We are evaluating a project that costs $690,000, has a five-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 71,000 units per year. Price per unit is $75, variable cost per unit is $50, and fixed costs are $790,000 per year. The tax rate is 35 percent, and we require a 15 percent return on this project.

We are evaluating a project that costs $690,000, has a five-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 71,000 units per year. Price per unit is $75, variable cost per unit is $50, and fixed costs are $790,000 per year. The tax rate is 35 percent, and we require a 15 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))

ΔNPV/ΔQ

$

  

c.	What is the sensitivity of OCF to changes in the variable cost figure? (Negative amount should be indicated by a minus sign.)

  

ΔOCF/ΔVC

$

Explanation: a.

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

Depreciation = $690,000/5

Depreciation = $138,000 per year

   

And the accounting breakeven is:

QA = ($790,000 + 138,000)/($75 – 50)

QA = 37,120 units

   

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

DOL = 1 + FC/OCF = 1 + FC/D

DOL = 1 + [$790,000)/$138,000)]

DOL = 6.725

b. 

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

  

OCFbase = [(P – v)Q – FC](1 – T) + TD

OCFbase = [($75 – 50)(71,000) – $790,000](0.65) + 0.35($138,000)

OCFbase = $688,550

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

NPVbase = –$690,000 + $688,550(PVIFA15%,5)

NPVbase = $1,618,126.39

  

To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the NPV at a different quantity. We will use sales of 76,000 units. The NPV at this sales level is:

OCFnew = [($75 – 50)(76,000) – $790,000](0.65) + 0.35($138,000)

OCFnew = $769,800

  

And the NPV is:

NPVnew = –$690,000 + $769,800(PVIFA15%,5)

NPVnew = $1,890,488.99

  

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

ΔNPV/ΔS = ($1,618,126.39 – 1,890,488.99)/(71,000 – 76,000)

ΔNPV/ΔS = +$54.473

  

If sales were to drop by 500 units, then NPV would drop by:

NPV drop = $54.473(500) = $27,236.26

You may wonder why we chose 76,000 units. Because it doesn’t matter! Whatever sales number we use, when we calculate the change in NPV per unit sold, the ratio will be the same.

c.

To find out how sensitive OCF is to a change in variable costs, we will compute the OCF at a variable cost of $51. Again, the number we choose to use here is irrelevant: We will get the same ratio of OCF to a one dollar change in variable cost no matter what variable cost we use. So, using the tax shield approach, the OCF at a variable cost of $51 is:

OCFnew = [($75 – 51)(71,000) – 790,000](0.65) + 0.35($138,000)

OCFnew = $642,400

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

ΔOCF/ΔVC = ($688,550 – 642,400)/($50 – 51)

ΔOCF/ΔVC = –$46,150

If variable costs decrease by $1 then, OCF would increase by $46,150