Question

a firm is considering investing in a new project with an upfront cost of $17 million. the project will generate an incremental free cash flow of $10 million in the first year and this cash flow is expected to grow at an annual rate of 4% forever. the firm's wacc is 12%. the project has similar risk to the firm. what is the value of this project (in million)?

Answer 1

To calculate the value of the project, you need to find the present value of all the future cash flows generated by the project, including the initial investment. We can use the formula for the present value of a growing perpetuity to calculate the present value of the cash flows beyond the first year:

PV = CF1 / (r - g)

where:

PV is the present value
CF1 is the cash flow in the first year
r is the discount rate (the firm's WACC)
g is the growth rate of the cash flows
In this case:

CF1 = $10 million
r = 12%
g = 4%
So the present value of the cash flows beyond the first year is:

PV = $10 million / (12% - 4%) = $125 million

To calculate the total value of the project, we need to add the initial investment of $17 million to the present value of the cash flows beyond the first year:

Total value = $17 million + $125 million = $142 million

Therefore, the value of the project is $142 million (in million).