Explanation:
To calculate the Net Present Value (NPV), we need to discount each cash flow back to the present value and subtract the initial investment.
Given:
$100 million (negative cash flow)$65 million$65 million$65 millionCalculation:
Present Value of Year 1 cash flow:
PV₁ = $65 million / (1 + 0.15)¹ = $65 million / 1.15 = $56.52 million
Present Value of Year 2 cash flow:
PV₂ = $65 million / (1 + 0.15)² = $65 million / (1.15)² = $65 million / 1.3225 = $49.15 million
Present Value of Year 3 cash flow:
PV₃ = $65 million / (1 + 0.15)³ = $65 million / (1.15)³ = $65 million / 1.520875 = $42.74 million
Total Present Value of cash inflows:
Total PV = $56.52 + $49.15 + $42.74 = $148.41 million
NPV = Total PV - Initial Investment:
NPV = $148.41 million - $100 million = $48.41 million
Result:
The NPV is approximately $48 million, which corresponds to option A.
Verification:
This can also be calculated as an annuity:
PV of annuity = $65 million × [1 - (1.15)⁻³] / 0.15 = $65 million × 2.2832 = $148.41 million
NPV = $148.41 million - $100 million = $48.41 million ≈ $48 million
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An analyst gathers the following information about a project:
| Initial outlay | $100 million |
|---|---|
| Cash flow at end of Year 1 | $65 million |
| Cash flow at end of Year 2 | $65 million |
| Cash flow at end of Year 3 | $65 million |
If the required rate of return is 15%, the NPV is closest to:
A
$48 million.
B
$95 million.
C
$148 million.