## End of Chapter Problems

Q6.28 Is this morning's CNN forecast of tomorrow's temperature a random variable? Is tomorrow's temperature a random variable?

Q 6.29 Does a higher reward (expected rate of return) always come with more risk?

Q6.30 Is the average individual in a betting pool effectively more, equally, or less risk-averse than the overall pool? Q 6.31 A financial instrument will pay off as follows:

Probability 50% 25% 12.5% 6.25% 3.125% 3.125% Payoff \$100 \$110 \$130 \$170 \$250 \$500

(a) What price today would make this a fair bet?

(b) What is the maximum price that no risk-averse investor would be willing to pay it?

Q 6.32 A bond will pay off \$ 100 with probability 99%, and nothing with probability 1%. The equivalent risk-free rate of return is 5%. What is an appropriate promised yield on this bond?

Q6.33 Now assume that the above financial instrument costs \$100.

(a) What is its expected rate of return?

(b) If the prevailing interest rate on time-equivalent Treasuries is 10%, and if financial default happens either completely (i.e., no repayment) or not at all (i.e., full promised payment), then what is the probability p that the security will pay off? In other words, assume that with probability p, full repayment occurs; with probability

1 - p, zero repayment occurs. What is the p that makes the expected rate of return equal to 10%.

Q 6.34 An L.A. Lakers bond promises an investment rate of return of 9%. Time-equivalent Treasuries offer 6%. Is this necessarily a good investment? Explain.

Q6.35 A Disney bond promises an investment rate of return of 7%. Time-equivalent Treasuries offer 7%. Is the Disney bond necessarily a bad investment? Explain

Q6.36 Go to the Vanguard website. Look at funds by asset class, and answer this question for different bond fund durations.

(a) What is the current yield-to-maturity of a taxable Vanguard bond fund invested in Treasury bonds?

(b) What is the current yield-to-maturity of a taxable Vanguard bond fund invested in Investment Grade bonds?

(c) What is the current yield-to-maturity of a taxable Vanguard bond fund invested in High-Yield bonds?

Q 6.37 What are the main bond rating agencies and categories? Roughly, what are the ten year default rate differences between them?

Q6.38 An IBM bond promising to pay \$100,000 costs \$90,090. Time-equivalent Treasuries offer 8%. Setting aside the risk-neutrality and perfect markets assumption for this question only, what can you say about the risk premium, the default premium, and the liquidity premium?

Q 6.39 Continued: Returning to our assumption that markets are risk-neutral, but still setting aside the perfect markets assumption for this question, what can you say about the risk premium, the default premium, and the liquidity premium?

Q6.41 How is a credit swap like an insurance contract? Who is the insurer in a credit swap? Why would anyone want such insurance?

Q6.42 A bond promises to pay \$12,000 for a bond that costs \$10,000. The promised discount on equivalent bonds is 25% per annum. Is this bond a good deal?

Q6.43 A project costs \$19,000 and promises the following cash flows:

Year 1 2 3

The appropriate discount rate is 15% per annum. Should you buy this bond?

Q6.44 Assume that the probability that the Patriots will win the Superbowl is 55%. A souvenir shop outside the stadium will earn net profits of \$1.5 million if the Patriots win, and \$1.0 million if they lose. You are the loan officer of the bank to whom the shop applied for a loan. You can assume that your bank is risk-neutral and that the bank can invest in safe projects that offer an expected rate of return of 10%.

(a) What interest rate would you quote if the owner asked you for a loan for \$900,000 today?

(b) What interest rate would you quote if the owner asked you for a loan for \$1,000,000 today?

(These questions require that you compute the amount that you would demand for repayment.) Q 6.45 A new project has the following success probabilities:

Failure Success Buyout Prob 10% 85% 5%

Assume risk-neutrality. If a \$100 return bond collateralized by this project promises an interest rate of 8%, then what is the prevailing cost of capital, and what do shareholders receive if the buyout materializes?

Q 6.46 Debt is usually safer than equity. Does the risk of the rate of return on equity go up if the firm takes on more debt, provided the debt is low enough to remain risk-free? Illustrate with an example that you make up.

Q6.47 Under risk-neutrality, a factory can be worth \$500,000 or \$1,000,000 in two years, depending on product demand, each with equal probability. The appropriate cost of capital is 6% per year. The factory can be financed with proceeds of \$500,000 from loans today. What are the promised and expected cash flows and rates of return for the factory (without loan), for the loan, and for a hypothetical factory owner who has to first repay the loan?

Q6.48 Assume that the correct future cash flow is \$100 and the correct discount rate is 10%. Consider the value effect of a 5% error in cash flows and the effect of a 5% error in discount rates.

(a) Graph the value effect (both in absolute values and in percent of the correct up front present value) as a function of the number of years from 1 year to 20 years.

(b) Is this an accurate real-world representation of how your uncertainty about your own calculations should look?