A company is planning to open 100 new outlets that are expected to generate, in total, $15 million in free cash flows per year, with a growth rate of 3% in perpetuity.
If the company’s WACC is 10%, what is the NPV of this expansion?
To calculate the NPV (Net Present Value) of the expansion, we need to discount the future cash flows of the 100 new outlets to their present value.
The formula to calculate NPV is:
NPV = CF0 + Σ (CFT / (1 + r)^t)
Where:
NPV = Net Present Value
CF0 = Initial cash flow (negative if it's an investment)
CFT = Cash flow in a given year
r = Discount rate (WACC)
t = Time period (number of years)
In this case, the initial cash flow (CF0) is the cost of opening 100 new outlets, which is not provided in the question. Therefore, we cannot calculate the NPV without that information.
If we assume that the initial cost is zero, we can calculate the NPV for the cash flows generated by the new outlets.
Let's assume that the cash flows generated by each outlet are equal and evenly distributed. Therefore, the cash flow per outlet per year would be $15 million / 100 outlets = $150,000.
Let's plug in the values into the formula and calculate the NPV:
NPV = 0 + Σ ($150,000 / (1 + 0.10)^t)
Since the cash flows are in perpetuity (ongoing indefinitely), we need to calculate the sum of the cash flows for all future years (t).
To calculate the sum, we can use the formula for the sum of an infinite geometric series:
Sum = a / (1 - r)
Where:
a = First term of the series ($150,000)
r = Growth rate (3%)
Sum = $150,000 / (1 - 0.03)
Once we have the sum, we can substitute it into the NPV formula to calculate the present value of the cash flows.
NPV = 0 + ($150,000 / (1 + 0.10)) * (1 / (1 - 0.03))
Now, all we need to do is calculate the NPV using the formulas above. If you provide the initial cost or any additional information, I can help you calculate the exact NPV.