Question

Modern Artifacts can produce keepsakes that will be sold for $81 each. Non-depreciated fixed costs are $1,020 per year and variable costs are $48 per unit.

a.	If the project requires an initial investment of $3,090 and is expected to last for 7 years and the firm pays no taxes, what are the accounting and NPV break-even levels of sales? The initial investment will be depreciated straight-line over 7 years to a final value of zero, and the discount rate is 11%. (Round your answers to the nearest whole dollar.)
	Accounting break-even sales level     $
	NPV break-even sales level      $

b.	How do your answers change if the firm's tax rate is 40%? (Round your answers to the nearest whole dollar.)
	Accounting break-even sales level      $
	NPV break-even sales level     $

Answer 1

Solution:

a)i)Calculation of Accounting break even sale level

Depreciation per year=$3,090/7=$441.43

Contribution per unit=Sale price-variable cost

=$81-$48=$33

BEP(unit)=(Depreciation per year+Fixed cost per year)/Contribution per unit

=($441.43+$1,020)/$33

=44.29 units

BEP sales level=44.29 units*$81=$3,587

ii)NPV break-even sales level(when there is no tax rate)

Let the quantity sold is Q

Cash flow from operation per year=Sales-expense

=$81Q-$48Q-$1020=$33Q-$1020

Present value of this cash flow for 7 year @11%

=$33Q-$1020*PVAF@11% for 7 year

=$33Q-$1020*4.7122

Now ,at Break even,

PV of cash flows=Investment

$33Q-$1020*4.7122=$3090

$33Q=$655.75+$1020

Q=50.78 units

Thus,NPV break-even sales level is;

=50.78 units*$81=$4113.18 per year

b)i)Accounting break-even sales level will be same as in case a above i.e $3,587 as there is no profit and consequently there is no income tax paid at this level.

Thus Accounting break-even sales is $3,587

ii)NPV break-even sales level

Let the quantity sold is Q

Cash flow from operation per year=(Sales-expense)*(1-tax rate)+(depreciation*Tax rate)

=($81Q-$48Q-$1020)*(1-0.40)+(441.43*0.40)

=(28.80Q-$612)+176.572

=28.8Q-435.428

Present value of this cash flow for 7 year @11%

=28.8Q-435.428*PVAF@11% for 7 year

=28.8Q-435.428*4.7122

Now at break even point;

PV of cash flows=Investment

28.8Q-435.428*4.7122=$3090

28.80Q=$655.75+435.428

Q=37.89 units

Thus,NPV break-even sales level is;

=37.89 units*$81=$3069 per year