1.
Calculate the present value in each of the following cases. Show your work.
a.
You are negotiating a book deal for your newest novel in which an economist singlehandedly saves the world. The publisher offers to pay you an advance of $1 million todayplus $500,000 at the end of each of the next three years. What is the present value of thesepayments, given your rate of discount of 5 percent?
b.
You counter the publishers offer with a counter-offer that will pay you $1.5 million todayplus $5 per book sold in each of the next three years. You think you will sell 80,000 bookseach year in that period, but the publisher thinks you will only sell 40,000 books each year.Explain why both you and the publisher like this offer better than the deal in part a.
2.
Julia is considering buying stock in only one of the following companies: (i) Uninvest.com,which runs a Web site geared toward older peoples retirement income and has a 10 percentprobability of returning 20 percent this year and a 90 percent probability of returning 7percent, or (ii) Speculate, Inc., which invests in derivative securities and has a 50 percentchance of returning 0 percent this year and a 50 percent chance of returning 50 percent.
a.b.c.d.
What are the expected returns to investing in Uninvest and Speculate?What are the standard deviations of the returns to Uninvest and Speculate?If Julia is very risk-averse, which companys stock should she buy?If Julia is risk-neutral (that is, she does not worry about risk at all), which companys stockshould she buy?
3.
Consider three alternative bonds that you might invest in, each of which matures in oneyear. The following table shows the probability that you will receive each possible return.For example, if you buy bond A, the probability is 90 percent that your return will be 20percent and the probability is 10 percent that your return will be 100 percent (in otherwords, you lose the entire amount invested).Bond
20%-100%
75%25%
40%-40%
Bond C
c.
90%
Bond B
b.
Return
Bond A
a.
Probability
60%40%
10%-10%
Calculate the expected return for all three bonds in percentage terms. Show all your work.In your calculations, you may round after two significant digits.Calculate the standard deviations of the returns on these bonds. Show all your work. If youare extremely risk averse, which of the three bonds would you buy? Why?Would a risk-averse investor ever buy Bond A instead of one of the other bonds? Why orwhy not?
4.
In each of the following scenarios, which security should an investor buy? Assume that thesecurities are identical in all ways except as described below. Explain your answer.
a.
Security A has an expected return of 12 percent, whereas security B has an expected returnof 10 percent.Interest on security C is 10 percent and is taxable, whereas interest on security D is 7percent and is not taxable, and the investors tax rate is 40 percent.Security E has a 20 percent chance of default, whereas security F has a 15 percent chance ofdefault.Security G and security H are both debt securities that cost $1,000 and mature in one year.An investor incurs a transactions cost of $50 to purchase security G, which has an expectedreturn of 8 percent. An investor incurs no transactions cost to purchase security H, whichhas an expected return of 5 percent.
b.c.d.
5.
Explain the reasons why bonds are risky. Give examples to support your answer.