Question

The technique for calculating a bid price can be extended to many other types of problems. Answer the following questions using the same technique as setting a bid price; that is, set the project NPV to zero and solve for the variable in question. Guthrie Enterprises needs someone to supply it with 146,000 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 $1,860,000 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 $156,000. Your fixed production costs will be $271,000 per year, and your variable production costs should be $10.00 per carton. You also need an initial investment in net working capital of $136,000. The tax rate is 21 percent and you require a return of 12 percent on your investment. Assume that the price per carton is $16.60.

  

a.	Calculate the project NPV. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b.	What is the minimum number of cartons per year that can be supplied and still break even? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

c.	What is the highest fixed costs that could be incurred and still break even? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a. NPV : $ 405,080.50

b. Minimum number of cartons : 124,448 cartons.

c. Highest fixed costs that can be afforded :$ 413,243.71

Workings:

a. Initial investment = Cost of the equipment + Working Capital = $ 1,860,000 + $ 136,000 = $ 1,996,000..............(1 )

Contribution margin per carton = $ 16.60 - $ 10.00 = $ 6.60

Annual EBITDA = Total Contribution Margin - Fixed Costs ( excluding depreciation ) = 146,000 x $ 6.60 - $ 271,000 = $ 692,600

Annual depreciation = $ 1,860,000 / 5 = $ 372,000

Annual Operating Cash Flows after Taxes ( OCFAT ) = EBITDA x ( 1 - T ) + Depreciation x T = $ 692,600 x 0.79 + $ 372,000 x 0.21 = $ 547,154 + $ 78,120 = $ 625,274.....................................( 2 )

Salvage value of equipment after taxes = $ 156,000 x 0.79 = $ 123,240

Terminal Cash Flows = Salvage Value after Taxes + Working Capital recovered = $ 123,240 + $ 136,000 = $ 259,240...... ( 3 )

PVA _{12 %, n= 5} = [ { 1 - ( 1 / 1.12 ) ⁵ } / 0.12 ] = 3.6048

PV _{12%, n=5} = ( 1 / 1.12 ) ⁵ = 0.5674

NPV = 625,274 x 3.6048 + 259,240 x 0.5674 - 1,996,000 = 2,253,987.72 + 147,092.78 - 1,996,000 = $ 405,080.50

b. Let the number of cartons be Q.

EBITDA = 6.60 Q - 271,000.

OCFAT = ( 6.60 Q - 271,000 ) x 0.79 + 78,120 = 5,214 Q - 135,970

At break-even, NPV = 0.

(5,214 Q - 135,970) x 3.6048 + 147,092.78 = 1,996,000

or 18.7954272 Q - 490,144.66 + 147,092.78 = 1,996,000

Break-even quantity = 124,447.92 cartons

c. Let the maximum fixed cost be C.

EBITDA = ( 146,000 x $ 6.60 - C ) = ( 963,600 - C)

OCFAT = ( 963,600 - C ) 0.79 + $ 78,120 = 761,244 - 0.79 C + 78,120 = 839,364 - 0.79 C

At break-even,

( 839,364 - 0.79 C ) x 3.6048 + 147,092.78 = 1,996,000.

or 3,025,739.35 - 2.847792 C + 147,092.78 = 1,996,000

or C = $ 413,243.71