You and your friends are thinking about starting a motorcycle company named Appl

Question

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 5 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. A. Accounting breakeven: How many choppers would you have to sell to break even, ignoring the costs of financing? B. Financial breakeven: How many choppers would you have to sell to break even, if you required a 15% return? (Hint: Use the 15% as the discount rate and calculate net present value. C. Assuming you could sell 60 choppers per year, what would be your IRR? D. 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? E. If you could sell 60 choppers in the first year, and your sales volume increased by 5% each year until the end of year 5, what would the net present value be at a 15% discount rate? F. If you need to invest 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? Do you think that working capital investments always reduce the net present value of projects? (Assume a 15% discount rate, and sales volume increases by 5% each year.)

Explanation / Answer

A) Accounting break even = Fixed costs/contribution per unit = (200000 +100000 - depreciation)/(10000 - 3000) = 300000/7000 = 42.86 = 43 Choppers

B) Financial break even:

For financial break-even the NPV should be zero.

Hence, [x*7000*0.6 - 200000*0.6 + 100000*0.4]*pvifa(15,5) - 500000 = 0, where x is the no of choppers.

x*4200*3.3522 - 120000*3.3522 + 40000*3.3522 - 500000 = 0

x*14079.24 = 402264 - 134088 + 500000; x = 768176/14079.24 = 54.56 = 55 Choppers.

C) IRR with 60 choppers:

Annual cash flows = 60*7000*0.6 -200000*.06 + 100000*0.4 = $172,000

IRR is that discount rate for which PV of 172000 equals 500000

Therefore, 172000*pvifa(i,5) = 500000

pvifa(i,5) = 2.9070

for i = 21% factor is 2.9260

for i = 22% factor is 2.8636

so i for 2.9070 = 22 - (2.9070-2.8636)/(2.9260-2.8636) = 21.304487 = 21.30%

D) Selling price for 60 choppers to get NPV of $150000:

[(60*p - 180000 - 200000)*0.6 + 100000*0.4]*pvifa(15,5) -500000 = 150000, where 'p' is the price to be charged.

[(60*p - 180000 - 200000)*0.6 + 40000]*3.3522 = 650000

[(60*p - 180000 - 200000)*0.6 + 40000] = 650000/3.3522

36p - 228000 + 40000 = 193902.51

36p = 381902.51

p = $10608.40 (price to be charged per unit to get NPV of $150,000.

E)

Sales in units 60 63 66 69 73 contribution 420000 441000 462000 483000 511000 depn 100000 100000 100000 100000 100000 other 200000 200000 200000 200000 200000 PBT 120000 141000 162000 183000 211000 tax 40% 48000 56400 64800 73200 84400 PAT 72000 84600 97200 109800 126600 depn 100000 100000 100000 100000 100000 CFAT 172000 184600 197200 209800 226600 pvif @ 15% 0.8696 0.7561 0.6575 0.5718 0.4972 pv 149565 139584 129662 119954 112660 PV of cash inflows-Yrs 1 to 5 651426 Less: initial investment 500000 NPV 151426

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