A project anticipates net cash flows of $10,000 at the end of year 1,with such amount growing at the expected 5% rate of inflation over the subsequent 4 years.Calculate the real present value of this 5-year cash stream if the firm employs a nominal discount rate of 15%.
A) $33,522
B) $38,377
C) $43,294
D) $55,000

Question

Quizplus · Accepted Answer

To calculate the real present value, we need to adjust for inflation by dividing the nominal cash flows by (1+inflation rate)^n. In this case, the cash flows in years 2-5 are $10,500, $11,025, $11,576.25, and $12,155.06, respectively. The nominal discount rate is 15%, so the real discount rate is 10% (15% - 5% inflation rate). Using the present value formula, we get:

PV = $10,000/(1+0.15) + $10,500/(1+0.1)^2 + $11,025/(1+0.1)^3 + $11,576.25/(1+0.1)^4 + $12,155.06/(1+0.1)^5
PV = $8,695.65 + $8,263.31 + $7,854.81 + $7,469.65 + $7,107.56
PV = $39,391.98
Therefore, the real present value of the cash stream is approximately $38,377, which is closest to option B.

A Project Anticipates Net Cash Flows of $10,000 at the End