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 60 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 20 percent chance that you will only sell 4,000 and also a 20 percent chance you will sell 14,000. The gas skateboards would sell for $120 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 $40,000 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 35 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 9 ​percent? What would the​project's NPV be if 10,000 skateboards were​ sold?

Answer 1

Calculation of expected annual sales units: Probability adjusted No. of units Probability Units 10,000 0.6 6,000 4,000 0.2 800 14,000 0.2 2,800 Total 9,600 Therefore, total expected sale (no. of units)= 9,600 units Solution (a) Calculation of initial outlay associated with the project: Purchase of new equipment Investment in net working capital Total initial outlay 12,00,000 40,000 12,40,000

Case 2 4,000 120 40 80 Case 3 14,000 120 40 80 Solution (b) Calculation of annual cash flows of the project for years 1 to 9 under different sales scenarios Case 1 No. of units sold 10,000 Selling price per unit 120 Variable cost per unit 40 Contribution per unit (selling price less variable cost) 80 Contribution for the year (contribution per unit* No. of units, i.e. 8,00,000 (10,000*80; 4,000*80; 14,000*80)] Fixed costs per year 1,30,000 Depreciation per year [Initial equipment price/10, i.e. 12,00,000/10) 1,20,000 Profit before tax (Contribution-fixed costs-depreciation) 5,50,000 Tax @ 35% (Profit before tax*35%) 1,92,500 Profit after tax (Profit before tax less taxes) 3,57,500 Free cash flow (Profit after taxes + Depreciation) 4,77,500 3,20,000 11,20,000 1,30,000 1,20,000 70,000 24,500 45,500 1,30,000 1,20,000 8,70,000 3,04,500 5,65,500 6,85,500 Calculation of expected annual cash flows of the project for years 1 to 9 9600 units 120 40 80 No. of units expected to be sold (as calculated at the top) Selling price per unit Variable cost per unit Contribution per unit (selling price less variable cost) Contribution for the year (contribution per unit* No. of units, i.e. 9,600*80] Fixed costs per year Depreciation per year [Initial equipment price/10, i.e. 12,00,000/10] Profit before tax (Contribution-fixed costs-depreciation) Tax @ 35% (Profit before tax*35%) Profit after tax (Profit before tax less taxes) Free cash flow (Profit after taxes + Depreciation) 7,68,000 1,30,000 1,20,000 5,18,000 1,81,300 3,36,700 4,56,700

Solution (c) Calculation of free cash flow in year 10 under different sales forecasts: Annual cash flow from operations (As calculated in (b) above) Recovery of working capital investment Total free cash flow for year 10 Case 1 4,77,500 40,000 5,17,500 Case 2 1,65,500 40,000 2,05,500 Case 3 6,85,500 40,000 7,25,500 Year 1 4,56,700 Year 2 4,56,700 Year 3 4,56,700 Year 4 4,56,700 Year 5 4,56,700 Year 6 | Year 7 | Year 8 | Year 9 | Year 10 4,56,700 4,56,700 4,56,700 4,56,700 4,56,700 Solution (d) Calculation of NPV of the project based on expected sales forecasts Year 0 (today) Expected annual cash flow from operations (As calculated in (b) above) Initial cash outlay (as calculated in (a) above) (12,40,000) Recovery of working capital investment Total free cash flow for the year (12,40,000) Present value factor @9% 1.00 Discounted FCF (12,40,000) Total NPV is sum of discounted FCF for all years and comes out to be $17,07,841 4,56,700 0.92 4,18,991 4,56,700 0.84 3,84,395 4,56,700 0.77 3,52,656 4,56,700 0.71 3,23,538 4,56,700 0.65 2,96,824 4,56,700 0.60 2,72,315 4,56,700 4,56,700 4,56,700 0.55 0.50 0.46 2,49,831 2,29,202 2,10,277 40,000 4,96,700 0.42 2,09,811 Calculation of NPV of the project based on sales of 10,000 units Year 0 (today) l Year 1 4,77,500 Year 2 4,77,500 Year 3 4,77,500 Year 4 4,77,500 Year 5 4,77,500 Year 6 4,77,500 | Year 7 4,77,500 | Year 8 4,77,500 | Year 9 4,77,500 Year 10 4,77,500 (12,40,000) Expected annual cash flow from operations (As calculated in (b) above) Initial cash outlay (as calculated in (a) above) Recovery of working capital investment Total free cash flow for the year 40,000 5,17,500 (12,40,000) 4,77,500 4,77,500 4,77,500 4,77,500 4,77,500 4,77,500 4,77,500 4,77,500 4,77,500 Present value factor @9% 1.00 Discounted FCF (12,40,000) Total NPV is sum of discounted FCF for all years and comes out to be $18,41,328 0.92 4,38,073 0.84 4,01,902 0.77 3,68,718 0.71 3,38,273 0.65 3,10,342 0.60 2,84,718 0.55 2,61,209 0.50 2,39,641 0.46 2,19,854 0.42 2,18,598