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 50 percent chance you will sell 12,000 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 25 percent chance that you will only sell 2,000 and also a 25 percent chance you will sell 17,000. The gas skateboards would sell for $130 each and have a variable cost of ​$50 each. Regardless of how many you​ sell, the annual fixed costs associated with production would be $160,000. In​ addition, there would be an initial expenditure of $1,100,000 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 8 percent? What would the​ project's NPV be if 12,000 skateboards were​ sold?

Answer 1

Answer a

Initial Outlay = Initial Expenditure+Investment on Working Capital = 1100000+60000 = $1,160,000

Answer b

Annual Fixed cost =$160,000

If Sales is 12000

Variable cost = 50*12000=$600,000

Sales = 130*12000=$1,560,000

Depreciation =1,100,000/10 = 110,000

Income Before tax = Sales - (Fixed+ Variable cost+Depreciation) = 1560000-(160000+600000+110000) = 1560000-870000=$690000

Profit After tax = 690000*(1-31%) = 690000*0.69 = $476100

Annual Free cashflow = Profit after tax+ Depreciation = 476100+110000=$586100

If Sales is 2000

Variable cost = 50*2000=$100,000

Sales = 130*2000=$260,000

Depreciation =1,100,000/10 = 110,000

Income Before tax = Sales - (Fixed+ Variable cost+Depreciation) = 260000-(160000+100000+110000) = 260000-370000=-$110000

Profit After tax = -$110000 (TAx will be 0 for losses)

Annual Free cashflow = Profit after tax+ Depreciation = -110000+110000=$0

If Sales is 17000

Variable cost = 50*17000=$850,000

Sales = 130*17000=$2,210,000

Depreciation =1,100,000/10 = 110,000

Income Before tax = Sales - (Fixed+ Variable cost+Depreciation) = 2210000-(160000+850000+110000) = 2210000-1120000=-$1090000

Profit After tax = 1090000*(1-31%) = 1090000*0.69 = $752100

Annual Free cashflow = Profit after tax+ Depreciation = 752100+110000=$862100

Expected Sales = 12000*50%+2000*25%+17000*25% = 6000+500+4250=10750

Variable cost = 50*10750=$537500

Sales = 130*10750=$1397500

Depreciation =1,100,000/10 = 110,000

Income Before tax = Sales - (Fixed+ Variable cost+Depreciation) = 1397500-(160000+537500+110000) = 1397500-807500=-$590000

Profit After tax = 590000*(1-31%) = 590000*0.69 = $407100

Expected Annual Free cashflow = Profit after tax+ Depreciation = 407100+110000=$517100

Answer c

In terminal cashflow, free cashflow + release of working capital

If Sales is 12000

Terminal Cashflow= 586100+60000=$646,100

If Sales is 2000

Terminal cashflow= 0+60000=$60000

If Sales is 17000

Terminal Cashflow= 862100+60000=$922100

Answer d

Expected cashflow for year 1 to 9=$517100

Expected Terminal Cashflow at year 10 = 517100+60000=577100

PV for year 1 to 9= 517100*(1-(1+8%)^-9)/8%

= 517100*(1-(1.08^-9)/0.08

=517100*(1-0.50025)/0.08

=517100*0.49975/0.08

=$3230265.74

PV of terminal flow = 577100/(1+8%)^10 = 577100/1.08^10=577100/2.1589=267308.96

NPV = -1160000+3230265.74+267308.96 = 2337574.70

Hence NPV =$2,337,574.70

If sales were 12000

Expected cashflow for year 1 to 9=$586100

Expected Terminal Cashflow at year 10 = 586100+60000=646100

PV for year 1 to 9= 517100*(1-(1+8%)^-9)/8%

= 586100*(1-(1.08^-9)/0.08

=586100*(1-0.50025)/0.08

=586100*0.49975/0.08

=$3661293.44

PV of terminal flow = 646100/(1+8%)^10 = 646100/1.08^10=646100/2.1589=$299272.78

NPV = -1160000+3661293.44+299272.78 = 2800566.22

Hence NPV =$2,800,566.22