You are expecting annual cash ﬂows of $80,000 in years 1-5; $95,000 in years 6-20; and $105,000 in years 21-50. If the rate of interest is 10% compounded annually, calculate the future value of this
Cash ﬂow stream.

Question

Quizplus · Accepted Answer

To calculate the future value, we need to find the present value of each cash flow stream and add them up. 
PV of years 1-5 = $80,000 x (1 + 0.10)⁵ ÷ (1 + 0.10)⁵ = $317,180.02
PV of years 6-20 = $95,000 x ((1 + 0.10)¹⁵ - 1) ÷ (0.10 x (1 + 0.10)¹⁵) = $1,179,194.76
PV of years 21-50 = $105,000 x ((1 + 0.10)³⁵ - 1) ÷ (0.10 x (1 + 0.10)³⁵) = $8,273,898.22
Total PV = $317,180.02 + $1,179,194.76 + $8,273,898.22 = $9,770,273.00
Therefore, the future value of this cash flow stream is:
FV = $9,770,273.00 x (1 + 0.10)⁵⁰ = $105,538,998.26, which rounds to $105.54 million. The answer is C.

You Are Expecting Annual Cash ﬂOws of $80,000 in Years