Question

Walmart is considering investing $3 million in an automatic sewing machine to produce a newly designed line of dresses. The dresses will be priced at $300, and management expects to sell 12,000 per year for six years. There is, however, some uncertainty about production costs associated with the new machine. The production department has estimated operating costs at 70% of revenues, but senior management realizes that this figure could turn out to be as low as 65% or as high as 75%. The new machine will be depreciated at a rate of $300,000 per year for six years (straight line, zero salvage). Walmart’s cost of capital is 15% and its marginal tax rate is 30%. Calculate a point estimate along with best and worst case scenarios for the project’s NPV.

Cash flow in years 1-5	65%	70%	75%
Revenues
Operating Costs
Depreciation
EBT impact
Tax
Eat impact
Add back depreciation
Cash flow

Best		Point Estimate		Worst

Answer 1

All financials below are in $.

There are two noticeable errors in the question:

1. The production will last for 6 years. Hence the cash flows in the table below are for year 1 to 6 and not 1 to 5 as given in the header of the table
2. Annual depreciation = Machine cost / Life = 3,000,000 / 6 = 500,000 and not 300,000 as stated in the question

Please see the table below for the annual cash flows in the year 1 to 6. The final answers are in the last row, also highlighted in yellow color. The second column explains the mathematics in terms of symbols. That will help you understand how each row has been calculated.

Operating cost as % of revenue	A	65%	70%	75%
Revenues	B = 300 x 12,000	3,600,000	3,600,000	3,600,000
Operating Costs	C = A x B	2,340,000	2,520,000	2,700,000
Depreciation	D = 3,000,000/6	500,000	500,000	500,000
EBT impact	E = B - C - D	760,000	580,000	400,000
Tax	F = E x 30%	228,000	174,000	120,000
Eat impact	G = E - F	532,000	406,000	280,000
Add back depreciation	D	500,000	500,000	500,000
Cash flow	H = G + D	1,032,000	906,000	780,000

Calculation of NPV

Operating Cash flow, H above occurs as an annuity. PV of Annuity = H / R x [1 - (1 + R)^-N] where N is the number of years and R is the discount rate.

NPV = - Initial investment + PV of annuity cash flows = - I + H / R x [1 - (1 + R)^-N]

Please see the table below. Best, Point and worst estimate of NPVs are shown below. They are highlighted in yellow colored cells. The column titled "Linkage" explains the formula against each row. That will help you understand the mathematics. FIgures in parenthesis mean negative numbers.

Parameter	Linkage	Best Estimate	Point Estimate	Worst Case
Initial Investment	I	3,000,000	3,000,000	3,000,000
Operating cash flows	H (calculated above)	1,032,000	906,000	780,000
Years	N	6	6	6
Cost of capital	R	15%	15%	15%
NPV	- I + H / R x [1 - (1 + R)-N]	905,586	428,741	(48,103)