You are expecting annual cash ﬂows of $1,000 in years 1-5; $2,000 in years 6-10; and $5,000 in years 11-20. If the rate of interest is 8% compounded annually, calculate the present value of this
Cash ﬂow stream.

Question

Quizplus · Accepted Answer

The present value of the cash flow stream can be calculated by discounting each cash flow to its present value and then adding them up. Using the formula for present value of an annuity:
PV = C*[1-(1+r)^-n]/r
where PV is the present value, C is the cash flow, r is the annual interest rate, and n is the number of periods.

For the first five years, the cash flow is $1,000, so the present value using 8% interest rate would be:
PV1-5 = $1,000*[1-(1+0.08)^-5]/0.08 = $3,580.75

For the next five years, the cash flow is $2,000, so the present value using 8% interest rate would be:
PV6-10 = $2,000*[1-(1+0.08)^-5]/0.08*(1+0.08)^5 = $7,596.23

For the last ten years, the cash flow is $5,000, so the present value using 8% interest rate would be:
PV11-20 = $5,000*[1-(1+0.08)^-10]/0.08*(1+0.08)^10 = $13,791.90

Therefore, the total present value of the cash flow stream is:
PV = $3,580.75 + $7,596.23 + $13,791.90 = $24,968.88.

The closest answer is choice A, which is $24,968, so that is the correct answer.

You Are Expecting Annual Cash ﬂOws of $1,000 in Years