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Homework answers / question archive / 1) You have deposited $5,000 in an account that pays 5% interest each year
1) You have deposited $5,000 in an account that pays 5% interest each year. How much will you have in the account at the end of six years?
2.A certain project will cost a firm $5,000 today. The project is not expected to produce any cash flows until the second year, at which point it is expected to produce $6,200. No other cash flows are anticipated. If the appropriate cost of capital is 15%, what is this project's NPV?
3.A certain project will cost $50,000 and is expected to produce cash flows of $15,563 for the next seven years. The appropriate cost of capital is 15%. Calculate the project's NPV?
4.A project returns 15% when the market returns 10% and 8% when the market returns 15%.
5.A zero-coupon bond has a beta of 0.15 and promises to pay $5,000 next year with a probability of 96%, $1,000 with a probability of 2%, and there is a 2% probability of total default. One-year Treasury securities are yielding 4%, and the expected return on the market is 10%.
What is the time premium for this bond investment?
6.A firm paid a dividend of $1.52 a share this year and had earnings per share of $5.42. It's market price per share is $69.10. What is its dividend yield?
7.Your project has a beta of 1.8. The risk-free rate is 5.3%, and the expected return on the market is 12%. What minimum rate of return should you require on this project?
8.The risk-free rate is 4.2%, and the expected return on the market is 10%. A publicly-traded bond promises to return 8%. The expected return on the bond investment is 5.5%. What is the bond's implied beta?
9.A firm has 1,000 shareholders. Both you and Ms. Hostile are among them. Ms. Hostile owns 150 shares and is trying to fire the management, so management is offering to buy her out for a $10 a share premium. The current market price per share is $30. What will be the value of each of your shares if Ms. Hostile takes this offer?
10.A firm has 1,000 shareholders, each of whom own $50 in shares. The firm uses $20,000 to repurchase shares. What percentage of the firm did each of the remaining shareholders own before the repurchase, and what percentage does each own now?
11.A firm has 200 shareholders, you among them. Each shareholder owns $20 worth of stock. In addition, Mr. Hostile owns 50 shares (for a firm total of 250 shares) and is trying to fire the management. In an attempt to buy him off, management has offered to buy Mr. Hostiles shares for $28. What will the new share price be?
12.The stock of Static Corporation has a beta of 0.7. If the expected return on the market increases by 6%, the expected return on Static Corporation should increase by?
13.How much must you deposit in a bank account today to have $1,000 at the end of 5 years if the bank quotes a rate of 5%, compounded daily? Assume a 365-day year and round your answer to the nearest dollar
15.Blake has borrowed $30,000 on a 3-year note to buy a car. The loan requires equal monthly payments of principal and interest, with the first payment due one month after the loan is signed. The quoted interest rate is 7%. What will Blake's monthly payments be? Round your answer to the nearest dollar
16.Calculate the monthly payment due on a 30 -year, fixed-rate, $250,000 mortgage if the quoted interest rate is 4.8%.
17.A $50,000, level-coupon Eurobond has a 6% coupon and matures in ten years. At what price should the bond sell today if the prevailing interest rate is 8% per annum? Round your answer to the nearest dollar.
18.A financial advisor says she has an investment that will pay you $500 a month forever. It will cost you $25,000 today. What effective annual rate (EAR) will you earn on this investment?
19.If you make an investment that earns 10% the first year, -5% the second year, -2% the third year, and 12% the fourth year, what is your total 4 -year return?
20.If you make an investment that earns 10% the first year and loses 10% the second year, what is your total 2-year return?
1) Computation of Amount in Account at the End of 6 Years or Future Value:
Future value = Present Value*( 1 + Interest Rate )^Time
= $5,000*( 1 + 0.05 )^6
= $6,700
2) Computation of Project's NPV:
NPV=Present value of inflows-Present value of outflows
Here,
Present Value of Inflows = Cash inflow*Present value of discounting factor(rate%,time period)
=$6200/1.15^2
=(6200*0.756143667)
=$4688.09
Present value of outflows = $5,000
NPV = $4688.09-$5000 =-$311.91 or -$312
3)
| Computation of Project's NPV: | |||
| Year | Cash Flows | PVIF @ 15% | Present Value of Cash Flows (Cash Flows*PVIF) |
| 0 | -50000 | 1 | -50,000.00 |
| 1 | 15563 | 0.86956522 | 13,533.04 |
| 2 | 15563 | 0.75614367 | 11,767.86 |
| 3 | 15563 | 0.65751623 | 10,232.93 |
| 4 | 15563 | 0.57175325 | 8,898.20 |
| 5 | 15563 | 0.49717674 | 7,737.56 |
| 6 | 15563 | 0.4323276 | 6,728.31 |
| 7 | 15563 | 0.37593704 | 5,850.71 |
| NPV = | 14,748.61 | ||
Workings:
| PVIF @ 15% |
| =1/(1+15%)^0 |
| =1/(1+15%)^1 |
| =1/(1+15%)^2 |
| =1/(1+15%)^3 |
| =1/(1+15%)^4 |
| =1/(1+15%)^5 |
| =1/(1+15%)^6 |
| =1/(1+15%)^7 |
4) Computation of Project's Beta:
Project Beta = Change in Project Rate / Change in Market Return
= [ 15% - 8% ] / [ 10% - 15% ]
= 7% / -5%
= -1.4
5) Computation of Time Premium for the Bond:
Required return = Risk free rate + beta*(Expected market return - risk free rate)
= 4 + 0.15*(10-4) = 4.9%.
Expected Cash Flow from the Bond = 0.96*5000 + 0.02*1000 + 0.02*0 = $4820
So,
Fair Market Value of the Bond Today = $4820/1.049 = $4594.85
Promised return = (5000/4594.85) - 1 = 8.82%
Promised Return = Time Premium + Default Premium + Risk Premium
Where time premium equals the risk free rate of T securities yield = 4%
6) Computation of Dividend Yield:
Dividend Yield = Annual Dividend/Current Stock Price
= $1.52/$69.10
Dividend Yield = 2.20%
7) Computation of Minimum Rate of Return:
Minimum Rate of Return = Risk-Free rate + Beta*(Return from the market - Risk-Free Rate)
= 5.3% + 1.8*(12% - 5.3%)
= 5.3% + 12.06%
Minimum Rate of Return= 17.36
8) Computation of Implied Beta:
Expected Return on Investment = Risk-free Rate + Implied Beta * (Expected Market Return - Risk-free Rate)
5.50% = 4.20% + Implied Beta * (10.00% - 4.20%)
1.30% = Implied Beta * 5.80%
Implied Beta = 0.22
9) Computation of Price per share offered to Mr. Hostile:
Price per share offered to Mr. Hostile = Current Market Price + Share Premium
= $30 + $10
Price per share offered to Mr. Hostile = $40
10) Computation of Percentage of firm each of share holders own before repurchase and percentage of the firm did each of the remaining shareholders own now:
Percentage of firm each of share holders own before repurchase = $192/($192*50) = 2%
Repurchase Amount = $6,000
Value after repurchase = ($192*50)-$6000 = $3600
percentage of the firm did each of the remaining shareholders own now= $192 /$3,6000= 5.33%
11) Computation of New Share Price:
Total value of firm = price of shares*no of shares
= 250 *20
= 5000
Amount paid to Mr hostile = 28 * 50
= 1400
Value of firm after Mr hostile takes shares = 5000 - 1400 = 3600
Shares remaining = 200
New share price = 3600/200 = 18
12) Computation of Increase in Expected Return on the Stock:
Expected return on stock = Risk free rate +Beta*(Expected return on market - Risk free rate)
For simplicity let's assume that initially the expected return on market is 10% and Rf is 0
Expected return on stock = 0.7*10% = 7%
Now, if the expected return on market increase by 6%
Expected return on stock = 0.7*(10%+6%) = 11.20%
INCREASE in the expected return on stock = 11.20% - 7% = 4.20%
13) Computation of Amount Deposited or Present Value using PV Function in Excel:
=-pv(rate,nper,pmt,fv)
Here,
PV = Present Value = ?
Rate = 5%/365
Nper = 5*365
PMT = 0
FV = $1,000
Substituting the values in formula:
=-pv(5%/365,5*365,0,1000)
PV or Present Value = $778.81
15) Computation of Blake's Monthly Payment using PMT Function in Excel:
=pmt(rate,nper,-pv,fv)
Here,
PMT = Monthly Payment = ?
Rate = 7%/12
Nper = 3 Years*12 Months = 36 Months
PV = $30,000
FV = 0
Substituting the values in formula:
=pmt(7%/12,36,-30000,0)
PMT or Monthly Payment = $926.31 or $926
16) Computation of Monthly Payment using PMT Function in Excel:
=pmt(rate,nper,-pv,fv)
Here,
PMT = Monthly Payment = ?
Rate = 4.8%/12
Nper = 30 Years*12 Months = 360 Months
PV = $2,50,000
FV = 0
Substituting the values in formula:
=pmt(4.8%/12,360,-250000,0)
PMT or Monthly Payment = $1,311.66 or $1,312
17) Computation of Sales Price of Bond using PV Function in Excel:
=-pv(rate,nper,pmt,fv)
Here,
PV = Sales Price of Bond = ?
Rate = 8%
Nper = 10 years
PMT = $50,000*6% = $3,000
FV = $50,000
Substituting the values in formula:
=-pv(8%,10,3000,50000)
PV or Sales Price of Bonds = $43,289.92 or $43,290
18) Computation of Effective Annual Rate (EAR):
Present value of Perpetuity = Periodic Payment / (APR/compounding per year)
25000 = 500/(APR/12)
APR/12 = 500/25000
= 2%
APR = 2*12
= 24%
EAR = (1+(APR/compounding per year))^compounding per year - 1
= (1+(.24/12))^12-1
= 1.02^12-1
= 1.26824179456-1
EAR= 26.8%
19) Computation of Total 4-year Return:
Lets assume you invest $1000
First year $1000*10% 100
Second year $1,100*-5% - 55
Third year $1,045 *-2% - 20.9
Fourth year $1024.1*12% 122.89
Total return 146.99
Return % = 146.99/1000= 0.14699 ~ 14.7%
20) Computation of 2 year Return:
Total compound return = [(1+I year return) * (1+I year return)] - 1
= [(1+10%) * (1+(-10%))] - 1
= [1.10*0.90] - 1
= 0.99 - 1
= -0.01 or -1%
