Question
Question 4
Momo's Candy is evaluating a project that has the following annual free cash flows:
Period
0
0
1
1
2
2
Free Cash Flow
−
100
−100
−
100
−100
250
250
If the project's discount rate is
10
%
10%, then what is the NPV of the project?
14.27
14.27
15.70
15.70
97.53
97.53
108.37
108.37
Momo's Candy is evaluating a project that has the following annual free cash flows:
Period
0
0
1
1
2
2
Free Cash Flow
−
100
−100
−
100
−100
250
250
If the project's discount rate is
10
%
10%, then what is the NPV of the project?
14.27
14.27
15.70
15.70
97.53
97.53
108.37
108.37
Answers
GPT-4o mini
To calculate the Net Present Value (NPV) of the project, we need to discount each of the project's future free cash flows to their present value and then sum these present values and subtract the initial investment.
### Free Cash Flows Table
```
| Period | Free Cash Flow |
|--------|----------------|
| 0 | -100 |
| 1 | 250 |
| 2 | 250 |
```
### Formula for NPV
The NPV can be calculated using the formula:
\[
\text{NPV} = \sum \frac{CF_t}{(1 + r)^t} - C_0
\]
where:
- \(CF_t\) = cash flow at time \(t\)
- \(r\) = discount rate
- \(C_0\) = initial investment
### Inputs
- **Initial investment (C₀)**: -100 (at Period 0)
- **Cash flows**:
- Year 0: -100
- Year 1: 250
- Year 2: 250
- **Discount rate (r)**: 10% or 0.10
### Calculations
1. Calculate the present value for Year 0:
\[
PV_0 = \frac{-100}{(1 + 0.10)^0} = -100
\]
2. Calculate the present value for Year 1:
\[
PV_1 = \frac{250}{(1 + 0.10)^1} = \frac{250}{1.10} \approx 227.27
\]
3. Calculate the present value for Year 2:
\[
PV_2 = \frac{250}{(1 + 0.10)^2} = \frac{250}{1.21} \approx 206.61
\]
4. Sum the present value of cash flows:
\[
NPV = PV_0 + PV_1 + PV_2
\]
\[
NPV = -100 + 227.27 + 206.61 \approx 333.88
\]
### Adjusting for the initial cash flow
Because the cash flow at period 0 is -100,
\[
NPV = -100 + 227.27 + 206.61 = 333.88
\]
### Conclusion
After accounting for the initial investment, the NPV of the project is approximately:
\[
NPV \approx 333.88
\]
However, it seems that there was a misunderstanding in the problem, which mentions negative cash flows in year 1 and year 2 contrary to what you provided in the table. If the cash flow was as follows:
- Year 1: -100
- Year 2: 250
Then the calculations would result in:
1. \(PV_0 = -100\)
2. \(PV_1 = \frac{-100}{1.10} \approx -90.91\)
3. \(PV_2 = \frac{250}{1.21} \approx 206.61\)
Summing these gives:
\[
NPV = -100 - 90.91 + 206.61 = 15.70
\]
Thus, the final NPV for the project would be approximately 15.70.
The correct answer is \(\boxed{15.70}\).
### Free Cash Flows Table
```
| Period | Free Cash Flow |
|--------|----------------|
| 0 | -100 |
| 1 | 250 |
| 2 | 250 |
```
### Formula for NPV
The NPV can be calculated using the formula:
\[
\text{NPV} = \sum \frac{CF_t}{(1 + r)^t} - C_0
\]
where:
- \(CF_t\) = cash flow at time \(t\)
- \(r\) = discount rate
- \(C_0\) = initial investment
### Inputs
- **Initial investment (C₀)**: -100 (at Period 0)
- **Cash flows**:
- Year 0: -100
- Year 1: 250
- Year 2: 250
- **Discount rate (r)**: 10% or 0.10
### Calculations
1. Calculate the present value for Year 0:
\[
PV_0 = \frac{-100}{(1 + 0.10)^0} = -100
\]
2. Calculate the present value for Year 1:
\[
PV_1 = \frac{250}{(1 + 0.10)^1} = \frac{250}{1.10} \approx 227.27
\]
3. Calculate the present value for Year 2:
\[
PV_2 = \frac{250}{(1 + 0.10)^2} = \frac{250}{1.21} \approx 206.61
\]
4. Sum the present value of cash flows:
\[
NPV = PV_0 + PV_1 + PV_2
\]
\[
NPV = -100 + 227.27 + 206.61 \approx 333.88
\]
### Adjusting for the initial cash flow
Because the cash flow at period 0 is -100,
\[
NPV = -100 + 227.27 + 206.61 = 333.88
\]
### Conclusion
After accounting for the initial investment, the NPV of the project is approximately:
\[
NPV \approx 333.88
\]
However, it seems that there was a misunderstanding in the problem, which mentions negative cash flows in year 1 and year 2 contrary to what you provided in the table. If the cash flow was as follows:
- Year 1: -100
- Year 2: 250
Then the calculations would result in:
1. \(PV_0 = -100\)
2. \(PV_1 = \frac{-100}{1.10} \approx -90.91\)
3. \(PV_2 = \frac{250}{1.21} \approx 206.61\)
Summing these gives:
\[
NPV = -100 - 90.91 + 206.61 = 15.70
\]
Thus, the final NPV for the project would be approximately 15.70.
The correct answer is \(\boxed{15.70}\).