Question

We are evaluating a project that costs $864,000, has an eight-year life, and has no salvage value. Assume that de-preciation is straight-line to zero over the life of the project. Sales are projected at 71,000 units per year. Price per unit is $49, variable cost per unit is $33, and fixed costs are $765,000 per year. The tax rate is 35 percent, and we require a return of 10 percent on this project.

Required:
a. Calculate the accounting break-even point. What is the degree of operating leverage at the accounting break-even point?
b. Calculate the base-case cash flow and NPV. What is the sensitivity of NPV to changes in the sales figure? Explain what your answer tells you about a 500-unit decrease in projected sales.
c. What is the sensitivity of OCF to changes in the variable cost figure? Explain what your answer tells you about a $1 decrease in estimated variable costs.

Answer 1

Depreciation = $864,000/8 = $108,000 per year

a. Accounting breakeven =

= ($765,000 + 108,000)/($49 - $33)

= 54,563 units

b&c. OCF base= [(P – v)Q – FC](1 – tc) + tc D

OCF base= [($49 – 33)(71,000) – $765,000](0.65) + 0.35($108,000)

OCF base=[$1,136,000-$765,000]0.65 +$37,800

OCF base= [$371,000] 0.65 +$37,800

OCF base=$241,150+$37,800

OCF base=$278,950

Calculating the NPV using our base-case projections. Also, no salvage value, hence the NPV=

NPV(base) = –$864,000+ $278,950 (PVIFA10%,8)

NPV(base) = -864,000+$278,950 x 5.335

NPV(base) = -864,000+ 1,488,178

NPV(base) = $624,178

We will use sales of 72,000 units in calculating the sensitivity of the NPV

OCF new = [($37 - 21)(72,000) - $765,000](0.65) + 0.35(108,000)

OCF new = [ $1,152,000-$765,000]0.65+0.35 (108,000)

OCF new = [387,000] 0.65 + $37,800

OCF new = $251,550+37,800

OCF new = $289,350

NPVnew= –$864,000 + $289,350(PVIFA15%,8)

NPVnew=-$864,000+$289,350 x 5.335

NPVnew=- $679,661

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

DNPV/DS = ($624,178 – 679,661)/(71,000 – 72,000)

NPV/DS = +$55.48

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

NPV drop = $55.48(500)

NPV drop = $27,742.