Question

Consider a project to supply Detroit with 27,000 tons of machine screws annually for automobile production. You will need an initial $4,600,000 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 $1,100,000 and that variable costs should be $205 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 $475,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $308 per ton. The engineering department estimates you will need an initial networking capital investment of $440,000. You require a return of 12 percent and face a tax rate of 23 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 Minimum level of output

Answer 1

Solution:

a. Using the tax shield approach, the OCF is

$OCF = [(P - VC)Q_{C} - FC](1 - t)+t*D$

OCF = [(308 - 205) (27,000) - 1,100,000] (1 - 0.23)] + 0.23 (4,600,000/5)

OCF = 1,371,490

To calculate the sensitivity to changes in quantity sold, we will choose a quantity of 28,000. The OCF at this level of sale is

$OCF = [(P - VC)Q_{C} - FC](1 - t)+t*D$

OCF = [(308 - 205) (28,000) - 1,100,000] (1 - 0.23)] + 0.23 (4,600,000/5)

OCF = 1,442,560

The sensitivity of changes in quantity sold is

$\Delta OCF/\Delta Q$ = (1,371,490 - 1,442,560)/(27,000 - 28,000)

$\Delta OCF/\Delta Q$ = +71.07

----------------------------------------------------------------------------------------------------------------------------------------------------

b. The NPV is calculated using the following equation

$NPV = - Initial Investment - NWC + (P - VC)Q (PVIFA @ i, n) + [NWC + SV(1 - t)](PVIF @ i, n)$

$NPV$ = -4,600,000 - 440,000 + [(308 - 205) (27,000)] (PVIFA @ 12%, 5) + [440,000 + (475,000) (1 - 0.23)] (PVIF @ 12%, 5)

NPV = -5,040,000 + 2,781,000 (PVIFA @ 12%, 5) + 805,750 (PVIF @ 12%, 5)

NPV = -5,040,000 + 2,781,000 (3.60478) + 805,750 (0.56743)

NPV = $5,442,087

At Q = 28,000, the NPV is

$NPV$ = -4,600,000 - 440,000 + [(308 - 205) (28,000)] (PVIFA @ 12%, 5) + [440,000 + (475,000) (1 - 0.23)] (PVIF @ 12%, 5)

NPV = -5,040,000 + 2,884,000 (PVIFA @ 12%, 5) + 805,750 (PVIF @ 12%, 5)

NPV = -5,040,000 + 2,884,000 (3.60478) + 805,750 (0.56743)

NPV = $5,813,379

The sensitivity of NPV to changes in quantity sold is

$\Delta NPV /\Delta Q$ = (5,442,087 - 5,813,379)/(27,000 - 28,000)

$\Delta NPV /\Delta Q$ = + 371.29

----------------------------------------------------------------------------------------------------------------------------------------------------

c. We know that quantity will not fall below the point where NPV is zero. Therefore,

5,442,087 = 371.29 Q

Q = 14,657

For zero, we need to decrease the sales by 14,657

Minimum level of output = 27,000 - 14,657 = 12,343