Question

To solve the bid price problem presented in the text, we set the project NPV equal to zero and found the required price using the definition of OCF. Thus the bid price represents a financial break-even level for the project. This type of analysis can be extended to many other types of problems.

Martin Enterprises needs someone to supply it with 125,000 cartons of machine screws per year to support its manufacturing needs over the next five years, and you’ve decided to bid on the contract. It will cost you $910,000 to install the equipment necessary to start production; you’ll depreciate this cost straight-line to zero over the project’s life. You estimate that, in five years, this equipment can be salvaged for $85,000. Your fixed production costs will be $485,000 per year, and your variable production costs should be $17.35 per carton. You also need an initial investment in net working capital of $90,000. Assume your tax rate is 21 percent and you require a 12 percent return on your investment.

a.	Assuming that the price per carton is $26, what is the NPV of this project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	Assuming that the price per carton is $26, find the quantity of cartons per year you need to supply to break even. (Do not round intermediate calculations and round your answer to nearest whole number.)
c.	Assuming that the price per carton is $26, find the highest level of fixed costs you could afford each year and still break even. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

PVA _{12%, n=5} = [ { 1 - ( 1 / 1.12 ) ⁵ } / 0.12 ] = 3.60478

PV _{12%, n= 5} = ( 1 / 1.12 ) ⁵ = 0.56743

Initial investment = Cost of Equipment + Working Capital = $ 910,000 + $ 90,000 = $ 1,000,000.

Annual depreciation = $ 910,000 / 5 = $ 182,000

Salvage value after taxes = $ 85,000 * ( 1 - 0.21 ) = $ 67,150.

a. NPV: $ 924,932.87

Contribution margin per unit = $ 26 - $ 17.35 = $ 8.65

Total contribution margin = 125,000 x $ 8.65 = $ 1,081,250

EBITDA = $ 1,081,250 - $ 485,000 = $ 596,250.

Operating cash flows after taxes = EBITDA * ( 1 - t ) + Depreciation * t = $ 596,250 x 0.79 + $ 182,000 x 0.21 = 471,037.50 + 38,220 = $ 509,257.50

Present value of cash inflows = 509,257.50 x 3.60478 + $ ( 67,150 + 90,000 ) * 0.56743 = 1,835,761.25 + 89,171.62 = $ 1,924,932.87

NPV = $ 1,924,932.87 - $ 1,000,000 = $ 924,932.87

b. 87,452 units

Let the break-even number of cartons be Q.

Annual operating cash flows after taxes = [ (8.65 Q - 485,000 ) * 0.79 + 38,220 = 6.8335 Q - 383,150 + 38,220 = 6.8335Q - 344,930

Present value of cash inflows = ( 6.8335 Q - 344,930) * 3.60478 + 89,171.62 = 24.63326 Q - 1,243,396.77 + 89,171.62 = 24.63326 Q - 1,154,225.15

At break-even, NPV = 0

24.63326 Q = 1,000,000 + 1,154,225.15

or Q = 87,451.89 units

c. $ 809,791.28

Let the highest fixed costs be F.

Operating cash flows after taxes = [ ( 1,081,250 - F ) * 0.79 + 38,220 ] = 892,407.50 - 0.79 F

Present value of cash inflows = ( 892,407.50 - 0.79 F ) * 3.60478 + 89,171.62 = 3,306,104.33 - 2.8477762F

At break-even, NPV = 0

2.8477762 F = 2,306,104.33

F = $ 809,791.28