Question

Dixie Chicken is considering installing a new Coke Freestyle machine in one of its franchise stores. The machine will cost $7,219.00 today, and have an annual operational cost of $1,181.00. The machine will increase store revenues by $2,669.00 in the first year. The owner expects that the additional revenues will increase by 5.00% per year going forward. The operational cost will remain at $1,181.00 per year. Dixie Chicken has a 15.00% cost of capital and will value this opportunity over 7.00 years. What is the NPV of the new freestyle machine?

Answer 1

What values do I enter for F0, C1, C2, C3, C4, C5, C5, C7 and I to solve this with a finance calculator?

Answer 2

To calculate the Net Present Value (NPV) of the new Coke Freestyle machine, we need to follow these steps:

1. **Calculate the annual cash flows:** The first-year cash flow is the increase in revenue minus the operational cost. The subsequent years will have revenue that increases by 5% per year.

2. **Discount the cash flows:** We will discount each cash flow back to its present value using the company's cost of capital.

3. **Subtract the initial investment:** Finally, we subtract the initial cost of the machine from the total present value of the cash flows to find the NPV.

### Step 1: Calculate Annual Cash Flows

- **Year 1 Revenue Increase:**
Revenue for Year 1 = $2,669.00

- **Operation Cost:**
Operating Cost = $1,181.00

- **Net Cash Flow for Year 1:**
\[
\text{Net Cash Flow Year 1} = \text{Revenue} - \text{Operational Cost} = 2669 - 1181 = 1488
\]

- **Subsequent Years Revenue Calculation:** The revenue increase grows at 5% annually.

- **Year 2 Revenue Increase:**
\[
\text{Year 2 Revenue} = 2669 \times 1.05 = 2802.45
\]
\[
\text{Net Cash Flow Year 2} = 2802.45 - 1181 = 1621.45
\]

- **Year 3 Revenue Increase:**
\[
\text{Year 3 Revenue} = 2802.45 \times 1.05 = 2942.57
\]
\[
\text{Net Cash Flow Year 3} = 2942.57 - 1181 = 1761.57
\]

- **Year 4 Revenue Increase:**
\[
\text{Year 4 Revenue} = 2942.57 \times 1.05 = 3084.71
\]
\[
\text{Net Cash Flow Year 4} = 3084.71 - 1181 = 1903.71
\]

- **Year 5 Revenue Increase:**
\[
\text{Year 5 Revenue} = 3084.71 \times 1.05 = 3238.95
\]
\[
\text{Net Cash Flow Year 5} = 3238.95 - 1181 = 2057.95
\]

- **Year 6 Revenue Increase:**
\[
\text{Year 6 Revenue} = 3238.95 \times 1.05 = 3399.90
\]
\[
\text{Net Cash Flow Year 6} = 3399.90 - 1181 = 2218.90
\]

- **Year 7 Revenue Increase:**
\[
\text{Year 7 Revenue} = 3399.90 \times 1.05 = 3569.89
\]
\[
\text{Net Cash Flow Year 7} = 3569.89 - 1181 = 2388.89
\]

### Summarized Cash Flows

- Year 1: $1,488.00
- Year 2: $1,621.45
- Year 3: $1,761.57
- Year 4: $1,903.71
- Year 5: $2,057.95
- Year 6: $2,218.90
- Year 7: $2,388.89

### Step 2: Discount the Cash Flows

The formula for the present value (PV) of each cash flow is:
\[
PV = \frac{CF}{(1 + r)^n}
\]
Where:
- \( CF \) = Cash Flow in the year
- \( r \) = discount rate (15% or 0.15)
- \( n \) = year

Now, we will calculate the present value for each year's cash flow.

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

### Present Value of Cash Flows
1. Year 1:
\[
PV = \frac{1488}{(1 + 0.15)^1} = \frac{1488}{1.15} \approx 1290.09
\]

2. Year 2:
\[
PV = \frac{1621.45}{(1 + 0.15)^2} = \frac{1621.45}{1.3225} \approx 1225.38
\]

3. Year 3:
\[
PV = \frac{1761.57}{(1 + 0.15)^3} = \frac{1761.57}{1.520875} \approx 1157.67
\]

4. Year 4:
\[
PV = \frac{1903.71}{(1 + 0.15)^4} = \frac{1903.71}{1.74901} \approx 1088.09
\]

5. Year 5:
\[
PV = \frac{2057.95}{(1 + 0.15)^5} = \frac{2057.95}{2.011357} \approx 1023.76
\]

6. Year 6:
\[
PV = \frac{2218.90}{(1 + 0.15)^6} = \frac{2218.90}{2.313217} \approx 958.42
\]

7. Year 7:
\[
PV = \frac{2388.89}{(1 + 0.15)^7} = \frac{2388.89}{2.659981} \approx 896.21
\]

### Total Present Value
Now we sum all the present values calculated:
\[
Total PV = 1290.09 + 1225.38 + 1157.67 + 1088.09 + 1023.76 + 958.42 + 896.21 \approx 6889.62
\]

### NPV Calculation
Finally, we subtract the initial investment from the total present value:
\[
NPV = Total PV - Initial Investment
\]
\[
NPV = 6889.62 - 7219 \approx -329.38
\]

### Conclusion
The NPV of installing the new Coke Freestyle machine is approximately **-$329.38**. Therefore, at a 15% cost of capital, the investment does not seem profitable over the 7-year horizon.

Answer 3

To solve the Net Present Value (NPV) of the Coke Freestyle machine investment using a financial calculator, you can use the cash flow inputs as follows:

### Cash Flow Inputs:
- **F0 (Initial Investment, CF0)**: This is the initial cash outflow for the investment. Enter this as a negative value since it's an outgoing cash flow.
- **F0 = -7219.00**

- **C1 (Cash Flow for Year 1, CF1)**: The cash flow for Year 1.
- **C1 = 1488.00**

- **C2 (Cash Flow for Year 2, CF2)**: The cash flow for Year 2.
- **C2 = 1621.45**

- **C3 (Cash Flow for Year 3, CF3)**: The cash flow for Year 3.
- **C3 = 1761.57**

- **C4 (Cash Flow for Year 4, CF4)**: The cash flow for Year 4.
- **C4 = 1903.71**

- **C5 (Cash Flow for Year 5, CF5)**: The cash flow for Year 5.
- **C5 = 2057.95**

- **C6 (Cash Flow for Year 6, CF6)**: The cash flow for Year 6.
- **C6 = 2218.90**

- **C7 (Cash Flow for Year 7, CF7)**: The cash flow for Year 7.
- **C7 = 2388.89**

### Interest Rate:
- **I (Discount Rate or Cost of Capital)**: The annual discount rate, which in this case is 15.00%.
- **I = 15% (0.15 in decimal form)**

### Summary for Input in a Financial Calculator:
- **F0** = -7219.00
- **C1** = 1488.00
- **C2** = 1621.45
- **C3** = 1761.57
- **C4** = 1903.71
- **C5** = 2057.95
- **C6** = 2218.90
- **C7** = 2388.89
- **I** = 15%

### Calculation Process on a Financial Calculator:
1. Enter **F0** as -7219.00.
2. Enter **C1** through **C7** with their respective values.
3. Set the interest rate **I** to 15%.
4. Calculate the NPV using the financial calculator's NPV function.

This will give you the NPV directly, which should confirm the calculated NPV of approximately -$329.38.