Question

Daily Enterprises is purchasing a $10.55 million machine. It will cost $58,505.00 to transport and install the machine. The machine has a depreciable life of five years using the straight-line depreciation and will have no salvage value. The machine will generate incremental revenues of $4.26 million per year along with incremental costs of $1.40 million per year. Daily’s marginal tax rate is 38.00%.

The cost of capital for the firm is 14.00%.

(answer in dollars..so convert millions to dollars)

The project will run for 5 years. What is the NPV of the project at the current cost of capital?

Answer 1

What value do I enter for F0,C1, C2, C3, C4, C5 and I to solve with a calculator?

Answer 2

To calculate the NPV (Net Present Value) of the project, we'll follow these steps:

1. **Calculate Initial Investment**:
- Cost of the machine = $10.55 million
- Transport and installation cost = $58,505.00
- Total Initial Investment = Cost of the machine + Transport and installation cost
\[
\text{Total Initial Investment} = 10,550,000 + 58,505 = 10,608,505
\]

2. **Calculate Annual Depreciation**:
- Depreciable life = 5 years
- Salvage value = $0
- Annual Depreciation = Initial Investment / Depreciable Life
\[
\text{Annual Depreciation} = \frac{10,608,505}{5} = 2,121,701
\]

3. **Calculate Annual Operating Cash Flow**:
- Incremental Revenues = $4.26 million = $4,260,000
- Incremental Costs = $1.40 million = $1,400,000
- Operating Income (EBIT) = Incremental Revenues - Incremental Costs - Depreciation
\[
\text{Operating Income (EBIT)} = 4,260,000 - 1,400,000 - 2,121,701 = 738,299
\]
- Tax (38%) = EBIT * Tax Rate
\[
\text{Tax} = 738,299 \times 0.38 = 280,561.62
\]
- Net Income = EBIT - Tax
\[
\text{Net Income} = 738,299 - 280,561.62 = 457,737.38
\]
- Operating Cash Flow = Net Income + Depreciation
\[
\text{Operating Cash Flow} = 457,737.38 + 2,121,701 = 2,579,438.38
\]

4. **Calculate NPV**:
- NPV Formula:
\[
\text{NPV} = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t} - \text{Initial Investment}
\]
where \( CF_t \) is the cash flow for each year, \( r \) is the cost of capital, and \( n \) is the project duration (5 years).
- Cost of Capital (r) = 14% = 0.14
- Annual Cash Flow (CF) = $2,579,438.38 (from above)
- We will sum the present values of the cash flows for 5 years.
- Present Value of Cash Flows:
\[
\text{PV} = CF \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)
\]
\[
\text{PV} = 2,579,438.38 \times \left( \frac{1 - (1 + 0.14)^{-5}}{0.14} \right)
\]
- First, calculate \( (1 + 0.14)^{-5} \):
\[
(1 + 0.14)^{-5} \approx 0.5432
\]
- Now calculate the fraction:
\[
\frac{1 - 0.5432}{0.14} \approx 3.246
\]
- Now, calculate the PV of cash flows:
\[
\text{PV} = 2,579,438.38 \times 3.246 \approx 8,379,208.89
\]

5. **Final NPV Calculation**:
\[
\text{NPV} = PV - \text{Initial Investment}
\]
\[
\text{NPV} = 8,379,208.89 - 10,608,505 \approx -2,229,296.11
\]

Thus, the **NPV of the project** at the current cost of capital is approximately **-$2,229,296.11**.

Answer 3

To use a financial calculator or Excel to calculate the NPV based on the values provided, you will enter the values as follows:

1. **F0**: This is the initial investment (cash outflow), which is a negative value since it is an expense.
- **F0 = -10,608,505**

2. **C1, C2, C3, C4, C5**: These represent the cash inflows for each of the 5 years.
- Since the operating cash flow from Year 1 to Year 5 is $2,579,438.38, you will enter this value for each cash flow from Year 1 to Year 5:
- **C1 = 2,579,438.38**
- **C2 = 2,579,438.38**
- **C3 = 2,579,438.38**
- **C4 = 2,579,438.38**
- **C5 = 2,579,438.38**

3. **I**: This is the interest or discount rate (cost of capital) used to discount the future cash flows. You will enter this as a percentage.
- **I = 14% or 0.14**

### Summary of Inputs:
- **F0 = -10,608,505** (Initial Investment)
- **C1 = 2,579,438.38**
- **C2 = 2,579,438.38**
- **C3 = 2,579,438.38**
- **C4 = 2,579,438.38**
- **C5 = 2,579,438.38**
- **I = 0.14 (or 14%)**

### Steps to Calculate NPV:
1. Enter the values into your financial calculator.
2. Ensure the initial outflow (F0) is entered as a negative number.
3. Input the cash inflows (C1 to C5) as positive numbers.
4. Input the interest rate (I) as a percentage.
5. Use the NPV function to compute the result.

The calculation will produce an NPV result, which should be consistent with our earlier calculation of approximately **-$2,229,296.11**.