Question

Jones Corp is evaluating a project that has the following annual free cash flows:

Period

0
0

1
1

2
2

Free Cash Flow

−
200
−200

150
150

−
70
−70

If the project's discount rate is
12
%
12%, then what is the NPV of the project?


−
119.94
−119.94



−
136.29
−136.29



−
121.875
−121.875

Answer 1

To calculate the Net Present Value (NPV) of the project, you will use the formula for NPV, which is:

\[
\text{NPV} = \sum \frac{CF_t}{(1 + r)^t} - \text{Initial Investment}
\]

where:

- \( CF_t \) = Cash Flow at time \( t \)
- \( r \) = discount rate
- \( t \) = time period

In this case, the cash flows are as follows:

- Year 0: -200
- Year 1: 150
- Year 2: -70

We are also given a discount rate of 12%, or 0.12 in decimal.

Calculating NPV step by step:

1. **Cash flow in Year 0**:
\[
CF_0 = -200
\]

2. **Cash flow in Year 1**:
\[
CF_1 = \frac{150}{(1 + 0.12)^1} = \frac{150}{1.12} \approx 133.93
\]

3. **Cash flow in Year 2**:
\[
CF_2 = \frac{-70}{(1 + 0.12)^2} = \frac{-70}{1.2544} \approx -55.78
\]

Now, plug these values into the NPV formula:

\[
\text{NPV} = (-200) + 133.93 - 55.78
\]
\[
\text{NPV} = -200 + 133.93 - 55.78
\]
\[
\text{NPV} = -200 + 78.15
\]
\[
\text{NPV} = -121.85
\]

So the NPV is approximately \(-121.85\).

Among the provided choices, the closest answer is:
- **−121.875**

Hence, the correct answer is **−121.875**.