • Return on Asset (ROA)= (Net Income)/(Total Asset) • Return on Sales (ROS)= (Net Income)/(Total Net Sales) • Return on Equity (ROE) = (Net Income)/(Total Equity) • Return on Common Equity • = (Net Income – Prefer Dividends)/Total Common Equity) Balance Sheet (in millions) 2014 2015 2016 Assets Cash Marketable securities Accounts Receivable Inventory Plant, Building, and Equipments (net) Investments in affiliates 230 50 1420 1230 1873 0 210 100 1350 1578 1305 430 970 0 1300 1450 990 1329 Total Assets 4803 4973 6039 Liabilities Short-term debts Advances from customers Accounts payable Interest payable Tax payable Other Accrued Expenses Bonds payable 107 421 685 75 117 20 2025 130 326 792 98 120 15 2076 1030 534 657 62 128 35 1450 Stockholders' Equity Common stock Additional paid-in capital Retained earning 1001 74 278 1201 156 59 1875 144 124 Income Statement(in millions) 2014 2015 2016 Net Sales 4629 4418 4983 Cost of Goods Sold 2215 3109 2310 Selling and General Expenses 771 812 759 Depreciation Expense 210 298 284 97 109 121 175 137 254 1161 -47 1255 Interest Expense Income Tax Expense Net Income Financial Ratios 1. Activity Analysis A/R turnover Inv turnover A/P turnover n.a. Working Capital Turnover Total Asset Turnover Assuming that marketable securities are cash equivalent 2. Liquidity Analysis Current ratio Quick ratio Cash ratio Working Capital ratio Operating cycle n.a. Cash cycle n.a. 3. Solvency Analysis Debt ratio Equity ratio Debt-to-equity ratio Liabilities-to-equity ratio 2014 2015 2016 3.260 1.801 3.273 1.970 4.364899 1.364 0.888 3.833 1.593 3.321157 1.340 0.825 4.277372263 2.481751825 0.408759124 3.277372263 4.088384 2.09596 0.391414 3.088384 296.7913 213.1697 5.6621 3.455099 1.476408 4.6621 324.3363 214.4348 0.443889236 0.281698938 1.575757576 0.974131559 0.443595 0.284738 1.55791 0.954096 0.410664 0.35486 1.157256 0.660756 1.580 0.964 And Profitability Analysis Return on assets 0.241723923 -0.00945 0.207816 Return on sales 0.25081011 -0.01064 0.251856 Return on invested capital 0.619861185 -0.02709 0.541182 Return on equity 0.858093126 -0.03319 0.585628 Introduction • The Purpose of Financial Statements: • 1) to summarize the transactions the entity has (potentially) accomplished, • 2) to identify the essential activities the entity is doing, • 3) to point out the current financial status of the entity, • 4) to describe the cash position they entity has achieved, • 5) to provide the investors the information for their investments. • Unfortunately, the statements may be stated, in terms of convenience of accounting practice, all are stated by the (current) or historical value of the items. Hence, the values of net income in (say) income statement, are reported in the money in a particular period. So, comparison across the periods, may not be entirely justifiable when comparison is done with many periods together. Asset: 1. Ownership: It indicates that the entity has the ownership for the benefit and economic resources of doing so. 2. Economic Resources: It is valuable and recognizable in the market. 3. for Future Growth and Prosperity: the purpose is to generate the benefit for the future. It has the potential or productivity to become more in return. Liability: obligation that one needs to retire in a short run or long terms. These obligations might include the employee payroll, bonds issued, customer pay in-advance…etc. Equity: the residual of the firm’s value after paying all the obligations. That’s why, based on this definition, the accounting identity such as Total Assets = Total Liability + Equity will hold in any case. Financial Asset: Different from the usual concept, these assets emphasize on the transferring the cash flows (or capitals) from sectors to other sectors. Hence, the value of them, depending on the future cash flows that they can provide from such provision in return. Financial Market: (what is a market?) Balance Sheet (or called Statement of Financial Position)-this is the financial statement that contains the information for the sources and usages of funding. Income statement (or called Statement of Operations)-this is the statement for the firm’s performance within the defined period. It is a subject to the concept of flows. Statement of Cash Flows- this is the statement of the firm’s performance in the cash basis. Some concepts: • Accrual Basis: The transactions are recognized as if the transactions are likely to accomplished with certain degree of confidence, complete the transactions and render the payments accordingly. In other words, the potential cash flows (inward or outward) will be provided successfully. Yet, the entire transaction may not necessarily finish in the cash flow transferred. • Cash Basis: The transactions are recognized and recorded only if the cash flows are involved. In other words, the transactions in the financial statements are reported only when cash flows are done. That means, the statements are reported with actual payments are completed. Financial Ratio Analysis Limitations of financial ratios: 1. There is a linear relationship between the numerator and denominator2. There is the possibility that the information for either the numerator or denominator is unavailable. 3. The financial ratios can only represent the information up to the present- if the information is available. The ratios can be used as the indicators for the institution of interest. 4. The accounting policy of the entity will influence the financial ratios calculated. Usage of Financial Ratios • 1. To identify the proportional relationship among certain items of financial reports. • 2. To possibly consider the relationship identified over different periods, • 3. To compare the identified relationship with the benchmark(s) chosen. • • • • To compare to the benchmarks for the ratios: 1. Compare to the industrial average, 2. Compare to the peer group, 3. Compare to the individual history. • *One must be careful in choosing the benchmark(s) to compare. CORPORATE FINANCE TU @ 12:50- 2:15PM -- MEET ONCE A WEEK Textbook Essentials of corporate finance FLOW OF CLASS MAJOR ASSIGNMENTS - Discussions - Quizzes - Homework: - MIDTERM: ch 1-8 - Final: comprehensive WEEK 1 LECTURE 1 1/14/21 THE PURPOSE OF FINANCIAL STATEMENT - To summarize the transactions the entry has (profitability) accomplished - To identify the essential activities the entity is doing - Point out the current financial status of the entry - Describe the cash position the entity has achieved - To describe the information for their investments ASSET - Something of value that the company OWNS - Economic resources: valuable and possibly recognizable in the market - Future growth and prosperity: the purpose is to generate the benefit for the future LIABILITY - Obligation that needs to retire in short or long term. YOU OWE. Ex-- payroll. Bonds issued, customer pay in-advance EQUITY: the residual (whats left over) of the firms value after paying obligations. EQUATION: TOTAL ASSETS= TOTAL LIABILITY + EQUITY FINANCIAL ASSETS - This is transferring the cash flows (or capitals) from sectors to other sectors. IN OTHER WORDS, its the transferring of $$ or capital to elsewhere for MORE assets FINANCIAL MARKET: providing capital and asking for a bigger return than the one you contributed. FINANCIAL STATEMENTS - BALANCE SHEETS assets= total liabilities + equity - Also known as statement of financial position - A snapshot of the financial position - This is the financial statement that contains the information for the sources and usages of funding - Contains the asset side, showing the firms usage of the capital obtained and how they make it grow - The opposite of asset is liability, which indicates the sources of financial obligations that need to be retired in the ST or LT - The equity is called the residual claim that the firm pays off the liability and the left-over amount - INCOME STATEMENT (statement of operations) - Shows the firms performance within the defined period ( operations of the institution, a more detailed) Shows you what is a PERIODIC TRANSACTION that can possibly be accomplished Concept of the transition for the firm, and how well they perform for this goal. STATEMENT OF CASH FLOW - Every transaction in terms of cash - Every transaction that CAN actually happen - Is represented in 3 different areas: operating cash flows, investing cash flows, and financing cash flows - How the business obtains and dispenses cash flows CONCEPTS ACCRUAL BASIS - Transactions as they are accrued, NOT paid. Meaning the underlying transaction in which it will be accomplished with a high likelihood to succeed. CASH BASIS (you can see this is the statement of cash flows) - Recognizing the transaction only when physical cash is involved (in other words, only when the cash flows are done). ** reported with actual payments are completed** FINANCIAL RATIO ANALYSIS Is used to reflect the truth and condition of the institution, the performance of the firm such as profit-generating activity in sales (ex: accounts receivable turnover rate= sales (or revenue)/ average (depends on the firm) account receivable.) - LIMITATIONS - Linear relationships between the numerator and denominator - Possibility that the information for either the numerator and denominator is unavailable - The financial ratios can only represent the information up to the present-- if the information is available. The ratios can be used as the indicators for the institution of interest. - Accounting policy of the entity will influence the financial ratios calculated (meaning that if the accounting rules change for the organization, so will the ratio calculations) - USAGE OF FINANCIAL RATIOS Need to identify which kind of industry and their activities to: - Identify the proportional relationship among certain items of financial reports - To possibly consider the relationship identified over different periods - To compare the identified relationship between the benchmark(s) chosen - TO COMPARE THE BENCHMARKS FOR THE RATIOS: - Compare the industrial average - Compare the peer group - Compare the individual history FINANCIAL RATIOS --- SALES INDUSTRY 1. Accounts receivable turnover a. Sales (or revenue) / average account receivable i. AVERAGE account receivable depends on the industry 2. Inventory turnover a. COGS/ Average level of inventory i. This tells you how much is sold compared to what isnt ii. The more efficient the sales are functioning the faster they can get the inventory down 3. Accounts payable turnover a. Lets you know the amount of inventory that has actually been paid to the firm b. COGS= beginning inventory + purchase - ending inventory c. In this, the beginning inventory can be considered as the ending inventory, which shows the amount of credit the firm is using to PURCHASE inventory. i. The more inventory is purchased on credit the better ii. The less the ratio is, the better because it is interpreted as a credit + cash purchase 4. Days of accounts receivable still standing a. Ratio that tells how many days the firm is about tti switch the accounts that are collectible to cash, namely b. Days of account receivable still outstanding= (365 days)/(account receivable turnover) 5. Days of account payable still outstanding a. 365 days/ account payable turnover b. This shows how many days the the firm can wait before paying a bill c. Interest free 6. Days of inventory still unsold a. 365 days/ inventory turnover b. How many days before the firm sells its product c. The shorter the better 7. Operating cycle a. Days of inventory still unsold + days of account receivable still outstanding 8. Cash cycle a. Operating cycle - days of account payable outstanding FINANCIAL RATIOS--- ALL INDUSTRIES 1. Liquidity analysis i. The area the firm is about to solve short-term obligations for ii. The faster = better b. Current ratio= current assets / current liabilities i. Current assets includes cash + cash equivalents + marketable securities + accounts receivable + inventories c. Quick ratio = current assets - inventories/ current liabilities d. Cash ratio= cash and cash equivalents/ current liabilities 2. Solvency analysis i. Is the analysis for the firms ability for retirement of long-term financial obligations b. Debt ratio= total debts/ total capitalization c. Equity ratio= total equity/ total capitalization d. Equity is usually both common stock and preferred stock, but most analyses focus on common SO THE ALTERNATIVE WOULD BE total equity ratio= common equity/ total capitalization e. Debt to equity ratio= total debts/ total equity f. Interest coverage ratio= earnings before interest and taxes/ interest expense 3. Profitability analysis: i. Is to investigate if the firm earned enough for their capital providers b. Return to asset= total net income/ total assets c. Return to sales= total net income/ total sales d. Return to equity= total net income/ total equity WEEK 2 LECTURE 1 1/19/21 Financial statements only give: 1. Estimates for most likely amounts of the transactions 2. To provide the general activities the firm has accomplished 3. When the accounting policy for the firm changes, the underlying amount (or transaction) will be reported differently 4. The numbers of the transactions are usually not subject to any adjustment for the inflation (MEANING that the transaction amount will not be the same today as it was tomorrow) FINANCIAL RATIO ANALYSIS (activity analysis for sales-oriented firms) Sales oriented firm 1. Accounts receivable turnover a. sales/ accounts receivable i. MEANING if you’ve received the $$ that is owed to you (something that you expect to receive) ii. SALES through credit iii. When this ratio is big, this means that your cash sales is lower, meaning that there are a lot of people (or accounts) that still need to pay you. 2. Inventory turnover a. Cost of goods sold/ inventory i. ii. (COGS= beginning inventory + purchase - inventory) Purchase will most likely not told, so you have to figure it out based on everything else thats provided 1. How much something in terms of inventory is able to be sold. 3. Accounts payable a. purchase/ account payable i. I can buy something, but i don't have to pay it immediately. THIS IS WHAT WE (YOU) OWE to others. ii. Smaller ratio= better Days of operating activity (for sales oriented firms) 1. Days of accounting receivable still outstanding - 365/ accounts receivable turnover - Tells you the days it takes for you to get the money people owe you 2. Days of accounts payable still outstanding - 365/ account payable turnover - Tells the days in which you need to pay someone else - The longer= the better 3. Days of inventory still unsold - 365/ inventory turnover - The shorter= the better because it shows that your inventory is being sold at a fast rate SERVICE ORIENTED INDUSTRY For example: 1. Miles per passenger (an airline industry) a. = miles per flight/ number of passengers 2. Expense per flight= cost/ number of flights 3. Passengers per flight= number of passengers/ number of flights CYCLE OF BUSINESS (SALES ORIENTED) 1. Operating cycle= days of account receivable outstanding + days of inventory turnover - You sold something between the # of days to receive the money and the # of days with raw materials 2. Cash cycle a. = operating cycle- days of account payable i. Cash cycle represents the # of days you have to maintain(or reserve) that internal cash flow. ii. The shorter= the better you are iii. Example: someone pays you within a 30 day period and you have 90 days to pay someone else back. LIQUIDITY ANALYSIS - Wanting to get enough cash to be able to retire the obligation that is still within a shirt term period (APPLIED TO ALL INDUSTRIES) 1. Current ratio= current assets/ current liabilities a. Current assets= cash + cash equivalents + marketable securities + accounts receivable + inventory b. Current liabilities=something you have to retire, an obligation within a year… account payable (debt) + overhead fees + c. CURRENT RATIO… THE BIGGER OR HIGHER THE BETTER YOU ARE. 2. Quick ratio= (current assets - inventory)/ current liabilities a. We take out inventory because we dont always sell our inventory quickly 3. Cash ratio= (cash + cash equivalents)/ current liabilities SOLVENCY ANALYSIS These ratios are for the firms capital structure 1. Debt ratio= (total debt)/ (total capitalization) a. Total debt= everything, total obligation that needs to retire. INTEREST BARRING 2. Equity ratio= total equity/ total capitalization 3. Debt to equity ratio= total debt / total equity 4. Interest coverage ratio= earnings before interest and tax/ interest expense a. Ex: boing b. EBIT = earnings prior to interest they have to pay c. The higher the better you are PROFITABILITY ANALYSIS 1. Return on assets (ROA)= net income/ total assets 2. Return on sales (ROS)= net income/ total net sales a. Net sales= total sales - sales subsidies 3. Return on equity (ROE)= net income/ total equity 4. Return on common equity= net income - prefer dividends / total common equity LOOKING AHEAD: 1. GETTING AN EMAIL LATER ON TODAY WITH QUIZ 1. THIS IS DUE NEXT TUESDAY. WEEK 3 LECTURE 1 I. II. III. 1/26/21 Why do we discount? A. To have the product now B. When we wait, we have financing cost + opportunity cost (the cost associated with making a decision over something else) + risk (the cost of having an uncertain outcome) Finance vs accounting: time value of money. A. Finance talks about time value of money B. Accounting talks about the transaction of the money The discount rate makes a net worth as present value IV. A. When you are in accounting, you are considering present value (PV=C/1+i), where c stands for the future cash flow. The future value A. Represents the amount of cash flow may be worth in terms of value it may have in the future 1. FV= PV(1+i) 2. ** however that is only for a single value. If its multiple periods: PV= C/(1+i)^n a) Future value = PV=(1+i)^n b) N = the period B. EXAMPLE: suppose you own a treasury bond that lasts for 30 years with 3% interest and face value $1,000 (face value means its denomination amount) and paid semi-anual interest 1. PV= ∑^60((3%*1000)/2) 1000 ----------------- + ______ (1+ 3%/2)^t (1+3%)^30 *** use fx in excel, choose PV + insert: rate (which is 3%/2 periods since its semi annual) VII. ANNUITY A. DEFINITION: A stream of (constant) payments for a finite number of periods of time B. Key features: (ex-- paying rent, tuition) a. Some finite payment b. A finite number of periods of time (something is fixed) c. Assuming theres no default d. The discount rate for the stream of payments is identical C. ANNUITY DUE a. The payment are carried out at the beginning of each period b. The present value and future value i. VIII. ORDINARY ANNUITY A. Key feature: each payment is done at the end of each period (ex-- paychecks, after youve done the work) a. The present value and future value b. Present value of the ordinary annuity i. PV= C/I(1-(1/(1+i)^n) 1. Where c is the cash flow per period and i is the discount rate IN EXCEL: WEEK 4 LECTURE 1 I. 02/01/21 Perpetuity and stock valuation A. Perpetuity is similar to annuity, but refers to infinite periods of cash flows B. PV OF A PERPETUITY= C/ i 1. c= the per-period cash flow and i= the discount rate or rate of return C. You can use this form to infer several things: 1. The stock value (using past history of stock prices to predict the stock price) 2. Rate of return a) Denominator is the possible rate of return for one to invest the money TODAY 3. DRAWBACKS FROM FORMULA @ B: a) The expected cash flows never grow over time. There is generalization that it incurs some growth rate of the cash flows so-called constant growth rate model of stock valuation b) PV OF STOCK= (1) C= cash flow per period and the cash flow are subject to constant growth rate over time (a) THIS CAN BE USED FOR INFER THE REQUIRED RATE OF RETURN c) Can be used used to assess the stock valuation in justifying the corporate finance decision (1) Assumptions implied in the equation above: (a) The expected cash flows in the numerator are not necessarily the genuine divided payment. They represent the expected cash flows the investor may get from the company’s earning in their operations **the format simply considers that the investor is entitled to get the earnings of the firm. (b) The DISCOUNT RATE is constant over time which means that the costs for the investor to buy the stock remains the same over time (c) Formula assumes that there are HIGH number of periods, and the entire infinite sum can be approximated by the perpetual model with a negligible error (INVESTOR BELIEVES THAT THE BUSINESS WILL ONLY LAST SO LONG) d) Application of the PV STOCK can be used to obtain the possible discount rate (or rate of return) the investors intended to have e) pv can be substituted for the current stock proce for the equation and abstain the possible rate of return of the stock from using the above equation (1) EXAMPLE --- Suppose the current stock price is $20.00 and the expected growth rate of earnings is 5%,let the expected cash flow is $2.00 currently, the equation will give us meaning that the markets expected rate of return is 15.5% (2) By the same token, if the rate of return is 15%, the growth rate of the dividend (or expected earning) is 5%, the current dividend is $2.00, the possible stock valuation is then, (3) TEST 2 WILL BE SENT OUT WEDNESDAY AND IT MUST BE TURNED IN BY NEXT WEDNESDAY AT 1 PM FOR TEST: NAME + CLASS YOU ARE IN WEEK 5 LECTURE 1 02/09/21 CAPITAL BUDGETING I. II. Capital budgeting A. CONCEPT: The allocation process for the capital obtained for the purpose of te firm investments B. OBJECTIVE: the optimality for the firms growth (using the $$ or capital of the business to get the most growth) C. CRITERIA: none of the criteria will overwhelm the others. Need to investigate them all D. ASSUMPTIONS: 1. the projects expected cash flows are forecasted or predetermined 2. The discount rate is given. That is, the rate is PRE-DETERMINED 3. The project is assumed as when one has started will continue until its done 4. No deferment, choice or change of mind is considered 5. All projects are considered manually exclusive E. IT IS TRYING TO ALLOCATE THE LIMITED CAPITAL YOU OBTAIN FROM THE INVESTOR THE DECISION RULES A. NET PRESENT VALUE (NPV): the present value of the project net of the initial outlay or present value of the entire costs 1. Choose the projects with positive NPV 2. Start with the project that has the highest NPV B. 1. Initial outlay (c1/1+i) is the initial cst of the present vakye of the cost involved over the years 2. a) This shows 3 different projects, with 3 different initial outlay values & the amount of money you would get back from it. YOU CAN DO THIS ON EXCEL TO FIND OUT WHICH PROJECT WILL GIVE MORE TO YOU. in this example, interest rate is 12% (0.12) b) -150 60 80 180 -300 80 120 100 -100 70 90 100 =NPV(0. 12)(-150 :180) 250 =NPV(0. 12)(-300 :250) =NPV(0. 12)(-100 :100) c) ACCORDING TO THE NVP RULE, you would choose project 3. If you have any $$ left over, you would do project 2. LAST would be project 1. 3. a) ^^ how to calculate by hand on calculator C. 1. NEW EXAMPLE^^ 2. In this example, NVP does not work because it requires different cash flows throughout the years. So, if the year is bad, the company has the option to discontinue the project. 3. a) Notice how 300, 400, 500 comes from “good” year b) 260, 160, 220= the amount of $$ you will get back c) so you insert those values into the equation^^ D. WEEK 6 LECTURE 1 I. 02/16/21 Capital Budget PT 2 Internal Rate of Return (IRR) A. The discount rate sets the dicounted cash flows of the project equal to the internal outlay. (IN OTHER WORDS, the disount rate that sets the net preent vaue of the project equal to zero). B. It is a break-even rate of the project C. It is the WORSE CASE SCENARIO, which indicated the highest disount rate that the project can undertake D. Decision rule: II. 1. Choose the projects that the IRR exceeds the actual financing costs 2. Start with the project of the highest IRR 3. Go to the 2nd best project if capital left-over 4. Go to the rest if additional capital is available Example: suppose you have three projects: A. B. TO DO ON EXCEL: 1. a) IRR1= 39.68% IRR2: 24.12% IRR3: 62.92% C. Now suppose the actual cost for financing is 20% then, all projects are double. Bug you will go with project 3, project 1, the project 2. 1. SOME LIMITATIONS a) 2. The decisions based on NVP and IRR may not be the same. Hense, simply use one decision rule to determine the capital budget is dangerous a) 3. OTHER DECISION RULES a) b) Discounted cash flows of the project break-eve with its initial payment (1) Suppose you have a discount rate of 12% (a) Discounted payback period for project 1=3 (b) ‘’Project 2= 4 (c) ‘’ project 3=3 (i) Decision: do 1 and 3, project 2 only if there is value left over (2) LIMITATIONS (a) D. WEIGHTED COST OF CAPITAL 1. Weighted average cost of capital (WACC) is the rate of financing the firms operation which represents the “minimum” requirement the investor may with respect to the portions of their contribution a) This is NOT the profibalility index. It does NOT represent the firm’s rate of return. 2. CALCULATION FORMAT a) WACC= (Debt ratio) * Cost of Debt * (1-TC) + (Equity Ratio) * Cost of Equity (1) IF THE FIRM IS FINANCED WITH DEBT AND EQUITY ONLY (a) Notice that the case debt + equity ration= 1 (b) TC is the corporate tax rate (because the debt payments are tax-deductible) b) WACC= (debt ratio)*Cost of Debt*(1-TC)+(common equity Ratio)*(cost of common equity)+(preferred equity ratio)*(cost of preferred Equity) (1) If the firm has issued preferred stock 3. The format a) The cost of debt and cost of equity are the required rates of return to return to the investors. “Required” means requirement to satisfy the said investors (1) If the firm issued bonds, the required rate of return for the firm is the bond’s yield (2) Cost of equity represents the rate that makes the investors in equity would consider the rate is fair enough for them to investigate in the stocks (a) EXAMPLE E. weighted average cost of capital 1. Discount rate is normally given, but the discount rate should consider the rate should suffice to cover what the investor may want 2. WACC is the rate of financing the firms operation which represents the minimum requirement the investor may with respect to the portion of their contribution (ex: 20% contribution from parents & 40% from your in laws, 20% from padrinos. The biggest is the 60% so because of that, it matters more). a) WACC is not the firms profitability index. It does not represent the firm rate of return, but the minimum the firm should obtain. 3. WACC CALCULATION FORMAT a) = (debt ratio)*Cost of Debt*(1-TC)+( equity Ratio)*(cost of common equity) ////// **** if the firm is financed by DEBT ONLY** (1) TC is the corporate tax rate b) WACC= (debt ratio)*Cost of Debt*(1-TC)+(common equity Ratio)*(cost of common equity)+(preferred equity ratio)*(cost of preferred Equity) /////// ******* If the firm has issued preferred stock (1) WHEN YOU CALCULATE WACC, IT IS a %. F. The format 1. The cost of debt and cost of equity are the required rates of return to returns to the investors. “Required” means minimal requirement to satisfy the said investors 2. If the firm issued bonds, the required rate of return for the firm is the bond’s yield. (the yield to maturity at least) 3. Cost of equity represents the rate ohat makes the investors in equity would consider the rate is fair enough for them to investigate in the stocks. a) EXAMPLE: suppose the firm has issued 200,000 share of common stock, no tax rate is given. In addition, they did 50,000 preferred stock, $400,000 in bonds. The value for each is: (1) Common stock $25 (2) Preferred stock price $15 (3) Cost of common stock= 25% (4) Cost oc preferred stock = 10% (5) Cost of debt= 5% (a) SO: total capital= (200,000*25)+(50,000*15)+400,000= 6,150.00 (b) WACC= (i) The 21.87% is the minimum requirement to satisfy equity, bond, and other shareholders. WEEK 7 LECTURE 1 02/23/21 RATE OF RETURN AND RISK I. rate of return and risk A. So far, we assume the discount rate is given. BUT IN REALITY: THIS IS THE SUBJECT TO ESTIMATION AND ASSESSMENT B. Two types of risk: 1. Systemanic -- when the risk may affect all the securities in the capital market (ex: COVID, ALL BUSINESSES) 2. Idiosyncratic --- when the risk is confined to a certain securities, certain industries and certain sectors C. How to estimate the systematic risk and its relationship with systematic risk 1. The capital asset pricing model (CAPM): The trade-off between the (required) expected rate of return and the so-called systematic risk a) It is a simple linear model b) It is feasible to calculate the expected rate of return once one can easily obtain with the market as a whole 2. EXAMPLE State of the world probability rate of return Recession ¼ -10 Recovery ½ 20% Boom ¼ 14 THE STATISTICS I. The expected rate of return (according to the assessment from the probability distribution assessment perhaps subjectively) is: A. ¼ (-10) + ½ (20%) + ¼ (14) = 11% ***** THIS IS WRONG BECAUSE YOU DID NOT TAKE INTO ACCOUNT HOW MUCH RISK YOU ARE UNDERTAKING*** B. Standard deviation: 3. EXAMPLE: WEEK 8 LECTURE 1 03/02/21 RATE OF RETURN AND RISK RATE OF RETURN & RISK The rate of return is usually subject to estimation & assessment. There are 2 types of risk: 1. Systematic -- when the risk may affect the risky securities in the capital market. THIS AFFECTS THE ENTIRE INDUSTRY, OR PERSON 2. Idiosyncratic : when the risk is confined to a certain securities, certain industries and certain sectors. ONLY HAPPENS TO A CERTAIN SECOR. HOW TO ESTIMATE THE SYSTEMATIC RISK AND ITS RELATIONSHIP WITH SYSTEMATIC RISK. you can use: 1. The capital asset pricing model (CAPM) a. The trade-off between the (required) expected rate of return and the so-called systematic risk b. It is a simple linear model c. It is feasible to calculate the expected rate of return once one can easily obtain the assessment that how sensitive the asses will be associated with the market as a whole Example found on next page EXAMPLE STATE OF THE WORLD PROBABILITY RATE OF RETURN RECESSION 1/4 -10% RECOVERY 1/2 20% BOOM 1/4 14% The expected rate of return )according to the assessment from probability assessed perhaps subjectively) is: - 1/4(10%)+ ½(20%)+¼(14%)= 11% - Standard deviation as - REPRESENTS YOUR UNDERTAKING OF UNDERTAKING RISK - THIS IS NOT SYSTEMATIC RISK ANOTHER EXAMPLE Suppose there are 2 assets of portfolio STATE OF THE WORLD PROBABILITY RATE OF RETURN (1) RATE OF RETURN (2) RECESSION 1/4 -10% 4% RECOVERY 1/2 20% 12% BOOM 1/4 14% 8% Rate of return is: 9% (calculate like this: 1/4(4%)+ ½(12%)+¼(8%)= 9% ) & the variance of asset 2 is: 44% The covariance of these 2 assets then: cov(r1,r2)=¼(-10%-115)(4%-9%)+½(20%-11%)(12%-9%)+¼(14%-11%)(8%-9%)=156%^2 REMEMBER: the covariance is defined with “two arguments only. That is, the covariance must explain the association between 2 arguments only. If one has more than 2 assets, one can only explain among all arguments in one co-variance alone. MEAN VARIANCE ANALYSIS - For any risk-averse investor, suppose there are only 2 assets, the objective is to: - MaxE(Rp) subject to: - W1+W2=1 - Rp=W1R1+W2R2, - Var(Rp)=W1Var(R1)+W^2v1(R1)+W^2v2Var(r2)+2W1W2COV(R1R2) - WHERE: E(Rp)=W1E(R1)+W2E(R2) - The problem is to maximize the expected rate of return & is subject to the constrains for the choice variables are the “weights” SYSTEMATIC RISK β? = ???(??,??) 2 σ? where Rm represents the rate of return for the market portfolio which can be 2 approximated by the market index’s rate of return σ ?is the variance of the rate of return for the market portfolio - The numerator represents the correspondence with the market altogether, while the denominator represents the vavolarity of the entire market. In other words, it shows how sensitive the rate of return for asset is within THE CAPITAL ASSET PRICING MODEL (CAPM) The model describes the “equilibrium” expected rate of return for a risky asset as: E(Ri)= EXAMPLE Suppose the stock with beta risk around 1.2 and the market index’s rate of return as 12% on the average. Let the basically EXAMPLE Suppose the firm’s stock jas the required rate of return as 12% and the T-bill rate as 2% and the market index’s rate of return as 10%, then we can find the firm’s stock is subject to the β?=(12%-2%) that ism the firms stock is somewhat more responsive than the market index in the impact from the systematic news --------------- = 1.25 (10%-2%) SO SINCE β?= 1.25 IT IS RISKIER THAN THE MARKET, because the market is at (1). WEEK 9 LECTURE 1 03/16/21 RATE OF RETURN AND RISK CAPITAL ASSET PRICING MODEL (CAPM) a. The model describes equilibrium expected rate of return for a risky asset as i. E(Ri)=Rf+Bi(E(Rm)-Rf) 1. Where E(Rm) is the expected rate of return for the market portfolio which is appropriate by the market index’s average rate of return 2. The tem as E(Rm)-Rf can be cled the market premium which shows how the capital market rewards the investor is taking extra risk ii. EXAMPLE: suppose there is a stock with beta risk around 1.2 and the market index’s rate of return as 12% on the average. Let the basically t-bill rate be 2%, the required rate of return for the stock is: 1. E(R)=2%+1.2(12%-2%)-2%=14% 2. b. Diversification with he systematic risk and applications in capital budgeting i. Asset 1 has the B1=1.5, asset 2 has B2=0.5 and asset 3 has B3=0.9. The combinations of the assets will have the systematic risk as 1. We are going to have the portfolio as 1. ii. By the capital asset pricing model with Rf=2% E(Rm)=12% 1. We have E(R1)=17% 2. E(R2) Capital budgeting with option Capital budgeting has 3 things assumed (so far): 1. The projects future cash flows are determined or assumed 2. The discount rate for the cash flows is given 3. The projects are continued until the projects are done a. The real time, the projects can be a. EXAMPLE b. c. project chance Year 1 Year 2 Year 3 1 60% 250 300 350 1 40% 100 -100 -200 2 60% 300 350 -450 2 d. THE USUAL ANALYSIS IS: Obtain the expected cash flows in the project together and consider whether it pays off. The expected cash flows are: THE NET PRESENT VALUE: QUIZ 4 WILL BE GIVEN ON WEDNESDAY (TOMORROW, 03/17/21) WEEK 10 LECTURE 1 IF BETA IS NOT KNOWN, YOU CANNOT USE CAPM. 03/23/21 WEEK 13 LECTURE 1 Capital structure theory 04/13/21 Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 347 11.4 Self-Test Suppose the probabilities of the recession or boom are each.30, while the probabil- ity of a normal period is.40. Would you expect the variance of returns on these two investments to be higher or lower? Why? Confirm by calculating the standard devia- tion of the auto stock. (Refer to Section 11.3 if you are unsure of how to do this.) The gold mining stock offers a lower expected rate of return than the auto stock and more volatility—a loser on both counts, right? Would anyone be willing to hold gold mining stocks in an investment portfolio? The answer is a resounding yes. To see why, suppose you do believe that gold is a lousy asset, and therefore, you hold your entire portfolio in the auto stock. Your expected return is 5% and your stan- dard deviation is 10.6%. We'll compare that portfolio to a partially diversified one, invested 75% in autos and 25% in gold. For example, if you have a $10,000 portfolio, you could put $7,500 in autos and $2,500 in gold. First, we need to calculate the return on this portfolio in each scenario. The portfo- lio return is the weighted average of returns on the individual assets with weights equal to the proportion of the portfolio invested in each asset. For a portfolio formed from only two assets, Portfolio rate of return (fraction of portfolio rate of return X in first asset on first asset (11.4) (fraction of portfolio rate of return + ? in second asset on second asset = For example, autos have a weight of .75 and a rate of return of —8% in the recession, and gold has a weight of .25 and a return of 20% in a recession. Therefore, the portfo- lio return in the recession is the following weighted average:9 Portfolio return in recession [.75 X(-8%)] + 0.25 x 20%) = -1% Table 11.8 expands Table 11.6 to include the portfolio of the auto stock and the gold mining stock. The expected returns and volatility measures are summarized at the bottom of the table. The surprising finding is this: When you shift part of your funds from the auto stock to the more volatile gold mining stock, your portfolio variability actually decreases. In fact, the volatility of the auto-plus-gold stock portfolio is con- siderably less than the volatility of either stock separately. This is the payoff to diversification. We can understand this more clearly by focusing on asset returns in the two extreme scenarios, boom and recession. In the boom, when auto stocks do best, the poor return on gold reduces the performance of the overall portfolio. However, when auto stocks are stalling in a recession, gold shines, providing a substantial positive return that boosts portfolio performance. The gold stock offsets the swings in the performance of the auto stock, reducing the best-case return but improving the worst-case return. The inverse relationship between the returns on the two stocks means that returns are more stable when the gold mining stock is added to an all-auto portfolio. 'Let's confirm this. Suppose you invest $7,500 in autos and $2,500 in gold. If the recession hits, the rate of return on autos will be -8%, and the value of the auto investment will fall by 8% to $6,900. The rate of return on gold will be 20%, and the value of the gold investment will rise 20% to $3,000. The value of the total portfo- lio falls from its original value of $10,000 to $6,900 + $3,000 = $9,900, which is a rate of return of -1%. This matches the rate of return given by the formula for the weighted average.