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 70 percent chance you will sell 9,000 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 15 percent chance that you will only sell 4,000 and also a 15 percent chance you will sell 16,000. The gas skateboards would sell for $ 140 each and have a variable cost of ​$50 each. Regardless of how many you​ sell, the annual fixed costs associated with production would be ​$120,000. In​ addition, there would be an initial expenditure of ​$800,000 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 $ 70,000 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 9,000 skateboards were​ sold?

Answer 1

a]	Cost of new production equipment	$      8,00,000
	Initial NWC	$          70,000
	Initial outlay	$      8,70,000
b]	Expected sale - 9000 units:	Years 1-9
	Sales	$    12,60,000
	-Variable cost	$      4,50,000
	-Fixed costs	$      1,20,000
	-Depreciation [800000/10]	$          80,000
	=EBIT	$      6,10,000
	-Tax at 35%	$      2,13,500
	=NOI	$      3,96,500
	+ Depreciation	$          80,000
	=Annual FCF [Years 1 through 9]	$      4,76,500
	Expected sale - 4000 units:	Years 1-9
	Sales	$      5,60,000
	-Variable cost	$      2,00,000
	-Fixed costs	$      1,20,000
	-Depreciation [800000/10]	$          80,000
	=EBIT	$      1,60,000
	-Tax at 35%	$          56,000
	=NOI	$      1,04,000
	+ Depreciation	$          80,000
	=Annual FCF [Years 1 through 9]	$      1,84,000
	Expected sale - 16000 units:	Years 1-9
	Sales	$    22,40,000
	-Variable cost	$      8,00,000
	-Fixed costs	$      1,20,000
	-Depreciation [800000/10]	$          80,000
	=EBIT	$    12,40,000
	-Tax at 35%	$      4,34,000
	=NOI	$      8,06,000
	+ Depreciation	$          80,000
	=Annual FCF [Years 1 through 9]	$      8,86,000
	EXPECTED ANNUAL FCF - t1 TO t9 = 476500*70%+184000*15%+886000*15% =	$      4,94,050
c]	Expected FCF Year 10	$      4,94,050
	Recapture of NWC	$          70,000
	Terminal cash flow in Year 10	$      5,64,050
d]	PV of expected FCF [t1 to t9] = 494050*(1.09^9-1)/(0.09*1.09^9) =	$    29,61,952
	PV of terminal cash flow = 564050/1.09^10 =	$      2,38,261
	PV of cash inflows	$    32,00,213
	Less: Initial outlay	$      8,70,000
	NPV	$    23,30,213
	NPV FOR 9000 UNITS:
	PV of expected FCF [t1 to t9] = 476500*(1.09^9-1)/(0.09*1.09^9) =	$    28,56,735
	PV of terminal cash flow = (476500+70000)/1.09^10 =	$      2,30,848
	PV of cash inflows	$    30,87,583
	Less: Initial outlay	$      6,10,000
	NPV	$    24,77,583