You are comparing two investment options, each of which will provide $15,000 of total income. Option A pays five annual payments starting with $5,000 the first year followed by four annual payments of $2,500 each. Option B pays five annual payments of $3,000 each. Which one of the following statements is correct given these two investment options? a.) Given a positive rate of return, Option A is worth more today than Option B. b.) Option A is preferable because it is an annuity due. c.) Option B has a higher present value than Option A given a positive rate of return. d.) Both options are of equal value today. e.) Option B has a lower present value than Option A given a zero rate of return.
Answer: a.) Given a positive rate of return, Option A is worth more today than Option
Explanations to the above answer
We will select the option A because in option A we will have higher prasent Value then option B
Suppose the interest rate is 5 % and we calculate the NPV the calculation would be as follow
Option A | |||
Year | Cash Flow | Pv factor | Prasent Value |
0 | 5000 | 1 | 5000 |
1 | 2500 | 0.95238 | 2380.952381 |
2 | 2500 | 0.90703 | 2267.573696 |
3 | 2500 | 0.86384 | 2159.593996 |
4 | 2500 | 0.82270 | 2056.756187 |
5 | 2500 | 0.78353 | 1958.815416 |
15823.69168 |
Option B | |||
Year | Cash Flow | Pv factor | Prasent Value |
0 | 0 | 1 | 0 |
1 | 3000 | 0.95238 | 2857.142857 |
2 | 3000 | 0.90703 | 2721.088435 |
3 | 3000 | 0.86384 | 2591.512796 |
4 | 3000 | 0.82270 | 2468.107424 |
5 | 3000 | 0.78353 | 2350.578499 |
12988.43001 |
Form the above calculation we could see that option A has higher Value so select Option A