## Question

###### Sensitivity Analysis. Emperor’s Clothes Fashions can invest $5 million in a new plant for producing invisible...

Sensitivity Analysis. 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 million a year, and variable costs are $1 per jar. The product will be priced at $2 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 percent, and the tax rate is 40 percent.

a. What is project NPV under these base-case assumptions?

b. What is NPV if variable costs turn out to be $1.20 per jar?

c. What is NPV if fixed costs turn out to be $1.5 million per year?

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

## Answers

OCF Base case Case 2 Case 3 Sales 6000000 6000000 6000000 Less: Fixed costs 2000000 2000000 1500000 Variable costs 3000000 3600000 3000000 Profit before depriciation 1000000 400000 1500000 Less: Depreciation 1000000 1000000 1000000 PBT 0 -600000 500000 Less: Tax 0 -240000 200000 Profit after tax 0 -360000 300000 Add depreciation 1000000 1000000 1000000 OCF 1000000 640000 1300000

Year Base case Case 2 Case 3 0 -5000000 -5000000 -5000000 1 1000000 640000 1300000 2 1000000 640000 1300000 3 1000000 640000 1300000 4 1000000 640000 1300000 5 1000000 640000 1300000 NPV -1395223.80 -2692943.23 -313790.94 CASE 4 : For NPV = 0

5000000= OCF*(1-1/1.12^5)/0.12

OCF = 1387048.66

WORKING backwards

PAT = OCF- depreciation = 1387048.66-1000000 = 387,048.66

PBT= PAT*100/60 = 645081.10

Profit before depreciation = 1,645,081.10

Add fixed costs = 2000000

Contribution = 3645081.10

Let sale price be x. Variable costs =1

Hence contribution =Units*(SP- Variablecost)

3645081.10 = 3000000*(x-1)

x= 2.215

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