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 comma 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 4 comma 000 and also a 25 percent chance you will sell 17 comma 000. The gas skateboards would sell for $ 120 each and have a variable cost of ​$30 each. Regardless of how many you​ sell, the annual fixed costs associated with production would be ​$150 comma 000. In​ addition, there would be an initial expenditure of ​$800 comma 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 comma 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 12 ​percent? What would the​ project's NPV be if 12 comma 000 skateboards were​ sold?

Answer 1

Part 1)

The initial outlay associated with the project is calculated as below:

Initial Outlay = -Cost of New Equipment - Initial Working Capital = -800,000 - 40,000 = -$840,000

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Part 2)

The annual cash flows associated with each sales forecast is calculated as below:

	Sales Forecast (Year 1 to Year 9)
Sales in Units	12,000	4,000	17,000
Total Sales Value (Sales in Units*120)	1,440,000	480,000	2,040,000
Less Variable Costs (Sales in Units*30)	360,000	120,000	510,000
Fixed Costs	150,000	150,000	150,000
Depreciation Expense (800,000/10)	80,000	80,000	80,000
EBT	850,000	130,000	1,300,000
Less Taxes	297,500	45,500	455,000
EAT	552,500	84,500	845,000
Add Depreciation Expense	80,000	80,000	80,000
Annual Free Cash Flow	$632,500	$164,500	$925,000

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The expected annual cash flows for years 1 through​ 9 is arrived as follows:

Expected Sales in Units (50%*12,000 + 25%*4,000 + 25%*17,000)	11,250
Total Sales Value (Sales in Units*120)	1,350,000
Less Variable Costs (Sales in Units*30)	337,500
Fixed Costs	150,000
Depreciation Expense	80,000
EBT	782,500
Less Taxes	273,875
EAT	508,625
Add Depreciation Expense	80,000
Expected Annual Free Cash Flow	$588,625

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Part 3)

The value of terminal cash flow in Year 10 is determined as follows:

Terminal Cash Flow in Year 10 = Expected Annual Free Cash Flow + Recovery of Working Capital = 588,625 + 40,000 = $628,625

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Part 4)

The formula for calculating NPV is given as below:

NPV = Cash Flow Year 0 + Cash Flow Year 1/(1+Required Rate of Return)^1 + Cash Flow Year 2/(1+Required Rate of Return)^2 + Cash Flow Year 3/(1+Required Rate of Return)^3 + Cash Flow Year 4/(1+Required Rate of Return)^4 + Cash Flow Year 5/(1+Required Rate of Return)^5 + Cash Flow Year 6/(1+Required Rate of Return)^6 + Cash Flow Year 7/(1+Required Rate of Return)^7 + Cash Flow Year 8/(1+Required Rate of Return)^8 + Cash Flow Year 9/(1+Required Rate of Return)^9 + Cash Flow Year 10/(1+Required Rate of Return)^10

Substituting values in the above formula, we get,

NPV = -840,000 + 588,625/(1+12%)^1 + 588,625/(1+12%)^2 + 588,625/(1+12%)^3 + 588,625/(1+12%)^4 + 588,625/(1+12%)^5 + 588,625/(1+12%)^6 + 588,625/(1+12%)^7 + 588,625/(1+12%)^8 + 588,625/(1+12%)^9 + 628,625/(1+12%)^10 = $2,498,741.46

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Part 5)

The NPV if 12,000 stakeboards (using the same formula as in Part 4) were sold is calculated as follows:

NPV = -840,000 + 632,500/(1+12%)^1 + 632,500/(1+12%)^2 + 632,500/(1+12%)^3 + 632,500/(1+12%)^4 + 632,500/(1+12%)^5 + 632,500/(1+12%)^6 + 632,500/(1+12%)^7 + 632,500/(1+12%)^8 + 632,500/(1+12%)^9 + (632,500 + 40,000)/(1+12%)^10 = $2,746,645