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Homework answers / question archive / Fordham University - ECON 3778 Homework 2 Corporate Finance 1)Suppose the risk-free rate of interest is 4%

Fordham University - ECON 3778

Homework 2

Corporate Finance

1)Suppose the risk-free rate of interest is 4%.

(a) Having $200 today is equivalent to having what amount in one year?

(b) Having $200 in one year is equivalent to having what amount today?

(c) Suppose you know that you will need $200 for an expense next year. Which would you prefer, $200 today or $200 in one year? Explain.

2. Your computer manufacturing firm must purchase 10,000 keyboards from a supplier. One supplier

demands a payment of $100,0000 today plus $10 per keyboard payable in one year. Another supplier will charge $21 per keyboard, also payable in one year. The first-free rate of interest is 6%.

(a) What is the difference in their offer in terms of dollars today? Which offer should your firm take?

Your firm should take the first offer.

(b) Suppose your firm does not have the cash to spend today. Which offer should your firm take? Explain.

3. Consider two securities that pay risk-free cash flows over the next two years and that have the current market prices shown here:

Security Price Today ($) Cash Flow in One Year ($) Cash Flow in Two Years ($)

B1 94 100 0

B2 85 0 100

1

(a) What is the no-arbitrage price of a risk-free security that pays cash flows of $100 in one year and

$100 in two years.

(b) What is the no-arbitrage price of a risk-free security that pays cash flows of $100 in one year and

$500 in two years.

(c) Suppose a security with cash flows of $50 in one year and $100 in two years is trading for a price of

$130. Is there an arbitrage opportunity available? Explain.

4. Xia Corporation is a company whose sole assets are $100,000 in cash and three projects that it will undertake. The projects are risk-free and have the following cash flows:

Security Price Today ($) Cash Flow in One Year ($)

A -20,000 30,000

B -10,000 25,000

C -60,000 80,000

Xia plans to invest any unused cash today at the risk-free interest rate of 10%. In one year, all cash will be paid to investors and the company will shut down.

(a) What is the NPV of each project? Which projects should Xia undertake and how much cash should it retain?

(b) What is the total value of Xia’s assets (projects and cash) today?

(c) Which cash flows will the investors in Xia receive? Based on these cash flows, what is the value of Xia today?

(d) Suppose Xia pays any unused cash to investors today, rather than investing it. What are the cash flows to the investors in this case? What is the value of Xia now?

(e) Explain the relationship in your answers to parts (b), (c), and (d).

5. Your brother has offered to give you either $5,000 today or $10,000 in 10 years. The risk-free interest rate is 7% per year.

(a) What is the value in ten years of $5,000 today?

(b) What is the value today of $10,000 in ten years?

(c) Which option is preferable?

6. Your daughter is currently eight years old. You anticipate that she will be going to college in 10 years. You would like to have $100,000 in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of 3% per year, how much money do you need to put into the account today to ensure that you will have $100,000 in 10 years?

7. Suppose you receive $100 at the end of each year for the next three years.

(a) If the interest rate is 8%, what is the present value of these cash flows?

(b) What is the future value in three years of the present value you computed in (a)?

(c) Suppose you deposit the cash in a bank account that pays 8% interest per year, What is the balance in the account at the end of each of the next three years (after your deposit is made)?

8. The British government has a consol bond outstanding paying £100 per year forever. Assume that the current interest rate is 4% per year.

(a) What is the value of the bond immediately after a payment is made?

(b) What is the value of the bond immediately before a payment is made?

9. You are the head of the Schwarz Family endowment for the Arts. You have decided to fund an arts school in the San Francisco Bay area with a 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?

10. You are 25 years old and decide to start saving for your retirement. You plan to save $5,000 at the end of each year and will make the last deposit when you retire at age 65. Suppose you earn 8% per year on your retirement savings.

(a) How much will you have saved for retirement?

(b) How much will you have saved if you started saving at age 35?

11. A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $1,000. 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. The interest rate is 12% per year.

(a) What is today’s value of the bequest?

(b) What is the value of the bequest immediately after the first payment is made? Immediately after the first payment, the cash flow stream looks like:

12. You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last for 17 years. You expect that the drug’s profits will be $2 million in its first year and that this amount

will grow at a rate of 5% per year for the next 17 years. Once the patent expires, other pharmaceutical

companies will be able to produce the same drug and competition will likely drive profits to zero. What is the present value of the new drug if the interest rate is 10%?

13. You are saving for retirement. To live comfortably, you decide that you will need to save $2 million by the time you are 65. Today is your 30th birthday, and you decide, starting today and continuing on every

birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 5%, how much must you set aside each year to make sure that you will have $2 million in the account on your 65th birthday?

14. You have investment opportunity that requires an initial investment of $5,000 today and will pay $6,000 in one year. What is the IRR of this opportunity?

15. Your grandmother bought an annuity from Rock Solid Life Insurance Company for $200,000 when she

retired. In exchange for the $200,000, Rock Solid will pay her $25,000 per year until she dies. The interest rate is 5%. How long must she live after the day she retired to come out ahead (that is, to get more value than she payed in)?

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