Consider a project to supply Detroit with 40,000 tons of machine screws annually

ID: 2725827 • Letter: C

Question

Consider a project to supply Detroit with 40,000 tons of machine screws annually for automobile production. You will need an initial $5,400,000 investment in threading equipment to get the project started; the project will last for six years. The accounting department estimates that annual fixed costs will be $800,000 and that variable costs should be $350 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the six-year project life. It also estimates a salvage value of $280,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $450 per ton. The engineering department estimates you will need an initial net working capital investment of $520,000. You require a return of 16 percent and face a marginal tax rate of 30 percent on this project.

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 final answer to 2 decimal places, e.g., 32.16.)

What is the sensitivity of NPV to changes in quantity supplied? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)

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 final answer to the nearest whole number, e.g., 32)

Explanation / Answer

a. quantity*(selling price - variable costs) = 40,000*(450 - 350) = $4,000,000

less: annual fixed costs = - 800,000. = 4,000,000 - 800,000 = $3,200,000. This is the income from the project. Net income = 3,200,000*(1-tax rate) = 3,200,000*(1-30%) = $2,240,000

depreciation tax shield: depreciation per year = 5,400,000/6 = 900,000. tax shield on depreciation = depreciation*tax rate = 900,000*30% = 270,000

Thus operating cash flow = 2,240,000+270,000 = $2,510,000. This is when quantity is 40,000 tons. Now suppose quantity is increased by 1 to make in 40,001 tons. Situation will then be:

Thus OCF is increasing by $70. If Quantity is decreased by 1 ton, OCF also decreases by 1 ton. Thus the sensitivity = $70 to i ton change in quantity.

b. salvage value = 280,000. after tax proceeds = 280,000*(1-30%) = 196,000

Formulas used in the below table: (i) discount factor = 1+discount rate (ii) PV = Cash flow/(discount factor)^time (iii) NPV = sum of all PVs

Now, if Q is increased by 1 ton to 40,001, NPV will become = 3,409,391.74. Thus sensitivity = 3,409,391.74 - 3,409,133.81 = $257.93

NPV for 40,001 tons:

c. We will want to operate till NPV is in the positive zone. Once it becomes negative, we will not want to operate. NPV is 53 at 26,783 units and becomes negative at 26,782 tons. Thus, the minimum level of output = 26,783 tons.

Quantity 40,001 Sales - variable costs 100 Quantity*(sales-variable costs) 4,000,100 Less: fixed costs -800,000 Income 3,200,100 Income after tax 2,240,070 Tax shield on depreciation 270,000 OCF 2,510,070

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Consider a project to supply Detroit with 40,000 tons of machine screws annually

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Consider a project to supply Detroit with 40,000 tons of machine screws annually

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