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 a cash flow stream is the sum of the present values of each individual cash flow. The present value of a cash flow is calculated by dividing the cash flow by (1 + r)^n, where r is the rate of interest and n is the number of years from the present to the cash flow.In this case, the present value of the cash flow stream is:PV = $1,000/(1 + 0.08)^1 + $1,000/(1 + 0.08)^2 + $1,000/(1 + 0.08)^3 + $1,000/(1 + 0.08)^4 + $1,000/(1 + 0.08)^5 + $2,000/(1 + 0.08)^6 + $2,000/(1 + 0.08)^7 + $2,000/(1 + 0.08)^8 + $2,000/(1 + 0.08)^9 + $2,000/(1 + 0.08)^10 + $5,000/(1 + 0.08)^11 + $5,000/(1 + 0.08)^12 + $5,000/(1 + 0.08)^13 + $5,000/(1 + 0.08)^14 + $5,000/(1 + 0.08)^15 + $5,000/(1 + 0.08)^16 + $5,000/(1 + 0.08)^17 + $5,000/(1 + 0.08)^18 + $5,000/(1 + 0.08)^19 + $5,000/(1 + 0.08)^20= $24,968.45Therefore, the present value of the cash flow stream is $24,968.45, which is closest to choice A.

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