Question

Problem 10-14 NPV Break-Even Analysis (LO3)

Modern Artifacts can produce keepsakes that will be sold for $100 each. Nondepreciation fixed costs are $1,300 per year, and variable costs are $70 per unit. The initial investment of $4,000 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?

b. What is the NPV break-even level of sales if the firm pays no taxes?

c. What is the accounting break-even level of sales if the firm’s tax rate is 30%?

d. What is the NPV break-even level of sales if the firm’s tax rate is 30%?

Answer 1

a. Accounting break-even level of sales if the firm pays no taxes

(Fixed costs+depn.)/Contribution per unit

ie. (1300+800)/30=

70

units

ie.70*$100=

$7,000

b.NPV break-even level of sales if the firm pays no taxes

At NPV break-even,

initial investment cash outflow will Equal the PV of 5 yrs.' Operating cash flows

ie. 4000=P/A, (x*(100-70)-1300)12%,5

where, x is the no.of sales units

ie. 4000=(x*(100-70)-1300)*3.60478

solving for x, we get the NPV no.of sales units as

80 units.

ie. 80*$ 100=

$8,600

c.Accounting break-even level of sales if the firm’s tax rate is 30%

is the same as in a.BEP is NO LOSS/NO PROFIT level of sales units & $ , in which case there are no TAXES.

So,

(Fixed costs+depn.)/Contribution per unit

ie. (1300+800)/30=

70

units

ie.70*$100=

$7,000

d.NPV break-even level of sales if the firm’s tax rate is 30%

At NPV break-even,

initial investment cash outflow will Equal the PV of 5 yrs.' after-tax Operating cash flows

ie. 4000=P/A,OCF,2%,5

where the annuity of after-tax OCF will be

if x is the no.of sales unit,

OCF=( x*(S.P.-V.C)-Fixed costs)*(1-Tax Rate)+(Depn.*tax Rate

OCF=((x*(100-70)-1300)*(1-30%))+(800*30%)

4000=(((x*(100-70)-1300)*(1-30%))+(800*30%))*3.60478

solving for x, we get the NPV no.of sales units as

85 units

or

85*100=

$8,500