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

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 2

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

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.