Question

1. Modern Artifacts can produce keepsakes that will be sold for $80 each. Non-depreciated fixed costs are $1000 per year and variable costs are $60 per unit.
   1. If he project requires an initial investment of $3000 and is expected to last for 5 years and the firm pays no taxes, what are the accounting and NPV break-even levels of sales? The initial investment will be depreciated straightline over 5 years to zero and the discount rate is 10%
   2. How do your answers change if the tax rate is 30%?
   3. What is the degree of operating leverage when sales are $8000
   4. What is the DOL when sales are $10,000? Why is the operating leverage different at these two levels of sales?

Answer 1

Accounting breakeven is given by

BEP= total fixed cost /contribution per unit

Total fixed cost =1000+depreciation =1000+3000/5=1600$

Contribution per unit = 80-60=$20 per unit

Break even point= 1600/20=80 units

NPV Break even means the no of units that makes the NPV=0

Let those no of units be = x

NPV = PV of inflows - PV of outflows

Cash inflows = operating profit before depreciation+ depreciation tax shield

= EBITDA ×(1-t)+D*t

Where

D= depreciation =3000/5=600

t = tax rate=0%

EBITDA= units × contribution per unit - Fixed cost

= x ×20-1000= 20x-1000

Since t=0

Cash inflows = 20x-1000

PV of cash inflows = (20x-1000)×annuity factor for 5 years @10%

Annuity factor AF (r,n)= (1-(1+r)^-n)/r

AF(10%,5) = (1-1.1^-5)/.1 = 3.791

PV of inflows = 3.791(20x-1000)

PV of outflows = initial cash outflows = 3000

Therefore

(3.791(20×-1000) -3000)=0

x=89.56 units

Part b

If tax rate i.e. t= 30%

Cash inflows = (20x-1000)×.70 +600×.30

PV of inflows = ((20x-1000)×.70+180)×3.791

Hence

((20x-1000)×.70+180)×3.791=3000

x= 93.67 units

Yes the answer would change,If we need to pay the tax our NPV breakeven would shift away.

Part c

Degree of operating leverage DOL = contribution/ EBIT

Let us first calculate contribution margin ratio (CMR) which is = contribution/sale = 20/80=25%

EBIT(operating profit)= EBITDA- depreciation

(Total Contribution = sales×CMR= 8000×25%=2000

EBIT= 2000- 1000-600= 400

DOL= 2000/400= 5

Part d

If sales are $10000

Contribution = 25%×10000=2500

EBIT = 2500-1000-600=900

DOL= 2500/900= 2.78

The DOL has decreased with the increase in sales, Because the fixed cost per (1600/units) has decreased resultingly profit per unit has increased this will continue with the increase in sales

Case 1

No of units = 8000/80= 100

fixed cost per unit = 1600/100=16

Ebit= 20-16=4

Dol= 20/4=5

Case2

Units= 10000/80=125

Fixed cost per unit = 1600/125=12.8

Ebit= 20-12.8= 7.2

Dol= 20/7.2= 2.78