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-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))
|
| b-1 |
Calculate the base-case cash flow and NPV. (Round your NPV answer to 2 decimal places. (e.g., 32.16))
|
| 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: 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 |
