Chapter 2 Questions, Edition 11.docx - BASIC 1. Future...

BASIC
1. Future values At an interest rate of 12%, the six-year discount factor is .507. How many dollars
is $.507 worth in six years if invested at 12%?
Answer
2. Discount factors If the PV of $139 is $125, what is the discount factor?
3. Present values If the cost of capital is 9%, what is the PV of $374 paid in year 9?
Answer
4. Present values A project produces a cash flow of $432 in year 1, $137 in year 2, and $797 in
year 3. If the cost of capital is 15%, what is the project's PV?
5. Futures values If you invest $100 at an interest rate of 15%, how much will you have at the end
of eight years?
Answer
6. Perpetuities An investment costs $1,548 and pays $138 in perpetuity. If the interest rate is 9%,
what is the NPV?
7. Growing perpetuities A common stock will pay a cash dividend of $4 next year. After that, the
dividends are expected to increase indefinitely at 4% per year. If the discount rate is 14%, what is the
PV of the stream of dividend payments?
Answer
8. Perpetuities and annuities The interest rate is 10%.
a. What is the PV of an asset that pays $1 a year in perpetuity?
b. The value of an asset that appreciates at 10% per annum approximately doubles in seven
years. What is the approximate PV of an asset that pays $1 a year in perpetuity
beginning in year 8?
c. What is the approximate PV of an asset that pays $1 a year for each of the next seven
years?
d. A piece of land produces an income that grows by 5% per annum. If the first year's
income is $10,000, what is the value of the land?
Answer
9. Future values and annuities
a. The cost of a new automobile is $10,000. If the interest rate is 5%, how much would you
have to set aside now to provide this sum in five years?
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b. You have to pay $12,000 a year in school fees at the end of each of the next six years. If
the interest rate is 8%, how much do you need to set aside today to cover these bills?
c. You have invested $60,476 at 8%. After paying the above school fees, how much would
remain at the end of the six years?

Answer
10. Continuous compounding The continuously compounded interest rate is 12%.
a. You invest $1,000 at this rate. What is the investment worth after five years?
b. What is the PV of $5 million to be received in eight years?
c. What is the PV of a continuous stream of cash flows, amounting to $2,000 per year,
starting immediately and continuing for 15 years?
11. Compounding intervals You are quoted an interest rate of 6% on an investment of $10 million.
What is the value of your investment after four years if interest is compounded:
a. Annually?
b. Monthly? or
c. Continuously?