Question

Emperor’s Clothes Fashions can invest $6 million in a new plant for producing invisible makeup. The plant has an expected life of 5 years, and expected sales are 7 million jars of makeup a year. Fixed costs are $2.2 million a year, and variable costs are $1.80 per jar. The product will be priced at $2.60 per jar. The plant will be depreciated straight-line over 5 years to a salvage value of zero. The opportunity cost of capital is 10%, 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 $2.00 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 $1.7 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

Ans.

Sales(7 * 2.60)	$18.2m
Less: costs
Variable cost(7 * 1.80)	$12.6m
Fixed costs	$2.2m
Depreciation	$1.2m
Total costs	$16m
Profit before tax	$2.2m
Less tax@30%	$0.66m
Profit after tax	$1.54m
Add: depreciation	$1.2m
Cash inflows	$2.74m

Depreciation = 6 / 5 =$1.2m.

Now, the present value of cash inflows.

Present value of cash inflows = $2.74 * PVIF ( 10% ,5)

= $2.74 * 0.621 = $ 1.70m

Net Present Value =  Present value of cash inflows - initial investment

= $ 1.7 - $ 6 = - $ 4.3 m

b)

If variable cost is $2 per jar, the cash inflows will be as :

Particulars	Amount
Sales(7 * 2.60)	$18.2m
Less: costs
Variable cost(7 * 2)	$14m
Fixed costs	$2.2m
Depreciation	$1.2m
Total costs	$17.4m
Profit before tax	$0.8m
Less tax@30%	$0.24m
Profit after tax	$0.56m
Add: depreciation	$1.2m
Cash inflows	$1.76m

Present value of cash inflows = $1.76 * 0.621 = $1.09m

NPV = $1.09 - $ 6 = -$ 4.91m

c)

If fixed costs is $1.7m per year, the cash inflows will be as :

Particulars	Amount
Sales(7 * 2.60)	$18.2m
Less: costs
Variable cost(7 * 1.80)	$12.6m
Fixed costs	$1.7m
Depreciation	$1.2m
Total costs	$15.5m
Profit before tax	$2.7m
Less tax@30%	$0.81m
Profit after tax	$1.89m
Add: depreciation	$1.2m
Cash inflows	$3.09m

Present value of cash inflows = $3.09 * 0.621 = $1.92m

NPV = $1.92 - $6 = -$4.08m

d)

Let the price per jar be x

The cash inflows will be as given below

Particulars	Amount in $m
Sales(7 * x)	7x
Less: costs
Variable cost(7 * 1.80)	$12.6m
Fixed costs	$2.2m
Depreciation	$1.2m
Total costs	$16m
Profit before tax	7x - $16m
Profit after tax( 70% of profit before tax)	4.9x - $11.2m
Add: depreciation	$1.2m
Cash inflows	4.9x - $10m

Present value of cash inflows = (4.9x - $10m) * 0.621 = 3.0429x - $6.21m

NPV is equal to zero when the present value of cash inflows should be equal to the initial investment.

3.0429x - $ 6.21 = $ 6

3.0429x = $12.21

x = $4.01

Price per jar = $4.01 per jar