Final answer:
The NPV of the coffee company's expansion is calculated using the perpetuity formula with a positive result of $189.67 million, indicating a profitable investment.
Step-by-step explanation:
To determine the net present value (NPV) of the coffee company's expansion involving the opening of 105 new coffee outlets, we need to use the perpetuity formula since the cash flows are expected to grow at a constant rate forever. The formula for the present value of a growing perpetuity is PV = C / (r - g), where PV is the present value, C is the initial cash flow, r is the discount rate (WACC in this case), and g is the growth rate. Given the parameters: initial cash flow (C) of $14.6 million, a discount rate (r) of 10.1%, and a growth rate (g) of 2.6%, the calculation would be:
PV = $14.6 million / (0.101 - 0.026) = $14.6 million / 0.075 = $194.67 million (rounded to two decimal places).
Since the present value of the free cash flows (FCF) is given as $5 million, the NPV of the expansion project would be calculated by subtracting the initial cash outlay from the present value of the cash inflows:
NPV = PV - Initial Investment
NPV = $194.67 million - $5 million = $189.67 million (rounded to two decimal places). The NPV of the expansion is positive, suggesting that it is a profitable venture for the company.