Question

We are evaluating a project that costs $832,000, has an eight-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 40,000 units per year. Price per unit is $40, variable cost per unit is $15, and fixed costs are $728,000 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.

Break even point ______ units

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

Cash flow______

NPV _______

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

change NPV/Change in Q _________

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

NPV would (increase/decrease) by $_____.

c. What is the sensitivity of OCF to changes in the variable cost figure?

Change in OCF/ Change in VC ___________

Answer 1

a) Calculating Accounting Break even point (BEP)

Total Fixed Cost = Fixed cost + Depreciation

Depreciation = Total cost of project / life of the project

Depreciation = $823,000/8 =$104,000

Total Fixed Cost = $728,000+$104,000 = $832,000

BEP ( in unit) = Total Fixed cost / Contribution per unit

Total fixed cost =$832,000

Contribution = Sale price - Variable cost

contribution per unit = $40 - $15 = $25

BEP ( in units) = $832,000/$25 = 33,280 units

Therefore, the accounting BEP is 33,280 units.

b-1 base case Cashflow.

OCF = operating Cashflow

OCF = Contribution - Fixed cost (1- Tax) + tax shield depreciation

OCF = ( 40,000units ($40-$15) - $728,000)(1-35%) + 35% × 104,000

OCF = $1,000,000-$728,000(65%)+$104,000(35%)

OCF = $213,200

NPV = Cashflow × Sum of discounted factor 18% - Investment

Discount factor 18% for 8years = ((1/(1+18%)^1)+(1/(1+18)^2)+(1/(1+18%)^3)+....+(1/(1+18%)^8))

= 0.847+0.718+0.609+0.516+0.437+0.370+0.314+0.266

= 4.077

NPV = $213,200 × 4.077 - $832,000 = $37,323

b-2 To calculate sensitivity,we have to take one more sales units

Let us take sales unit 50,000

OCF = Contribution - Fixed cost (1-35%) + Depreciation tax shield

OCF = ((50,000× $25) - $728,000)(1-0.35)+(0.65)$104,000

OCF =$375,700

NPV = ( cashflow × sum of discounted factor at 18% for 8 years )- Investment

NPV = $375,700 × 4.077 - $832,000 =$699,728.9

To sensitivity of NPV to Change in unit

=( $699,728.9 - $37,323)/50,000-40,000

= $662,405.9/10,000 = 66.24

b-3 If sales drop by 500units

then, NPV decrease by 66.24× 500units = 33,120.29

c To calculate sensitivity,we have to take change variable cost

Let us take variable cost $20

OCF = (40,000($40-$20) - $728,000)(1-0.35)+0.65($104,000)

OCF = $83,200

The sensitivity of OCF to change in variable cost

The sensitivity of OCF to Change in variable cost = (83,200-$213,200)/($20-$15)

=-26,000