## Question

Product line

Initial cash outlay for building modifications $65,000

Initial building outlay for equipment $205,000

Annual pretax revenues (generated for 15 years) $165,000

Annual pretax expenditures (generated for 15 years) $75,000

The building will be used for only 15 years. After 15 years the building will be too small for efficient production. At that time, Arnold plans to rent the building to firms similar to the current occupants. To rent the building again, Arnold will need to restore the building to its present layout. The estimated cash cost of restoring the building is $35,000. The cash cost can be deducted for tax purposes in the year the expenditures occur. Arnold will depreciate the original building shell (purchased for $850,000) over a 30-year life to zero, regardless of which alternative it chooses. The building modifications and equipment purchases are estimated to have a 15-year life. They will be depreciated by the straight-line method. The firm’s tax rate is 34 percent, and its required rate of return on such investments is 12 percent. For simplicity, assume all cash flows occur at the end of the year. The initial outlays for modifications and equipment will occur today (year 0), and the restoration outlays will occur at the end of year 15. Which use of the building would you recommend to management?

2) Justin Bloomberg just turned 20. He has no job, no income, but a talented father who is a famous singer. His father has put in the will that he will bequest $100 million to Justin on Justin’s 50th birthday. Knowing this, Justin decides not to find any job, but to borrow against his father’s will to finance his consumption until age 50. Justin expects to live to age 90. Suppose the interest rate is constant at 3%. Ignore taxes and social security.

(a) What is Justin’s permanent income?

(b) How much does Justin need to borrow in present value terms?

3) Suppose there are two states of nature in the future. In the asset market, there are the two contingent claims, one for each state. There’s a third security with payoffs x=(4,2). Suppose the prices of the contingent claims are both 1/2: p(c(s1))= p(c(s2))=1/2. The price of the third security is 4.

a) What is the payoff matrix X of the asset market? Is the market complete or incomplete? Why? Is there any redundant security?

b) What is the price vector p of the securities market?

c) The law of one price says that the securities with the same payoffs must have the same price. Does the LOOP hold here? Why or why not?

d) Find an arbitrage portfolio. Show that one can possibly receive some positive payoffs without any cost or risk using the arbitrage portfolio.

4) Vice Corp. issued 12-year coupon bonds 2 years ago at a coupon rate of 8%. The bond was issued at par and pays semiannual coupon payments. Hardy Corp. has 8% coupon bond outstanding, with semiannual coupon payments. The Hardy Corp. bonds currently have 3 years to mature. The interest rate has been unchanged, and both bonds have been priced at par value until just now, when the Fed announced to cut the annual interest rate by 1 percent.

Walter bought one Vice Corp. bond at the time of issuing 2 years ago. He has already received four semiannual coupon payments. And he decides to sell the bond after the Fed’s announcement. Assume that bond prices change instantaneously to reflect the new interest rate. What is Walter’s annualized holding period return? Why is it higher or lower than 8%?

What is the percentage change in the price of these bonds?

Suppose instead the Fed announced to raise the interest rate by 1 percent. What is the percentage change in the price of these bonds? Illustrate your answers in (b) and (c) by graphing bond prices versus YTM. What does this problem tell you about the interest rate risk of longer-term bonds?

(5) XYZ Inc. has 2 million shares outstanding. The company currently pays out all its earnings as dividends and just paid a dividend of $5 per share. Its annual earnings are expected to be in perpetuity. It is considering a new project that requires retaining $1 million one year from now as an initial investment. The project will generate annual earnings of $0.5 million in perpetuity starting one year after the initial investment. The same opportunity will continue to exist indefinitely. Suppose in each subsequent year the company will retain and invest the same percentage of annual earnings as the first year. The return on the new investments will remain 50% in perpetuity. The required rate of return for the company is 10%.

What is the per share stock price if the company undertakes no new investment? What are the annual earnings of the company without new investment?

What is the return on the new investment? Would undertaking the infinite series of new investment opportunities increase the firm’s value? Explain intuitively without calculating the NPVs of the new investments.

What is the growth rate of the firm if the new investment opportunities are undertaken?

What is the (per share) stock price if the company announces to undertake the infinite series of the investment opportunities?

Does the P/E (where E is the current earnings per share) increase, stay constant, or decrease after the announcement? Why?

6) There are two states of nature (s1, s2) with equal probabilities. Suppose there is a representative agent who is endowed with 1 unit of consumption today, and (2, 1) tomorrow. The agent has power utility

u(c) = - (c - 3)2 , c≤3

and β=1. In the asset market, there is a security with payoff (1,0) and a riskfree bond that pays (1,1).

What are the risk-neutral probabilities?

What is the gross return (Rf) of the riskfree bond?

What is the expected gross return of the security with payoff (1,0)? Is the expected risk premium (also known as the risk correction) of this security positive or negative? Please explain intuitively.

## Solution Preview

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In order to determine the best option, the cash flows have been computed for each of the two options - Renting and Modification.The Net present value (NPV) has been found using the rate of 12% and the option with the highest NPV should be considered, everything else the same.

Option 1: Renting to the present occupants

Present value of net benefits $264.769,16 The rate of 12% has been used to discount the cash flows.

Option 2: Modification for the first 15 years and then renting

Present value of net benefits $279.190,86

Decision

As such, it is suggested that they should opt for the 2nd option i.e. modification for use during the 1st 15 years and then rent it, since the present value of benefits with this option is higher. ...