Question

Problem 10-8 Sensitivity Analysis (LO3)

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 $2.5 million a year, and variable costs are $2.60 per jar. The product will be priced at $3.40 per jar. The plant will be depreciated straight-line over 5 years to a salvage value of zero. The opportunity cost of capital is 10%, 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 $2.70 per jar?

c. What is NPV if fixed costs turn out to be $2.2 million per year?

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

Answer 1

a.

Annual depreciation = Initial investment/ useful life

                              = $ 6,000,000/5 = $ 1,200,000

Computation of future annual cash flow:

Sales revenue ($ 3.4 x 7,000,000)	$ 23,800,000
Variable cost ($ 2.6 x 7,000,000)	$ 18,200,000
Contribution	$ 5,600,000
Less: Fixed cost	$ 2,500,000
Operating income	$ 3,100,000
Less: Depreciation	$ 1,200,000
EBT	$ 1,900,000
Less: Tax @ 30 %	$ 570,000
Net income	$ 1,330,000
Add: Depreciation	$ 1,200,000
Annual cash flow	$ 2,530,000

Computation of Base-case NPV:

NPV = Annual cash flow x PVIFA (i, n) – Initial investment

        = $ 2,530,000 x PVIFA (10%, 5) – $ 6,000,000

         = $ 2,530,000 x [{1 – (1+0.1)^-5}/0.1] – $ 6,000,000

         = $ 2,530,000 x [{1 – (1.1)^-5}/0.1] – $ 6,000,000

         = $ 2,530,000 x [(1 – 0.6209213231)/0.1] – $ 6,000,000

         = $ 2,530,000 x [(0.3790786769/0.1)] – $ 6,000,000

         = $ 2,530,000 x 3.7907867694 – $ 6,000,000

         = $ 9,590,690.53 – $ 6,000,000

        = $ 3,590,690.53

b.

Computation of future annual cash flow if VC increases to $ 2.7 per jar:

Sales revenue ($ 3.4 x 7,000,000)	$                        23,800,000
Variable cost ($ 2.7 x 7,000,000)	$                        18,900,000
Contribution	$                          4,900,000
Less: Fixed cost	$                          2,500,000
Operating income	$                          2,400,000
Less: Depreciation	$                          1,200,000
EBT	$                          1,200,000
Less: Tax @ 30 %	$                              360,000
Net income	$                              840,000
Add: Depreciation	$                          1,200,000
Annual cash flow	$                          2,040,000

NPV = Annual cash flow x PVIFA (i, n) – Initial investment

       = $ 2,040,000 x PVIFA (10%, 5) – $ 6,000,000

       = $ 2,040,000 x 3.7907867694 – $ 6,000,000

       = $ 7,733,205.01 – $ 6,000,000

       = $ 1,733,205.01

c.

Computation of future annual cash flow if FC will be $ 2,200,000 per jar:

Sales revenue ($ 3.4 x 7,000,000)	$                        23,800,000
Variable cost ($ 2.6 x 7,000,000)	$                        18,200,000
Contribution	$                          5,600,000
Less: Fixed cost	$                          2,200,000
Operating income	$                          3,400,000
Less: Depreciation	$                          1,200,000
EBT	$                          2,200,000
Less: Tax @ 30 %	$                             660,000
Net income	$                          1,540,000
Add: Depreciation	$                          1,200,000
Annual cash flow	$                          2,740,000

NPV = Annual cash flow x PVIFA (i, n) – Initial investment

       = $ 2,740,000 x PVIFA (10%, 5) – $ 6,000,000

       = $ 2,740,000 x 3.7907867694 – $ 6,000,000

       = $ 10,386,755.75 – $ 6,000,000

       = $ 4,386,755.75

d.

NPV = Annual cash flow x PVIFA (i, n) – Initial investment

$ 0 = Annual cash flow x PVIFA (10%, 5) – $ 6,000,000

$ 0 = Annual cash flow x 3.7907867694 – $ 6,000,000

Annual cash flow x 3.7907867694 = $ 6,000,000

Annual cash flow = $ 6,000,000/3.7907867694 = $ 1,582,784.88

Computation of annual sales revenue:

Annual cash flow	$1,582,784.88
Less: Depreciation	$1,200,000.00
Net income	$382,784.88
Add: **Tax @ 30 %	$164,050.66
*EBT	$546,835.54
Add: Depreciation	$1,200,000.00
Operating income	$1,746,835.54
Add: Fixed cost	$2,500,000.00
Contribution	$4,246,835.54
Add: Variable cost	$18,200,000.00
Sales revenue	$22,446,835.54

*EBT = Net income/0.7 = $ 382,784.88/0.7 = $ 546,835.5429 or $ 546,835.54

** Tax = $ 546,835.54 x 0.3 = $ 164,050.6620 or $ 164,050.66

Sales per unit = Total sales revenue / Number of units sales

                          = $ 22,446,835.54/7,000,000

                          = $ 3.2066907918 or $ 3.21

At sales price of 3.21 per jar, NPV will be zero.