In: Finance
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 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 |