Project L requires an initial outlay at T equals 0 of $45,000. Expected cash inflows are $15,000 per year for 9 years and WACC is 11%. What is the project’s NPV?
The correct answer and explanation is :
To calculate the Net Present Value (NPV) of Project L, we can use the formula for NPV:
[
NPV = \sum \frac{C_t}{(1 + r)^t} – C_0
]
Where:
- ( C_t ) represents the cash inflows at time ( t ),
- ( r ) is the discount rate (in this case, WACC = 11% or 0.11),
- ( t ) is the time period (1 to 9 years),
- ( C_0 ) is the initial investment (in this case, $45,000).
Step-by-Step Calculation:
- Initial Outlay (C₀):
The initial investment is $45,000, which is the amount spent at ( t = 0 ). - Cash Inflows (Cₜ):
Expected cash inflows of $15,000 per year for 9 years. - Discount Rate (r):
The WACC is 11%, or 0.11. - Formula for NPV:
Since the cash inflows are the same every year (an annuity), we can use the formula for the NPV of an annuity: [
NPV = C_0 – \left[ \text{Annuity Factor} \times \text{Annual Cash Flow} \right]
] The annuity factor is given by the following formula: [
\text{Annuity Factor} = \frac{1 – (1 + r)^{-n}}{r}
] Where:
- ( r = 0.11 ),
- ( n = 9 ) (years).
Calculation of Annuity Factor:
[
\text{Annuity Factor} = \frac{1 – (1 + 0.11)^{-9}}{0.11} = \frac{1 – (1.11)^{-9}}{0.11} = \frac{1 – 0.42257}{0.11} = \frac{0.57743}{0.11} = 5.231
]
Now, calculate the NPV:
[
NPV = 15,000 \times 5.231 – 45,000
]
[
NPV = 78,465 – 45,000 = 33,465
]
Conclusion:
The NPV of the project is $33,465.
Explanation:
The NPV is a measure of the value created by a project or investment. A positive NPV indicates that the project is expected to generate more cash than it costs, making it a worthwhile investment. In this case, the NPV of $33,465 suggests that Project L will create value for the company, as the future cash inflows, discounted at the WACC of 11%, exceed the initial investment of $45,000.