Question

Emperor’s Clothes Fashions can invest $5 million in a new plant for producing invisible makeup. The plant has an expected life of 5 years, and expected sales are 6 million jars of makeup a year. Fixed costs are $2.8 million a year, and variable costs are $1.40 per jar. The product will be priced at $3.00 per jar. The plant will be depreciated straight-line over 5 years to a salvage value of zero. The opportunity cost of capital is 14%, and the tax rate is 30%.

A. what is project NPV under these base-case assumptions
B. What is NPV if variable costs turn out to be $2.10 per jar
c.What is NPV if fixed costs turn out to be $2.6 million per year?
d. At what price per jar would project NPV equal zero?

Answer 1

A. what is project NPV under these base-case assumptions

Sales Revenue	18000000
Variable Cost	8400000
Contribution	9600000
Less Fixed Cost	2800000
Net Income	6800000
Less Tax 30%	2040000
Add Tax Saving in Depreciation 5000000/5*.30	300000
Operating Cash flow	5060000

Year	0	1	2	3	4	5
Initial Investment	-5000000
Operating Cash flow		5060000	5060000	5060000	5060000	5060000
PV factor		0.8772	0.7695	0.6750	0.5921	0.5194
PV	-5000000	4,438,596.49	3,893,505.69	3,415,355.87	2,995,926.20	2,628,005.44
NPV	12,371,389.70

B. What is NPV if variable costs turn out to be $2.10 per jar

Sales Revenue	18000000
Variable Cost	12600000
Contribution	5400000
Less Fixed Cost	2800000
Net Income	2600000
Less Tax 30%	780000
Add Tax Saving in Depreciation 5000000/5*.30	300000
Operating Cash flow	2120000

Year	0	1	2	3	4	5
Initial Investment	-5000000
Operating Cash flow		2120000	2120000	2120000	2120000	2120000
PV factor		0.8772	0.7695	0.6750	0.5921	0.5194
PV	-5000000	1,859,649.12	1,631,271.16	1,430,939.61	1,255,210.19	1,101,061.57
NPV	2,278,131.65

c.What is NPV if fixed costs turn out to be $2.6 million per year?

Sales Revenue	18000000
Variable Cost	8400000
Contribution	9600000
Less Fixed Cost	2600000
Net Income	7000000
Less Tax 30%	2100000
Add Tax Saving in Depreciation 5000000/5*.30	300000
Operating Cash flow	5200000

Year	0	1	2	3	4	5
Initial Investment	-5000000
Operating Cash flow		5200000	5200000	5200000	5200000	5200000
PV factor		0.8772	0.7695	0.6750	0.5921	0.5194
PV	-5000000	4,561,403.51	4,001,231.15	3,509,851.88	3,078,817.44	2,700,717.05
NPV	12,852,021.04

d. At what price per jar would project NPV equal zero?

Let = X Operating Cash Flow

0=-5000000+X*PVIFA 14% 5

=5,000,000/3.43308

Operating Cash Flow=1456417.73

Operating Cash Flow =(6000000*(Sales price-1.4)-2800000)*(1-.30)+5000000/5*0.3

1456417.73=(6000000*(Sales price-1.4)-2800000)*(1-.30)+5000000/5*0.3

Sales Price Per unit =2.142004