Question

6.1     You and your friends are thinking about starting a motorcycle company named Apple Valley Choppers. Your initial investment would be $500,000 for depreciable equipment, which should last five years, and your tax rate would be 40%. You could sell a chopper for $10,000, assuming your average variable cost per chopper is $3000, and assuming fixed costs, such as rent, utilities, and salaries, would be $200,000 per year.

1. Accounting breakeven: How many choppers would you have to sell for net income to equal zero, ignoring the costs of financing?                                                            (1 mark)
2. Financial breakeven: How many choppers would you have to sell to generate NPV of zero, if you required a 15% return? (Hint: Use the 15% as the discount rate and calculate net present value. In Excel, you may want to use the Goal Seek command, or simply use trial and error to find the correct amount.)
3. Assuming you could sell 60 choppers per year, what would be your IRR?       
4. Assuming you could sell 60 choppers per year, what would your selling price have to be to generate a net present value of $150,000 at a 15% discount rate?                       
5. If you could sell 60 choppers in the first year, and your sales volume increased by 5% each year until the end of year five, what would the net present value be at a 15% discount rate?        
6. If, at the beginning of each year, you expect to need working capital equal to 10% of the next (coming) year’s sales revenue, what would be the effect on the net present value of the project? Only changes in the amount of working capital require cash flows. Assume a sales price of $10,000 per chopper and a sales quantity of 60 choppers.                                                                     

Remember that any money invested in working capital (i.e., inventory, accounts receivable, accounts payable) would usually be recovered in its entirety at the end of the project.

Do you think that the need for working capital always reduces the net present value of projects? Can you think of circumstances where working capital could increase the NPV of a project? (Hint: Think of airline tickets purchased in advance.)

Answer 1

(a) Accounting Breakeven:

=2000000/(10000-3000)= 28.57 i.e 29 Choppers.

(b)Finacail breakeven:

Financial break even:
(4200 * x - 160000) * PVIFA(15%,5) = 500000
(4200 * x - 160000) * 5 * 3.3522 = 500000
x = 73.6 = 74 choppers

(c)

cash flow at 60 choppers per year = 4200 * 60 - 160000 = 92000
For IRR 92000 * PVIFA(IRR%,5) = 500000

IRR = -2.72%

(d)

let us assume that x be the selling price
operating cash flow per year = ( 60 * x - 3000*60 -200000) * (1-0.4) + 100000 * 0.4
= 36*x - 188000
NPV =-500000 + (36*x - 188000) * PVIFA(15%,5) = 150000
-500000 + (36*x - 188000) * 3.3522 = 150000
selling price x = 10608.4

(e)cash flow year 1 = 4200 *60 - 160000 = 92000
cash flow year2 = 4200 *63 - 160000 = 104600
cash flow year3 = 4200 *66 - 160000 = 117200
cash flow year4 = 4200 *69 - 160000 = 129800
cash flow year5 = 4200 *73 - 160000 = 146600
NPV = -500000 + 92000/1.15 + 104600/1.15^2 + 117200/1.15^3 + 129800/1.15^4 +
146600/1.15^5
= - 116746.79