Question

We are evaluating a project that costs $670,000, 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 59,000 units per year. Price per unit is $44, variable cost per unit is $24, and fixed costs are $760,000 per year. The tax rate is 35 percent, and we require a return of 18 percent on this project A. Calculate the accounting break-even point (Units) B1. Calculate the base-cash flow and NPV B2. What is the sensitivity of NPV to changes in the sales figure? C. What is the sensitivity of OCF to changes in the variable cost figure?

Answer 1

A. Accounting break-even point (Units)= Fixed cost+Depriciation/Contri per unit

Contribution per unit= SP-Variable cost

Contri=44-24

Contri=20

Depriciation=670000/5=134000$

BEP in units=760000+134000/20

BEP= 44700 units

B1. Base cash flows=Fbase= [ (P- V) Q-FC](1-Tc)+Tc*depriciation

=(44-24)*59000

=1180000-760000

=420000*0.65

=273000+.35*134000

=319900

NPV= Base cash flow(PVIFA18%,5) - Cost of the asset

=319900(3.12714)-670000

=330372.086$

B2. Sensitivity of NPV to changes in the sales figure

To calculate the NPV we can assume the sales = 60,000 units

Base cash flows at this sales level is= [ (P- V) Q-FC](1-Tc)+Tc*depriciation

=44-24*60,000

=12,00,000-7,60,000

=4,40,000*0.65

=286000+.35*134000

=332900$

New NPV=  $332900(PVIFA18%,5)-670000

=$332900(3.12714)-670000

=371024.90$

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

= ($330372.086 – 371024.90 )/(59,000 – 60,000)

=-40652.814 / -1000

= $40.652

If sales were to drop by 500 units, then NPV would drop by:NPV drop = $40.652(500) = $20326

C. Sensitivity of OCF to changes in the variable cost figure

= [($44 – 25)(59,000) – 760,000](0.65) + 0.35($134000)

=234650+46900

=281550

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

CHANGE IN OCF/CHANGE IN v = ($319900 – 281550 )/($24 – 25)

= –$-38350

If variable costs decreasees by $1 then, OCF would increase by 38350$.