Time Value of Money
Question 1: Future values and annuities
1. The cost of a new automobile is $10,000. If the interest rate is 596, how much would
you have to set aside now to provide this sum in five years?
2. 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 896, how much do you need to set aside today to cover
3. You have invested $60,476 at 896. After paying the above school fees, how much
would remain at the end of the six years?
Question 2: IRR rule
Consider the following two mutually exclusive projects:
1. Calculate the NPV of each project for discount rates of 096, 1096, and 2096.
2. What is the approximate IRR for each project?
3. In what circumstances should the company accept project A?
4. Calculate the NPV of the incremental investment (8 – A) for discount rates of 096,
1096, and 2096- What can you conclude?
Question 3: IRR rule
The TTL Shipbuilding Company has a noncancelable contract to build a small cargo
vessel. Construction involves a cash outlay of $250,000 at the end of each of the next
two years. At the end of the third year the company will receive payment of $650,000-
The company can speed up construction by working an extra shift. In this case, there
will be a cash outlay of $550,000 at the end of the first year followed by a cash
payment of $650,000 at the end of the second year. Use the IRR rue to show the
(approximate) range of opportunity costs of capital at which the company should work
the extra shift.
Question 4: Capital Rationing
BGMT Pharmaceuticals has $1 million allocated for capital expenditures. Which of the
following projects should the company accept to stay within the $1 million budget?
How much does the budget limit cost the company in terms of its market value? The
opportunity cost of capital for each project is 11
Project Investment (3 thousands) NP’V ($ thousands) IRR (96)
1 300 66 17-2
2 200 -4 10.7
3 250 43 16-6
4 100 14 12-1
5 100 7 11.8
6 350 63 18-0
7 400 48 13-5