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

Question

Quizplus · Accepted Answer

First, we need to calculate the nominal cash flows for each year, by multiplying the previous year's cash flow by (1+5%) to account for inflation:
Year 1: $10,000
Year 2: $10,500
Year 3: $11,025
Year 4: $11,576.25
Year 5: $12,155.06
Then we can discount each nominal cash flow back to its present value using the nominal discount rate of 15%:
PV of Year 1 cash flow = $10,000 / (1+15%)^1 = $8,695.65
PV of Year 2 cash flow = $10,500 / (1+15%)^2 = $7,655.96
PV of Year 3 cash flow = $11,025 / (1+15%)^3 = $6,673.84
PV of Year 4 cash flow = $11,576.25 / (1+15%)^4 = $5,741.26
PV of Year 5 cash flow = $12,155.06 / (1+15%)^5 = $4,851.57
Finally, we add up all the present values to get the real present value of the cash stream:
Real present value = $8,695.65 + $7,655.96 + $6,673.84 + $5,741.26 + $4,851.57 = $33,618.28
The closest option is B) $38,377, which is incorrect.

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