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 a70percent chance you will sell 8,000 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 5,000 and also a 15 percent chance you will sell 15,000.

The gas skateboards would sell for $100 each and have a variable cost of $50 each. Regardless of how many you​ sell, the annual fixed costs associated with production would be $140,000. In​ addition, there would be an initial expenditure of ​$1,100,000 associated with the purchase of new production equipment which will be depreciated using the bonus depreciation method in year 1. 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 $30,000 in net working​ capital, and​ working-capital investment will be recovered when the project is shut down.​ Finally, assume that the​ firm's marginal tax rate is 22 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, and 2 through 9 under each sales​ forecast? What are the expected annual free cash flows for year​ 1, and years 2 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 12 ​percent? What would the​ project's NPV be if 8,000 skateboards were​ sold?

Answer 1

		Present Value(PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=discount rate=Required Return =12%=0.12
	a	Initial Outlay
	A	Production Equipment	$1,100,000
	B	Investment in Net working Capital	$30,000
	C=A+B	Initial Outlay Associated with the project	$1,130,000
	b		Sales Forecast	Sales Forecast	Sales Forecast
	D	Sales Forecast	8,000	5,000	15,000
		Cash Flow in Year 1:
	E=D*($100-$50)	Contribution Margin	$400,000	$250,000	$750,000
	F	Fixed Costs	-$140,000	-$140,000	-$140,000
	G	Depreciation	-$1,100,000	-$1,100,000	-$1,100,000
	H=E+F+G	Operating Income Before tax	-$840,000	-$990,000	-$490,000
	I=H*(1-0.22)	After Tax Operating Income	-$655,200	-$772,200	-$382,200
	J	Add: Depreciation (Non cash expense)	$1,100,000	$1,100,000	$1,100,000
	K=I+J	Operating Cash Flow	$444,800	$327,800	$717,800
		Probability of Cash Flow	0.70	0.15	0.15	SUM
		Cash Flow*Probability	$311,360	$49,170	$107,670	$468,200
		Expected Cash Flow in Year1	$468,200
		Cash Flow in Year 2-9
	D	Sales Forecast	8,000	5,000	15,000
	E=D*($100-$50)	Contribution Margin	$400,000	$250,000	$750,000
	F	Fixed Costs	-$140,000	-$140,000	-$140,000
	H=E+F	Operating Income Before tax	$260,000	$110,000	$610,000
	I=H*(1-0.22)	After Tax Operating Income	$202,800	$85,800	$475,800
	K	Operating Cash Flow	$202,800	$85,800	$475,800
		Probability of cash flow	0.70	0.15	0.15	SUM
		Cash Flow*Probability	$141,960	$12,870	$71,370	$226,200
		Expected Cash Flow in Year2-9	$226,200
	c	Terminal Cash Flow in Year10
	K	Operating Cash Flow	$202,800	$85,800	$475,800
	L	Release of net working capital	$30,000	$30,000	$30,000
	M	Terminal Cash Flow in Year10	$232,800	$115,800	$505,800
		Probability of Cash Flow	0.70	0.15	0.15	SUM
		Cash Flow*Probability	$162,960	$17,370	$75,870	$256,200
		Expected Cash Flow in Year10	$256,200
							8,000 $400,000 $140,000 $260,000 $202,800 $202,800 0.70 $141,960 $226,200 5,000 $250.00 $140,000 $110,000 $85,800 $85,800 0.15 $12,870 15,000 $750,000 $140,000 $610,000 $475,800 $475,800 0.15 SUM $71,370 $226,200 Cash Flow in Year 2- Sales Forecast E=D*($100-$50) Contribution Margin Fixed Costs HEE+F Operating Income Before tax I=H*(1-0.22) After Tax Operating Income Operating Cash Flow Probability of cash flow Cash Flow* Probability Expected Cash Flow in Year2-9 Terminal Cash Flow in Year10 Operating Cash Flow Release of net working capital Terminal Cash Flow in Year10 Probability of Cash Flow Cash Flow* Probability Expected Cash Flow in Year10 N Year Expected Cash Flow PV=CF/(1.124N) Present Valure NPV=Sum of PV Net Present Value $202,800 $30,000 $232,800 0.70 $162,960 $256,200 $85,800 $30,000 $115,800 0.15 $17,370 $475,800 $30,000 $505,800 0.15 SUM $75,870 $256,200 10 $1,130,000 $1,130,000 $373,811 $468,200 S418,036 $226,200 $180,325 $226,200 $161,005 $226,200 $143,754 $226,200 $128,352 $226,200 $114,600 $226,200 $102,321 $226,200 $91,358 $226,200 $81,570 $256,200 SUM $82,490 $373,811 NPV if 8000 Skateboards were sold: Year Net Cash Flow PV=CF/(1.124N) Present Valure NPV=Sum of PV Net Present Value $1,130,000 $1,130,000 $241,596 $444,800 $397,1431 $202,800 $161,671 $202,800 $144,349 $202,800 $128,883 $202,800 $115,074 $202,800 $102,745 $202,800 $91,736 $202,800 $81,908 $202,800 $73,132 10 $232,800 SUM $74,955 $241,596