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 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 2020 percent chance that you will only sell 2,000 and also a 20 percent chance you will sell 14,000. The gas skateboards would sell for $100 each and have a variable cost of ​$45 each. Regardless of how many you​ sell, the annual fixed costs associated with production would be ​150,000. In​ addition, there would be an initial expenditure of ​1,000,000 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 $30,000 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 12,000 skateboards were​ sold?

Answer 1

Initial investment	-1000000
Initial NWC	-30000
Initial outlay associated with the project	-1030000

b.Annual free cash flows associated with the project for years 1 through 9 under each sales​ forecast
Probable sales	12000*60%	2000*20%	14000*20%
	7200	400	2800	12000
1.Sales $ at $ 100 /unit	720000	40000	280000	1200000
2.Less: Variable cost at $ 45 /unit	324000	18000	126000	540000
3.Less: Fixed cost	150000	150000	150000	150000
4.Less: Depn.(1000000/10)	100000	100000	100000	100000
5.EBT(1-2-3-4)	146000	-228000	-96000	410000
6.Less: Tax at 31%	45260	-70680	-29760	127100
7.EAT	100740	-157320	-66240	282900
8.Add Back: depn.	100000	100000	100000	100000
9.Opg. Cash flows/FCFs (7+8)	200740	-57320	33760	382900
Expected annual free cash flows for years 1 through​ 9
(200740*60%)+(-57320*20%)+(33760*20%)=
115732

c. Terminal cash flow in year 10​ (that is, free cash flow in year 10 plus any additional cash flows associated with the termination of the​ project
Expected annual free cash flows as above	115732
NWC recovered	30000
Total FCF in Yr.10	145732

d.NPV of the project using the expected free cash flows at 11% discount rate
-1030000+(115732*5.53705)+(145732*0.35218)=
-337862
NOTE: P/A & PV factors
(1-1.11^-9)/0.11= 5.53705
1/1.11^10=0.35218

If 12000 nos were sold (refer last column in Table)
NPV will be
-1030000+(382900*5.53705)+((382900+30000)*0.35218)=
1235552