Question

Emperor’s Clothes Fashions can invest $4 million in a new plant for producing invisible makeup. The plant has an expected life of 5 years, and expected sales are 5 million jars of makeup a year. Fixed costs are $3.4 million a year, and variable costs are $2.60 per jar. The product will be priced at $3.80 per jar. The plant will be depreciated straight-line over 5 years to a salvage value of zero. The opportunity cost of capital is 11%, and the tax rate is 30%.

a. What is project NPV under these base-case assumptions? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

b. What is NPV if variable costs turn out to be $2.70 per jar? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

c. What is NPV if fixed costs turn out to be $3.2 million per year? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

d. At what price per jar would project NPV equal zero? (Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

a)

NPV under base case assumptions

Particulars	Amount
Sales per year (5,000,000 x $3.80)	$19,000,000
Less : Variable costs per year (5,000,000 x $2.60)	$13,000,000
Less : Fixed costs per year	$3,400,000
Less : Depreciation per year ($4,000,000 / 5)	$800,000
Earnings before tax	$1,800,000
Less : Tax @30%	$540,000
Earnings after tax	$1,260,000
Add : Depreciation per year	$800,000
Cash Inflows per year	$2,060,000
PVIFA (11%, 5)	3.6958970176
Present value of cash inflows	$7,613,547.86
Less : Initial investment	$4,000,000
NPV	$3,613,547.86

b)

NPV

Particulars	Amount
Sales per year (5,000,000 x $3.80)	$19,000,000
Less : Variable costs per year (5,000,000 x $2.70)	$13,500,000
Less : Fixed costs per year	$3,400,000
Less : Depreciation per year ($4,000,000 / 5)	$800,000
Earnings before tax	$1,300,000
Less : Tax @30%	$390,000
Earnings after tax	$910,000
Add : Depreciation per year	$800,000
Cash Inflows per year	$1,710,000
PVIFA (11%, 5)	3.6958970176
Present value of cash inflows	$6,319,983.90
Less : Initial investment	$4,000,000
NPV	$2,319,983.90

c)

NPV under base case assumptions

Particulars	Amount
Sales per year (5,000,000 x $3.80)	$19,000,000
Less : Variable costs per year (5,000,000 x $2.60)	$13,000,000
Less : Fixed costs per year	$3,200,000
Less : Depreciation per year ($4,000,000 / 5)	$800,000
Earnings before tax	$2,000,000
Less : Tax @30%	$600,000
Earnings after tax	$1,400,000
Add : Depreciation per year	$800,000
Cash Inflows per year	$2,200,000
PVIFA (11%, 5)	3.6958970176
Present value of cash inflows	$8,130,973.44
Less : Initial investment	$4,000,000
NPV	$4,130,973.44

d)

NPV would be zero when Present value of cash inflows is equal to the initial investment of $4,000,000. Let the price per jar be "p".

NPV under base case assumptions

Particulars	Amount
Sales per year (5,000,000 x p)	5,000,000p
Less : Variable costs per year (5,000,000 x $2.60)	$13,000,000
Less : Fixed costs per year	$3,400,000
Less : Depreciation per year ($4,000,000 / 5)	$800,000
Earnings before tax	5,000,000p - $17,200,000
Less : Tax @30%	1,500,000p - $5,160,000
Earnings after tax	3,500,000p - $12,040,000
Add : Depreciation per year	$800,000
Cash Inflows per year	3,500,000p - $11,240,000
PVIFA (11%, 5)	3.6958970176
Present value of cash inflows	12,935,639.5616p - $41,541,882.4778

Now, Present value of cash inflows = Initial Investment

or, 12,935,639.5616p - $41,541,882.4778 = $4,000,000

or, p = $3.52065 or $3.52