Question

Martin Enterprises needs someone to supply it with 133,000 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 $950,000 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 $109,000. Your fixed production costs will be $525,000 per year, and your variable production costs should be $18.15 per carton. You also need an initial investment in net working capital of $106,000. If your tax rate is 23 percent and you require a return of 11 percent on your investment.

A. Assuming the price per carton is $27.60, what is the NPV of this project?

B. Assuming the price per carton is $27.60, find the quantity of cartons per year you can supply and still break even.

C. Assuming the price per carton is $27.60, find the highest level of fixed costs you could afford each year and still break even.

Answer 1

A. NPV of the project : $ 1,300,964.49

B. Break-even number of cartons : 84,624.81 cartons

C. Highest level of fixed costs : $ 982,145.56

Computations :

PVA _{11 %, n = 5} = [ { 1 - ( 1 / ( 1.11 ) ⁵ } / 0.11 ] = 3.6959

PV _{11 %, n= 5} = ( 1 / 1.11 ) ⁵ = 0.5935

A. NPV =

Contribution margin per carton = $ 27.60 - $ 18.15 = $ 9.45

Total contribution margin = 133,000 x $ 9.45 = $ 1,256,850

EBITDA = $ 1,256,850 - $ 525,000 = $ 731,850

Annual depreciation = $ 950,000 / 5 = $ 190,000

Annual operating cash flows after taxes = $ 731,850 x 0.77 + $ 190,000 x 0.23 = $ 563,524.50 + $ 43,700 = $ 607,224.50

Present value of cash inflows = 607,224.50 x 3.6959 + 109,000 x 0.77 x 0.5935 + 106,000 x 0.5935 = 2,356,964.49

NPV = $ 2,356,964.49 - $ 1,056,000 = $ 1,300,964.49

B. Let the break-even number of cartons be Q.

[( 9.45 Q - 525,000) x 0.77 + 43,700 ] x 3.6959 + 112,723.46 = 1,056,000

( 7.2765 Q - 404,250 + 43,700 ) x 3.6959 = 255,222.42

7.2765 Q = 615,772.42

Q = 84,624.81 units

C. Let the amount of fixed cost be F

[ (1,256,850 - F ) x 0.77 + 43,700 ] x 3.6959 + 112,723.46 = 1,056,000

or ( 967,774.50 - 0.77F + 43,700 ) = 255,222.42

F = $ 982,145.56