Question

Consider a project to supply Detroit with 25,000 tons of machine screws annually for automobile production. You will need an initial $4,500,000 investment in threading equipment to get the project started; the project will last for 5 years. The accounting department estimates that annual fixed costs will be $1,075,000 and that variable costs should be $200 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the 5-year project life. It also estimates a salvage value of $450,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $302 per ton. The engineering department estimates you will need an initial net working capital investment of $430,000. You require a return of 11 percent and face a tax rate of 22 percent on this project. a. Suppose you're confident about your own projections, but you're a little unsure about Detroit's actual machine screw requirement. What is the sensitivity of the project OCF to changes in the quantity supplied? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the sensitivity of NPV to changes in quantity supplied? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. Given the sensitivity number you calculated, what is the minimum level of output below which you wouldn't want to operate? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32) AOCFIAQ b. ANPVIAQ c. Minimum level of output

Answer 1

a) OCF = [(SP- VC)*Q - FC] (1-t)+ t*(initial investment / life) = [(302-200)*25000 - 1,075,000] (1-0.22) + 0.22*4,500.000 / 5 = $1,348,000

Changing quantity to 26000

OCF = [(SP- VC)*Q - FC] (1-t)+ t*(initial investment / life) = [(302-200)*26000 - 1,075,000] (1-0.22) + 0.22*4,500.000 / 5 = $1,428,060

$\Delta$OCF = 1428060-134800 = 79,560

$\Delta$OCF / $\Delta$Q = 79560/1000 = 79.56

b) NPV at 25000 Qty

NPV = -4,500,000 - 430,000 + 1,348,000 PVIF 11%,5 + (430,000 + 450,000 (1-0.22))/1.12^5 = $517,402

NPV at 26000

NPV = -4,500,000 - 430,000 + 1,428,060 PVIF 11%,5 + (430,000 + 450,000 (1-0.22))/1.12^5 = $811,448

$\Delta$ NPV = $811,448 - $517,402 = $294,045

$\Delta$ NPV / $\Delta$ Q = $294,045 / 1000 = 294.045

c) Break even point

Sensitivity for NPV is 294.045

The fall in quantity where NPV is 0 will be

NPV at 25000 = NPV sensitivity*Q fall

517402 = 294.045*Q

Q = 1759.6 = 1760

Min Q =25000-1760 = 23240