An investment project has an installed cost of $516,358. The cash flows over the 4-year life of the investment are projected to be $272,499, $203,496, $103,802, and $91,614, respectively. What is the NPV of this project if the discount rate is zero percent? (round answer to nearest dollar)
The correct answer and explanation is:
Let’s analyze the problem step-by-step:
Given Data:
- Installed cost (initial investment): $516,358
- Cash flows over 4 years:
- Year 1: $272,499
- Year 2: $203,496
- Year 3: $103,802
- Year 4: $91,614
- Discount rate: 0%
What is NPV?
Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. The formula for NPV is: NPV=∑t=1nCFt(1+r)t−Initial InvestmentNPV = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t} – \text{Initial Investment}
where:
- CFtCF_t = cash flow at time tt
- rr = discount rate
- nn = number of periods
Since the discount rate is 0%, the present value of each cash flow is simply the cash flow itself because:
CFt(1+0)t=CFt\frac{CF_t}{(1 + 0)^t} = CF_t
Calculate the total cash inflows:
272,499+203,496+103,802+91,614=671,411272,499 + 203,496 + 103,802 + 91,614 = 671,411
Calculate NPV:
NPV=Total cash inflows−Initial investment=671,411−516,358=155,053NPV = \text{Total cash inflows} – \text{Initial investment} = 671,411 – 516,358 = 155,053
Final answer:
155,053\boxed{155,053}
Explanation:
When the discount rate is zero, it means money today and money in the future have the same value — no interest or opportunity cost is considered. So, the NPV calculation simplifies to just summing all future cash inflows and subtracting the initial cost.
Here, the project’s cash inflows total $671,411 over four years, and the initial cost is $516,358. This means the project is expected to generate $155,053 more than the initial investment in nominal terms.
A positive NPV, like this one, indicates that the investment is financially viable and profitable under these assumptions. However, in real life, discounting is crucial because future money is worth less than money today due to risks, inflation, and opportunity cost.
If the discount rate were higher than zero, the future cash flows would be worth less in today’s dollars, and the NPV might be lower. But at zero percent, you treat all future cash flows as having full value, making this a straightforward calculation.
In conclusion, the project’s NPV is $155,053, meaning it adds this amount of value beyond the initial investment with no discounting applied.