Question

We are evaluating a project that costs $756,000, has a six-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 67,000 units per year. Price per unit is $60, variable cost per unit is $25, and fixed costs are $693,000 per year. The tax rate is 35 percent, and we require a return of 20 percent on this project.

a. Calculate the accounting break-even point.

b-1 Calculate the base-case cash flow and NPV.

b-2 What is the sensitivity of NPV to changes in the sales figure? ΔNPV/ΔQ

b-3 Calculate the change in NPV if sales were to drop by 500 units.

c. What is the sensitivity of OCF to changes in the variable cost figure? ΔOCF/ΔVC $

Answer 1

Answer and Explanation:

a)Break-even Point:

Break-even analysis is useful in determining the sales level at which the company will be in no profit no loss situation.

Break-even Point = Fixed cost/ Contribution margin per unit

Accounting Break Even Points Units

Depreciation = Asset PriceLife of Asset

Depreciation = 756,000/ 6

Depreciation = 126,000

Break Even Point = (Fixed Cost + Depreciation)(Sale Price − Variable Cost)Break Even Point

= (693,000 + 126,000)(60 − 25)

= 23,400 units

DOL at accounting break-even point

= 1 + (Fixed cost) / OCF (Derpreciation)

= 1 + 693,000/126,000

= 6.5

b-1)

OCF base = ((P - V) * Q - FC) * (1 - tax) + TD

OCF base = ((60 - 25) * 67,000 - 693,000) * (1 - 0.35) + 0.35 * 126,000

OCF base = 1,117,900

NPV = OCF * (PVIFA 20%, 6 years) - Initial Cost

NPV = 1,117,900 * (PVIFA 20%, 6 years) - 756,000

NPV = 1,117,900 * 3.3255 - 756,000

NPV = 2,961,576.45

b-2)

NPV when units = 68,000 units

OCF base = ((P - V) * Q - FC) * (1 - tax) + TD

OCF base = ((60 - 25) * 68,000 - 693,000) * (1 - 0.35) + 0.35 * 126,000

OCF base = 1,140,650

NPV = OCF * (PVIFA 20%, 6 years) - Initial Cost

NPV = 1,140650 * (PVIFA 20%, 6 years) - 756,000

NPV = 3,037243.116

ΔNPVΔQ/ΔNPVΔQ = ( 3,037243.116 − 2,961,576.45) / (68,000 − 67,000) =$75.66

b-3)

NPV when units = 66,500 units

OCF base = ((P - V) * Q - FC) * (1 - tax) + TD

OCF base = ((60 - 25) * 66,500 - 693,000) * (1 - 0.35) + 0.35 * 126,000

OCF base = 1,106,525

NPV = OCF * (PVIFA 20%, 6 years) - Initial Cost

NPV = 1,140650 * (PVIFA 20%, 6 years) - 756,000

NPV = 2,923,760.084

ΔNPVΔQ/ΔNPVΔQ = ( 2,961,576.45 − 2,923,760.084) / (67,000 − 66,500) =$75.63

C)

NPV when variable cost decreases by $1.

OCF = ((P - V) * Q - FC) * (1 - tax) + TD

OCF = ((60 - 24) * 67,000 - 693,000) * (1 - 0.35) + 0.35 * 126,000

OCF = 1,161,450

ΔOCF/ΔVC = 1,117,900 − 1,161,450 = -$43550