Question

Modem Artifacts can produce keepsakes that will be sold for $76 eachNon-depreciated fixed costs are $1,070 per year and variable costs are $51 per unit.

a. If the project requires an initial investment of 2,980 and is expected to last for 6 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 years to a final value of zeroand the discount rate is 14%. Round your answers to the nearest whole dollar .)

Accounting break-even sales level =

NPV break-even sales levels =

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 levels. =

Answer 1

(a) Accounting and NPV Break -Even level of sales when firm pays no taxes:

Accounting Break - Even level of sales:

Given,

Selling price = $76, Variable cost = 51,

Fixed cost other than depreciation = $1,070

Initial investment = $2,980, Life = 6 Years

Required: Accounting Break -Even level of sales:

Contribution per unit = Selling price - Variable cost

Contribution per unit = 76 - 51 = $25 per unit

Fixed cost other than depreciation = $1,070

Depreciation [2,980÷6] = $496.67

Total Fixed cost = 1,566.67 i.e., (1,070+496.67)

Break even point

= Fixed cost ÷ Contribution per unit

Break even point = 1,566.67÷25 = 62.67 units

Therefore Accounting Break -Even level of sales = 62.67 units

NPV Break -Even level of sales:

This means the level of sales at which Present value of cash inflows is equal to Present value of cash outflows i.e., NPV to be zero

Present value of cash outflows:

Initial investment = $2,980

Present value of cash inflows:

Let level of sales i.e., no.of units be X

Particulars	Year 1 to 6
selling price per unit	76
Less: Variable cost per unit	(51)
Contribution per unit	25
Total contribution	25X
Less: Fixed cost	(1,070)
Less: Depreciation	(496.67)
EBT	25X - 1,566.67
Less: Tax	-
EAT	25X - 1,566.67
Add: Depreciation	496.67
CFAT	25X - 1,070
PVAF(14%, 6) = 1-1÷(1+0.14)^6	3.8887
Present value of CFAT	97.22X - 4,160.91

NPV = Present value of cash inflows - Present value of cash outflows

NPV = (97.22X - 4,160.91) - 2,980

97.22X - 4,160.91-2,980 = 0

97.22X = 7,140.91

X = 7,140.91÷97.22

X = 73.45 units

Therefore level of sales at which NPV is zero is 73.45 units

(b) Accounting and NPV Break -Even level of sales when firm pays Tax@40%:

Accounting Break -Even level of sales:

Accounting Break -Even level of sales remains same irrespective of tax paid or not

Therefore Accounting Break -Even level of sales is same as calculated above i.e., 62.67 units

NPV Break -Even level of sales:

Let no.of units when NPV becomes zero is X

Present value of cash outflows:

Initial investment = $2,980

Present value of cash inflows:

Particulars	Year 1 to 6
Selling price per unit	76
Less: Variable cost per unit	(51)
Contribution per unit	25
Total contribution	25X
Less: Fixed cost	(1,070)
Less: Depreciation	(496.67)
EBT	25X - 1,566.67
Less: Tax@40%	(10X - 626.67)
EAT	15X - 940
Add: Depreciation	496.67
CFAT	15X - 443.33
PVAF(14%,6)	3.8887
Present value of CFAT	58.33X - 1,723.98

NPV = (58.33X - 1,723.98) - 2,980

NPV = 58.33X - 4,703.98

58.33X - 4,703.98 = 0

58.33X = 4,703.98

X = 4,703.98÷58.33

X = 80.64 units

Therefore level of sales at which NPV becomes zero is 80.64 units.