1. Suppose a friend offers to borrow $100 from you today and in return pay you $110 one year from today. Looking in the market for other options for investing the $100, you find your best alternative option that you view as equally risky as lending to your friend. That option has an expected return of 8%. What should you do?
2. The yield to maturity of a $1,000 bond with a 7% coupon rate, semiannual coupons and two years to maturity is 7.6% APR, compounded semiannually. What must its price be?
3. Compute the internal rate of return for the cash flows of the following 2 projects:
Cash flows ($)
Year
Project A
Project B
0
-5,300
-2,900
1
2,000
1,100
2
2,800
1,800
3
1,600
1,200
4. Suppose the following zero-coupon bonds are trading at the prices shown below per $100 face value. Determine the corresponding yield to maturity for each bond.
Maturity
1 year
2 years
3 years
4 years
Price
$96.62
$92.45
$87.63
$83.06
5. Consider a five-year, $1,000 bond with a 2.2% coupon rate and semiannual coupons. If this bond is currently trading for a price of $963.11, what is the bond's yield to maturity?
6. The Robb Computer Corporation is trying to choose between the following two mutually exclusive design projects:
Cash flows ($)
Year
Project A
Project B
0
-30,000
-12,000
1
18,000
7,500
2
18,000
7,500
3
18,000
7,500
a. If the required return is 10% and Robb Computer applies the profitability index decision rule, which project should the firm accept?
b. If the company applies the NPV decision rule, which project should it take?
c. Explain why your answers in (a) and (b) are different.
7. Conrad Willig, an entrepreneur, recently learned of a chemical treatment causing water to freeze at 100 degrees Fahrenheit rather than 32 degrees. Of all the many practical applications for this treatment, Mr. Willig liked the idea of hotels made of ice more than anything else. Conrad estimated the annual cash flows from a single ice hotel to be $2 million, based on an initial investment of $12 million. He felt that 20% was an appropriate discount rate, given the risk of this new venture.
a. Calculate the NPV of the project.
b. Conrad reasons that NPV analysis missed a hidden source of value. While he was pretty sure that the initial investment would cost $12 million, there was some uncertainty concerning annual cash flows. His cash flow estimate of $2 million per year actually reflected his belief that there was a 50% probability that annual cash flows would be $3 million and a 50% probability that annual cash flows would be $1 million. Calculate the NPV for the 2 forecasts.
c. What is the average of the two forecasts?
d. If the optimistic forecast turns out to be correct, what would Mr. Willig want to do? Assume there are 10 locations in the country that can support an ice hotel.
e. Imagine Mr. Willig now believes that there is a 50% probability that annual cash flows will be $6 million and a 50% chance that annual cash flows will be -$2 million. Moreover, Mr. Willig wants to own, at most, just one ice hotel. Calculate the NPV for the project. Should he build the hotel?
f. Does his decision change when we consider the abandonment option?
8. Given the following zero-coupon yields, compare the yield-to-maturity for a 3-year zero-coupon bond, a 3-year coupon bond with 4% annual coupons, and a 3-year coupon bond with 10% annual coupons.
Maturity
1 year
2 years
3 years
4 years
Zero-coupon YTM
3.5%
4%
4.5%
4.75%