You are offered an investment that will make three $5,000 payments. The first payment will occur four years from today.

Question

You are offered an investment that will make three $5,000 payments. The first payment will occur four years from today. The second will occur in five years, and the third will follow in six years. If you can earn 11 percent, what is the most this investment is worth today? What is the future value of the cash flows?

Accepted Answer

We will answer the questions in reverse order to illustrate a point. The future value of the cash flows in six years is:

[latex]( \$5,000×1.11^{2})+(5,000×1.11)+5,000[/latex]=$6,160. 50+5,550+5,000

=$16, 710. 50

The present value must be:

$[latex]16,710.50/1.11^{6}[/latex]=$8,934.12

Let’s check this. Taking them one at a time, the PVs of the cash flows are:

$5,000×[latex]1/1.11^{6}[/latex]=$5,000/1.8704=$2,673.20

$[latex]5,000×1/1.11^{5}[/latex]=$5,000/1.6851=2,967.26

$[latex]5,000×1/1.11^{4}[/latex]=$5,000/1.5181=[latex]\underline{3,293.65}[/latex]

Total present value=$[latex]\underline{\underline{8,934.12}}[/latex]

This is as we previously calculated. The point we want to make is that we can calculate present and future values in any order and convert between them using whatever way seems most convenient. The answers will always be the same as long as we stick with the same discount rate and are careful to keep track of the right number of periods.

Question 6.4: You are offered an investment that will make three $5,000 pa...

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