Question 1

Ms. Maple is considering two securities, A and B, and the relevant information is given below:

State of the economy	Probability	Return on A(%)	Return on B(%)
Bear	0.4	3	6.5
Bull	0.6	15	6.5

1. Calculate expected return and standard deviation of two securities.

1. Suppose Miss Maple invested $2,500 in security A and $3,500 in security B. Calculate the expected return and standard deviation of her portfolio.

Question 2

Suppose that you want to buy a 2-year 5% coupon bond, which pays semi-annual coupons and costs $997.

1. Find the yield to maturity on this bond (YTM)
2. Find the effective annual rate of return that you earn on this bond (EAR)?

Question 3

The current market price of a security is $40, the security's expected return is 13%, the riskless rate of interest is 7%, and the market risk premium is 8%.

• According to CAPM, what is the current beta of this security?
• What will be the beta of this security if the covariance of its rate of return with the market portfolio doubles?
• According to CAPM, what is the new expected return on this security?
• What is the new price of this security?
• How is your result consistent with our understanding that assets with higher systematic risks must pay higher returns on average?

Question 4

Consider the following risk-free T-bill and coupon bonds available for sale in the bond market (annual coupons):

Maturity	Price	Coupon
1	942	T-bill (zero coupon bond)
2	995	6.3%
3	998	7.5%
4	985.25	6.75%

Construct the term structure of interest rates for these four years.

Your company plans to issue four-year maturity bonds. You plan to issue bonds priced at $1010. At what level should you plan to set the coupon on your bond to justify this price?

Question 5

Two retail corporations, both equity financed with no debt, are essentially in the same business. However, whereas one of the corporations has a stable earnings and dividend record, paying out all its earnings in dividends, the other is a growth stock increasing its earnings and dividends annually through a different management strategy. The current dividend is $5 per share for both corporations. The stable corporation?s stock trades for $40 per share, whereas the price of the growth stock is $50.

• Estimate the investors? required rate of return on these stocks
• Estimate the steady future growth rate of the growing corporation as perceived by the market.

Question 6

The common stock of the STABBLES Corporation has been trading in a narrow price range for the past month, and you are convinced it is going to break far out of that range in the next three months. You do not know whether it will go up or down, however. The current price of the stock is $100 per share, and the price of a three-month call option at an exercise price of $100 is $10.

• If the risk-free interest rate is 10% per year, what must be the price of a 3-month put option on STABLES stock at an exercise price of $100? The stock pays no dividend.
• What would be a simple options strategy to exploit your conviction about the stock price?s future movements? How far would it have to move in either direction for you to make a profit on your initial investment? (The answer to this question should include a payoff table for your strategy and a graph to support your argument).

Question 7

You are interested in purchasing a shoe machine XYZ, especially designed for men's fashion shoes. The machine costs $10,000. You expect to recover $6,000 a year in operating cash flows for only two years because of rapidly changing fashions. You estimate the salvage value of the machine at the end of two years to be $1,200. Assume that the tax rate is zero. Assume that the $6,000 per year after tax operating cash flow is received at the end of each year.

(a) What is the Net Present Value (NPV) of this project, if cash flows are to be discounted at 20% cost of capital?

(b) What is the IRR of this project?

You decide to invest in machine XYZ. But just before you place an order for the machine you hear about another machine UVW. This machine costs $15,000 and has operating flows of $18,000 during the first year and, for some unknown reason, only $50 during the second year, with no salvage value at the end of two years. (Assume all cash flows occur at the end of the year for the purpose of discounting.)

(c) You know that whether you prefer XYZ or UVW depends upon your cost of capital. Draw the graph showing how NPVs of these two machines relate to their cost of capital. Both NPVs should be on the same graph.

(d) At what cost of capital both machines have the same Net Present Value? (Please do not forget to show the equation you need to solve with the help of Excel to answer this question).

(e) What is the IRR of machine UVW?

(f) Without making any further calculations, state the region(s) of cost of capital that make XYZ preferable to UVW, assuming you must choose either one of these machines but not both.

Instructions: 1. Please type all your answers into this file. The answer to each question should follow the question itself. 2. Please, write short VERBAL conclusion at the end of each problem summarizing your answer in words. Verbal answers are not substitute for the quantitative solution. Question 1 Ms. Maple is considering two securities, A and B, and the relevant information is given below: State of the economy Bear Bull Probability Return on A(%) Return on B(%) 0.4 0.6 3 15 6.5 6.5 a Calculate expected return and standard deviation of two securities. b Suppose Miss Maple invested $2,500 in security A and $3,500 in security B. Calculate the expected return and standard deviation of her portfolio. Question 2 Suppose that you want to buy a 2-year 5% coupon bond, which pays semi-annual coupons and costs $997. a b Find the yield to maturity on this bond (YTM) Find the effective annual rate of return that you earn on this bond (EAR)? Question 3 The current market price of a security is $40, the security's expected return is 13%, the riskless rate of interest is 7%, and the market risk premium is 8%. a. According to CAPM, what is the current beta of this security? b. What will be the beta of this security if the covariance of its rate of return with the market portfolio doubles? c. According to CAPM, what is the new expected return on this security? 1 d. What is the new price of this security? e. How is your result consistent with our understanding that assets with higher systematic risks must pay higher returns on average? Question 4 Consider the following risk-free T-bill and coupon bonds available for sale in the bond market (annual coupons): Maturity 1 2 3 4 Price 942 995 998 985.25 Coupon T-bill (zero coupon bond) 6.3% 7.5% 6.75% a. Construct the term structure of interest rates for these four years. b. Your company plans to issue four-year maturity bonds. You plan to issue bonds priced at $1010. At what level should you plan to set the coupon on your bond to justify this price? Question 5 Two retail corporations, both equity financed with no debt, are essentially in the same business. However, whereas one of the corporations has a stable earnings and dividend record, paying out all its earnings in dividends, the other is a growth stock increasing its earnings and dividends annually through a different management strategy. The current dividend is $5 per share for both corporations. The stable corporation's stock trades for $40 per share, whereas the price of the growth stock is $50. a. Estimate the investors' required rate of return on these stocks b. Estimate the steady future growth rate of the growing corporation as perceived by the market. Question 6 The common stock of the STABBLES Corporation has been trading in a narrow price range for the past month, and you are convinced it is going to break far out of that range in the next three months. You do not know whether it will go up or down, however. The current price of the stock is $100 per share, and the price of a three-month call option at an exercise price of $100 is $10. a If the risk-free interest rate is 10% per year, what must be the price of a 3-month put option on STABLES stock at an exercise price of $100? The stock pays no dividend. b What would be a simple options strategy to exploit your conviction about the stock price's future movements? How far would it have to move in either direction for you to make a profit on your initial investment? (The answer to this question should include a payoff table for your strategy and a graph to support your argument). 2 Question 7 You are interested in purchasing a shoe machine XYZ, especially designed for men's fashion shoes. The machine costs $10,000. You expect to recover $6,000 a year in operating cash flows for only two years because of rapidly changing fashions. You estimate the salvage value of the machine at the end of two years to be $1,200. Assume that the tax rate is zero. Assume that the $6,000 per year after tax operating cash flow is received at the end of each year. (a) What is the Net Present Value (NPV) of this project, if cash flows are to be discounted at 20% cost of capital? (b) What is the IRR of this project? You decide to invest in machine XYZ. But just before you place an order for the machine you hear about another machine UVW. This machine costs $15,000 and has operating flows of $18,000 during the first year and, for some unknown reason, only $50 during the second year, with no salvage value at the end of two years. (Assume all cash flows occur at the end of the year for the purpose of discounting.) (c) You know that whether you prefer XYZ or UVW depends upon your cost of capital. Draw the graph showing how NPVs of these two machines relate to their cost of capital. Both NPVs should be on the same graph. (d) At what cost of capital both machines have the same Net Present Value? (Please do not forget to show the equation you need to solve with the help of Excel to answer this question). (e) What is the IRR of machine UVW? (f) Without making any further calculations , state the region(s) of cost of capital that make XYZ preferable to UVW, assuming you must choose either one of these machines but not both. 3