Question

You expect to receive $5,000 next year, cash flows of $4,000 annually over the following 6 years, and one last cash flow of $8,000 the following year. If the appropriate discount rate is 7%, what is this stream of cash flows worth to you today? Round to the nearest cent. ​[Hint: Timeline is very important here. As with all advanced TVM questions, first convert the annuity into its single cash-flow equivalent, in this case using the PV annuity formula. In the second step, you will have three single cash-flows you need to discount back to time zero using different n's.

Answer 1

Answer:

The cash flows can be depicted as follows:

CF 1 = $5,000

CF 2 TO CF 7 = $4,000 and

CF 8 = $8,000

Step 1:

First let us get the present value of the annuity from year 2 to year 7 (highlighted yellow in table above) :

PV at the end of year 1 of annuity $4,000 over 6 years = 4000 * (1 - 1/ (1 + 7%) ⁶) / 7% = $19,066.15864

PV of this annuity at Year 0 = 19066.15864 / (1 + 7%)

Step 2:

Now let us calculate PV at time 0:

PV of cash flows at time 0 = PV of CF1 + PV of annuity CF 2 to CF 7+ PV of CF 8

PV of cash flows at time 0 = 5000 /(1 + 7%) + 19066.15864 / (1 + 7%) + 8000 /(1 + 7%) ⁸

= $27,147.81

Stream of cash flows worth to you today = $27,147.81