Question

Asset X is expected to deliver 3 future payments. They have present values of, respectively, \(1,000, \)2,000, and \(7,000. Asset Y is expected to deliver 10 future payments, each having a present value of \)1,000. Which of the following statements correctly describes the relationship between the current price of Asset X and the current price of Asset Y?

1. Asset X and Asset Y should have the same current price.

2. Asset X should have a higher current price than Asset Y.

3. Asset X should have a lower current price than Asset Y.

Short answer

The correct option is (a): Asset X and Asset Y should have the same current price.

Step-by-step solution

Step 1. Explanation of correct option

The total present value of Asset X is $10,000 (=$1,000 + $2,000 + $7,000). The total present value of Asset Y is $10,000 (=$1,000 * 10). When the present value is the same, the current price will also be the same.

The time frame for the delivery of payments isn't specified, however, it is irrelevant, as the present value will reflect distant payments as less valuable.

Additionally, the real value of each payment can't be determined, however, the real value is included in the present value calculation.

That is why the 10 payments are still equal to the 3 payments because present value accounts for both the time and monetary value of future returns.

(the 10th payment may be years away but its real dollar value is much greater, however, its present value is $1000)

Step 2. Explanation for incorrect option

Options (b) and (c) are incorrect as the present value provides all the necessary information to the value of the payments. If the present values are equal, then the difference in time of payment and dollar value is accounted for.