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 $2.7 million a year, and variable costs are $1.20 per jar. The product will be priced at $2.40 per jar. The plant will be depreciated straight-line over 5 years to a salvage value of zero. The opportunity cost of capital is 12%, and the tax rate is 40%.

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 $1.30 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 $2.6 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 at the base case scenario:

Contribution per Makeup Jar

Selling Price(SP) = $2.40

Variable Cost(VC) =($1.20)

Contribution per unit = $1.2 ( SP - VC)

No.of Jars sold = 5 million

Total Contribution = $1.2 * 5 million = $ 6 Million

Total Fixed Costs= ($2.7 million)

Depreciation = ($0.80 million)(4 Million/5 years)

Total Profit before Tax = $2.5 million

Tax @ 40% = ($1 million) ($2.5 million*40%)

Net profit = $1.5 Million

Add back: Depreciation : $0.8 Million

Net Cash Flow : $2.3 Million

Year	Cash Flow	Discount Factor@12%	Discounted Cash Flow
0	- $ 4M	1	-$4 M
1	$2.3M	1/(1+0.12)^1=0.893	2.054M
2	$2.3M	1/(1+0.12)^2=0.797	1.834M
3	$2.3M	1/(1+0.12)^3=0.712	1.637M
4	$2.3M	1/(1+0.12)^4=0.636	1.462M
5	$2.3M	1/(1+0.12)^5=0.567	1.305M
		Total	4.291M

NPV is $4.291 Million in this case. From the next case onwards we will use the Annuity function to find the present value of the Inflows as the inflow vale remains same every year

B&C)

Particulars	Base Case	VC@$1.3	Fixed [email protected]
Selling Price	$2.4	$2.4	$2.4
Variable Cost	$1.2	$1.3	$1.2
Contribution	$1.2	$1.1	$1.2
No.Of Units	5 Million	5 Million	5 Million
Total Contribution	$ 6 Million	$5.5 Million	$6 Million
Fixed Costs	$2.7Million	$2.7 Million	$ 2.6 Million
Depreciation	$0.8Million	$0.8Million	$0.8Million
Net profit Before Tax	$2.5Million	$2 Million	$2.6Million
Tax @40%	1 Million	$0.8Million	$1.04Million
Net Proft after Tax	$1.5 Million	$1.2 Million	$1.56 Million
Add Back Depreciation	$0.8Million	$0.8Million	$0.8Million
Cash Flow	$2.3 Million	$2.0 Million	$2.36 Million
Annuity Factor@12%	3.605	3.605	3.605
Cash Inflows	8.2915M	7.21M	8.5078M
Cash Outflow	4M	4M	4M
NPV	4.2915	3.21M	4.5078M

Annuity Factor derivation = 1/(1.12)^1+1/(1.12)^2+1/(1.12)^3+1/(1.12)^4+1/(1.12)^5

d) Sale Price at which NPV is at 0

This is a difficult question as we need to make some iterations towards the selling price, try with various selling prices, if we reduce the price by $0.5 and follow the same approach as before we come close to an NPV very close to 0.