Question

The most likely outcomes for a particular project are estimated as follows:

Unit price:	$	50
Variable cost:	$	30
Fixed cost:	$	410,000
Expected sales:		40,000	units per year

Modern Artifacts can produce keepsakes that will be sold for $60 each. Nondepreciation fixed costs are $1,400 per year, and variable costs are $30 per unit. The initial investment of $5,000 will be depreciated straight-line over its useful life of 5 years to a final value of zero, and the discount rate is 12%.

a. What is the accounting break-even level of sales if the firm pays no taxes? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

b. What is the NPV break-even level of sales if the firm pays no taxes? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

c. What is the accounting break-even level of sales if the firm’s tax rate is 20%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

d. What is the NPV break-even level of sales if the firm’s tax rate is 20%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Answer 1

a. Break even point is the point at which (Sales- Variable cost)* no of units- Fixed Costs=0

= (60-30)*x-(1400+1000)=0

x=80

where x= no of units to be produced, Depreciation as per straight line = 5000/5=1000.

b. NPV break even value is the point at which Present value of future cash inflows- Present Value of future cash outflows=0

For this we need to calculate the annuity factor @ 12% discount rate=(1/1.12+1/(1.12)^2+...1/(1.12)^5)=3.60

Express the Initial investment of 5000 @ 5 year annuity factor of 3.60=1388.89

Fixed cost=1400

Annual depreciation=1000

Sales Price - variable cost = 30

NPV break even point= (1388.89+1400-1000)/30=59.63 ~ 60 units

c. With tax of 20% tax the formula will be=( Fixed cost + Dep)*(1-0.2)/ (Sales- Variable cost)*0.2=

= 1920/24= 80

d.With tax of 20% depreciation acts as a tax sheild which lowers tax bill. Hence the Npv Break even is calculated as follows:

Express the Initial investment of 5000 @ 5 year annuity factor of 3.60=1388.89

Fixed cost=1400

Annual depreciation=1000

Sales Price - variable cost = 30

BEP=[Annualised initial investment +Annual Fixed Cost*(1-tax)-annual dep*tax rate]/(sales price-variable cost)*(1-t)

=[1388.89+ 1400*0.8+1000*0.2]/30*0.8

=61.57 i.e. ~62 units