Question

​(Calculating free cash flows​) At​ present, Solartech Skateboards is considering expanding its product line to include​ gas-powered skateboards;​ however, it is questionable how well they will be received by skateboarders. Although you feel there is a 40 percent chance you will sell 10,000 of these per year for 10 years​ (after which time this project is expected to shut down because​ solar-powered skateboards will become more​ popular), you also recognize that there is a 30 percent chance that you will only sell 1,000 and also a 30 percent chance you will sell 17,000. The gas skateboards would sell for $100 each and have a variable cost of $40 each. Regardless of how many you​ sell, the annual fixed costs associated with production would be $130,000. In​ addition, there would be an initial expenditure of $1,200,000 associated with the purchase of new production equipment. It is assumed that this initial expenditure will be depreciated using the simplified​ straight-line method down to zero over 10 years. Because of the number of stores that will need​ inventory, the working capital requirements are the same regardless of the level of sales. This project will require a​ one-time initial investment of $60,000 in net working​ capital, and that​ working-capital investment will be recovered when the project is shut down.​ Finally, assume that the​ firm's marginal tax rate is 31 percent.

a. What is the initial outlay associated with the​ project?

b. What are the annual free cash flows associated with the project for years 1 through 9 under each sales​ forecast? What are the expected annual free cash flows for years 1 through​ 9?

c. What is the terminal cash flow in year 10​ (that is, what is the free cash flow in year 10 plus any additional cash flows associated with the termination of the​ project)?

d. Using the expected free cash​ flows, what is the​ project's NPV given a required rate of return of 11 ​percent? What would the​ project's NPV be if 10,000 skateboards were​ sold?

***PLEASE, be as detailed as possible, I couldn't figure this problem out so please only answer if you know how to do this!***

Answer 1

a). Initial outlay (Year 0 cash flow) = initial investment in equipment + initial investment in net working capital

= 1,200,000 + 60,000 = 1,260,000

b). Free Cash Flow (FCF) = EBIT*(1-Tax rate) + (Depreciation*Tax rate)

Number of units sold = sum of probability weighted numbers = (40%*10,000) + (30%*1,000) + (30%*10,000) = 9,400

EBIT = Number of units sold*(price per unit - variable cost per unit) - fixed cost

= 9,400*(100-40) - 130,000 = 434,000

Depreciation = initial investment in equipment/life of project = 1,200,000/10 = 120,000

FCF = 434,000*(1-31%) + (120,000*31%) = 336,660 (FCF from Year 1 to Year 9)

c). Terminal value in Year 10 = FCF + return of net working capital = 336,660 + 60,000 = 396,660

d). NPV = -initial outlay + Present Value (PV) of FCFs from Year 1 to Year 9 + PV of Terminal value in Year 10

Present Value (PV) of FCFs from Year 1 to Year 9: PMT = 336,660; N = 9; rate = 11%, solve for PV.

PV = 1,864,102.42

PV of Terminal value in Year 10 = 396,660/(1+11%)^10 = 139,697.50

NPV = -1,260,000 + 1,864,102.42 + 139,697.50 = 743,799.92

If 10,000 skateboards are sold then FCF = (10,000*(100-40)-130,000)*(1-31%) + (120,000*31%) = 361,500

Terminal value = 361,500 + 60,000 = 421,500

PV of FCFs: PMT = 361,500; N = 9; rate = 11%, solve for PV. PV = 2,001,642.68

PV of Terminal value = 421,500/(1+11%)^10 = 148,445.76

NPV = -1,260,000 + 2,001,642.68 + 148,445.76 = 890,088.44