17. a. The value of the call is the maximum of the stock price minus the present value of the exercise
price, or zero, so:
The option isn’t worth anything.
b. The stock price is too low for the option to finish in the money. The minimum return on the
stock required to get the option in the money is:
which is much higher than the risk-free rate of interest.
18. B is the more typical case; A presents an arbitrage opportunity. You could buy the bond for $800 and
19. a. The conversion ratio is given at 18. The conversion price is the par value divided by the
conversion ratio, so:
The conversion premium is the percent increase in stock price that results in no profit when the
bond is converted, so:
b. The straight bond value is:
And the conversion value is the conversion ratio times the stock price, so:
c. We need to set the straight bond value equal to the conversion ratio times the stock price, and
solve for the stock price, so:
d. There are actually two option values to consider with a convertible bond. The conversion option
CHAPTER 24 – 2
20. a. The NPV of the project is the sum of the present value of the cash flows generated by the
project. The cash inflows from this project are an annuity, so the NPV is:
b. The company should abandon the project if the PV of the revised cash flows for the next seven
years is less than the project’s aftertax salvage value. Since the option to abandon the project occurs in
Aftertax salvage value = C2(PVIFA11%,7)
$21,000,000 = C2(PVIFA11%,7)
Challenge
21. The straight bond value today is:
And the conversion value of the bond today is:
We expect the bond to be called when the conversion value increases to $1,300, so we need to find
The bond will be called in 10.52 years.
The bond value is the present value of the expected cash flows. The cash flows will be the annual
coupon payments plus the conversion price. The present value of these cash flows is:
CHAPTER 24 – 3
22. We will use the bottom up approach to calculate the operating cash flow. Assuming we operate the
project for all four years, the cash flows are:
Year 0 1 2 3 4
Sales $9,100,000 $9,100,000 $9,100,000 $9,100,000
Operating costs 3,700,000 3,700,000 3,700,000 3,700,000
Change in NWC –$900,000 0 0 0 $900,000
There is no salvage value for the equipment. The NPV is:
b. The cash flows if we abandon the project after one year are:
Year 0 1
Sales $9,100,000
Change in NWC –$900,000 $900,000
The book value of the equipment is:
CHAPTER 24 – 4
So, the taxes on the salvage value will be:
This makes the aftertax salvage value:
The NPV if we abandon the project after one year is:
If we abandon the project after two years, the cash flows are:
Year 0 1 2
Sales $9,100,000 $9,100,000
Operating costs 3,700,000 3,700,000
Change in NWC –$900,000 0 $900,000
The book value of the equipment is:
So the taxes on the salvage value will be:
This makes the aftertax salvage value:
CHAPTER 24 – 5
The NPV if we abandon the project after two years is:
If we abandon the project after three years, the cash flows are:
Year 0 1 2 3
Sales $9,100,000 $9,100,000 $9,100,000
Operating costs 3,700,000 3,700,000 3,700,000
Change in NWC –$900,000 0 0 $900,000
The book value of the equipment is:
So the taxes on the salvage value will be:
This makes the aftertax salvage value:
The NPV if we abandon the project after three years is:
We should abandon the equipment after three years since the NPV of abandoning the project after
three years has the highest NPV.
CHAPTER 24 – 6
