We are evaluating a project that costs $832,000, has an eight-year life, and has

Question

We are evaluating a project that costs $832,000, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 40,000 units per year. Price per unit is $40, variable cost per unit is $15, and fixed costs are $700,000 per year. The tax rate is 35 percent, and we require a 18 percent return on this project. a-1 Calculate the accounting break-even point. Break-even point units a-2 What is the degree of operating leverage at the accountin g break-even point? (Round your answer to 3 decimal places. (e.g., 32.161)) DOL b-1 Calculate the base-case cash flow and NPV. (Round your NPV answer to 2 decimal places. (e.g., 32.16)) Cash flow NPV b-2 What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161)) c. What is the sensitivity of OCF to changes in the variable cost figure? (Negative amount should be indicated by a minus sign.)

Explanation / Answer

Solution:

a-1.To calculate the accounting breakeven OCF, we first need to find the depreciation for each year. The depreciation is:

Depreciation = $832,000 / 8

Depreciation = $104,000 per year

And the accounting breakeven is:

QA= ($700,000 + 104,000) / ($40 – 15)

QA= 32,160 units

a-2: To calculate the accounting breakeven, we must realize at this point (and only this point), the OCF isequal to depreciation. So, the DOL at the accounting breakeven is:

DOL = 1 + FC / OCF

= 1 + FC / DDOL

= 1 + ($700,000 / $104,000)

DOL = 7.731

b-1. We will use the tax shield approach to calculate the OCF. The OCF is:

OCFbase= [(P – v)Q – FC](1 –TC) +TCD

OCFbase= [($40 – 15)(40,000) – $700,000](1 .35) + .35($104,000)

OCFbase= $231,400

Now we can calculate the NPV using our base-case projections. There is no salvage value or NWC, sothe NPV is:

NPVbase= –$832,000 + $231,400(PVIFA18%,8)

NPVbase= $111,548.72

b-2 To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the NPV at adifferent quantity. We will use sales of 45,000 units. The NPV at this sales level is:

OCFnew= [($40 – 15)(45,000) – $700,000](1 .35) + .35($104,000)

OCFnew= $312,650

And the NPV is:

NPVnew= –$832,000 + $312,650(PVIFA18%,8)

NPVnew= $442,850.93

So, the change in NPV for every unit change in sales is:

NPV/S = ($111,548.72 – 442,850.93) / (40,000 – 45,000)

NPV/S = +$66.26

c.To find out how sensitive OCF is to a change in variable costs, we will compute the OCF at a variablecost of $16. Again, the number we choose to use here is irrelevant: We will get the same ratio of OCF toa one dollar change in variable cost no matter what variable cost we use. So, using the tax shieldapproach, the OCF at a variable cost of $16 is:

OCFnew= [($40 – 16)(40,000) – 700,000](1 – .35) + .35($104,000)

OCFnew= $205,400

So, the change in OCF for a $1 change in variable costs is:

OCF/VC = ($231,400 – 205,400) / ($15 – 16)

OCF/VC = –$26,000

If variable costs decrease by $1 then, OCF would increase by $26,000

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