Delft University of Technology - MOT 1461 Exercises based on Lecture 2 Chapters 3 1)Suppose your employer offers you a choice between a $5000 bonus and 100 shares of the company stock

Delft University of Technology - MOT 1461

Exercises based on Lecture 2

Chapters 3

1)Suppose your employer offers you a choice between a $5000 bonus and 100 shares of the company stock. Whichever one you choose will be awarded today. The stock is currently trading for $63 per share.

1. Suppose that if you receive the stock bonus, you are free to trade it. Which form of the bonus should you choose? What is its value?
2. Suppose that if you receive the stock bonus, you are required to hold it for at least one year. What can you say about the value of the stock bonus now? What will your decision depend on?

2.         Your firm has a risk-free investment opportunity where it can invest $160,000 today and receive

$170,000 in one year. For what level of interest rates is this project attractive?

3. Your computer manufacturing firm must purchase 10,000 keyboards from a supplier. One supplier demands a payment of $100,000 today plus $10 per keyboard payable in one year. Another supplier will charge $21 per keyboard, also payable in one year. The risk-free interest rate is 6%.

1. 1. What is the difference in their offers in terms of dollars today? Which offer should your firm take?
   2. Suppose your firm does not want to spend cash today. How can it take the first offer and not spend $100,000 of its own cash today?

4. Consider the following alternatives:

1. $100 received in one year
2. $200 received in five years
3. $300 received in ten years

1. Rank the alternatives from most valuable to least valuable if the interest rate is 10% per year.
2. What is your ranking if the interest rate is only 5% per year?
3. What is your ranking if the interest rate is 20% per year?

5.         Your grandfather put some money in an account for you on the day you were born. You are now 18 years old and are allowed to withdraw the money for the first time. The account currently has

$3996 in it and pays an 8% interest rate.

1. How much money would be in the account if you left the money there until your 25th birthday?
2. What if you left the money until your 65th birthday?
3. How much money did your grandfather originally put in the account?

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6. Your buddy in mechanical engineering has invented a money machine. The main drawback of the machine is that it is slow. It takes one year to manufacture $100. However, once built, the machine will last forever and will require no maintenance. The machine can be built immediately, but it will cost $1000 to build. Your buddy wants to know if he should invest the money to construct it. If the interest rate is 9.5% per year, what should your buddy do?

7.         How would your answer to Problem 16 change if the machine takes one year to build?

8. You are head of the Schwartz Family Endowment for the Arts. You have decided to fund an arts school in the San Francisco Bay area in perpetuity. Every five years, you will give the school $1 million. The first payment will occur five years from today. If the interest rate is 8% per year, what is the present value of your gift?

9.     When you purchased your house, you took out a 30-year annual-payment mortgage with an interest rate of 6% per year. The annual payment on the mortgage is $12,000. You have just made a payment and have now decided to pay the mortgage off by repaying the outstanding balance. What is the payoff amount if:

1. You have lived in the house for 12 years (so there are 18 years left on the mortgage)?
2. You have lived in the house for 20 years (so there are 10 years left on the mortgage)?
3. You have lived in the house for 12 years (so there are 18 years left on the mortgage) and you decide to pay off the mortgage immediately before the twelfth payment is due?

10.     A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $1000. Each year after that, you will receive a payment on the anniversary of the last payment that is 8% larger than the last payment. This pattern of payments will go on forever. If the interest rate is 12% per year,

1. What is today’s value of the bequest?
2. What is the value of the bequest immediately after the first payment is made?

11.      You are thinking of building a new machine that will save you $1000 in the first year. The machine will then begin to wear out so that the savings decline at a rate of 2% per year forever. What is the present value of the savings if the interest rate is 5% per year?

12. A rich aunt has promised you $5000 one year from today. In addition, each year after that, she has promised you a payment (on the anniversary of the last payment) that is 5% larger than the last payment. She will continue to show this generosity for 20 years, giving a total of 20 payments. If the interest rate is 5%, what is her promise worth today?

13.   You are thinking of purchasing a house. The house costs $350,000. You have $50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires annual payments and has an interest rate of 7% per year. What will your annual payment be if you sign up for this mortgage?

14.      You would like to buy the house and take the mortgage described in Problem 36. You can afford to pay only $23,500 per year. The bank agrees to allow you to pay this amount each year, yet still borrow $300,000. At the end of the mortgage (in 30 years), you must make a balloon payment; that is, you must repay the remaining balance on the mortgage. How much will this balloon payment be?

15.       Suppose you invest $2000 today and receive $10,000 in five years.

1. What is the IRR of this opportunity?
2. Suppose another investment opportunity also requires $2000 upfront, but pays an equal amount at the end of each year for the next five years. If this investment has the same IRR as the first one, what is the amount you will receive each year?

16.       A local bank is running the following advertisement in the newspaper: “For just $1000 we will pay you $100 forever!” The fine print in the ad says that for a $1000 deposit, the bank will pay

$100 every year in perpetuity, starting one year after the deposit is made. What interest rate is the bank advertising (what is the IRR of this investment)?

17. You are considering purchasing a warehouse. The cost to purchase the warehouse is $500,000. Renting the equivalent space costs $20,000 per year. If the annual interest rate is 6%, at what rate must rental cost increase each year to make the cost of renting comparable to purchasing?

18.       Your bank is offering you an account that will pay 20% interest in total for a two-year deposit.

Determine the equivalent discount rate for a period length of:

1. Six months.
2. One year.
3. One month.

19.       Many academic institutions offer a sabbatical policy. Every seven years a professor is given a year free of teaching and other administrative responsibilities at full pay. For a professor earning

$70,000 per year who works for a total of 42 years, what is the present value of the amount she will earn while on sabbatical if the interest rate is 6% (EAR)?

20.       You are considering moving your money to new bank offering a one-year CD that pays an 8% APR with monthly compounding. Your current bank’s manager offers to match the rate you have been offered. The account at your current bank would pay interest every six months. How much interest will you need to earn every six months to match the CD?

21.       Suppose you invest $100 in a bank account, and five years later it has grown to $134.39.

1. What APR did you receive, if the interest was compounded semiannually?
2. What APR did you receive if the interest was compounded monthly?

22. Your son has been accepted into college. This college guarantees that your son’s tuition will not increase for the four years he attends college. The first $10,000 tuition payment is due in six months. After that, the same payment is due every six months until you have made a total of eight payments. The college offers a bank account that allows you to withdraw money every six months and has a fixed APR of 4% (semiannual) guaranteed to remain the same over the next four years. How much money must you deposit today if you intend to make no further deposits and would like to make all the tuition payments from this account, leaving the account empty when the last payment is made?

23.       Oppenheimer Bank is offering a 30-year mortgage with an EAR of 5 3 8 %. If you plan to borrow

$150,000, what will your monthly payment be?

24.     You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is $2356 and you have made every payment on time. The original term of the mortgage was 30 years, and the mortgage is exactly four years and eight months old. You have just made your monthly payment. The mortgage interest rate is 63⁄8% (APR). How much do you owe on the mortgage today?

25.       You have just purchased a home and taken out a $500,000 mortgage. The mortgage has a 30-year term with monthly payments and an APR of 6%.

1. How much will you pay in interest, and how much will you pay in principal, during the first year?
2. How much will you pay in interest, and how much will you pay in principal, during the 20th year (i.e., between 19 and 20 years from now)?

26. In 1975, interest rates were 7.85% and the rate of inflation was 12.3% in the United States. What was the real interest rate in 1975? How would the purchasing power of your savings have changed over the year?

27.       If the rate of inflation is 5%, what nominal interest rate is necessary for you to earn a 3% real interest rate on your investment?

28. You are enrolling in an MBA program. To pay your tuition, you can either take out a standard student loan (so the interest payments are not tax deductible) with an EAR of 5 1 2 % or you can use a tax-deductible home equity loan with an APR (monthly) of 6%. You anticipate being in a very low tax bracket, so your tax rate will be only 15%. Which loan should you use?

29.      You are considering investing in a start-up company. The founder asked you for $200,000 today and you expect to get $1,000,000 in nine years. Given the riskiness of the investment opportunity, your cost of capital is 20%. What is the NPV of the investment opportunity? Should you undertake the investment opportunity? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

30.      Bill Clinton reportedly was paid $10 million to write his book My Way. The book took three years to write. In the time he spent writing, Clinton could have been paid to make speeches. Given his popularity, assume that he could earn $8 million per year (paid at the end of the year) speaking instead of writing. Assume his cost of capital is 10% per year.

1. What is the NPV of agreeing to write the book (ignoring any royalty payments)?
2. Assume that, once the book is finished, it is expected to generate royalties of $5 million in the first year (paid at the end of the year) and these royalties are expected to decrease at a rate of 30% per year in perpetuity. What is the NPV of the book with the royalty payments?

31. You are considering making a movie. The movie is expected to cost $10 million upfront and take a year to make. After that, it is expected to make $5 million when it is released in one year and $2 million per year for the following four years. What is the payback period of this investment? If you require a payback period of two years, will you make the movie? Does the movie have a positive NPV if the cost of capital is 10%?

32.       Use the incremental IRR rule to correctly choose between the investments in Problem 21 when the cost of capital is 7%. At what cost of capital would your decision change?

33. Natasha’s Flowers, a local florist, purchases fresh flowers each day at the local flower market. The buyer has a budget of $1000 per day to spend. Different flowers have different profit margins, and also a maximum amount the shop can sell. Based on past experience, the shop has estimated the following NPV of purchasing each type:

What combination of flowers should the shop purchase each day?

34. Orchid Biotech Company is evaluating several development projects for experimental drugs. Although the cash flows are difficult to forecast, the company has come up with the following estimates of the initial capital requirements and NPVs for the projects. Given a wide variety of staffing needs, the company has also estimated the number of research scientists required for each development project (all cost values are given in millions of dollars).