Question

We are evaluating a project that costs $924,000, has a four-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 87,600 units per year. Price per unit is $34.55, variable cost per unit is $20.80, and fixed costs are $756,000 per year. The tax rate is 35 percent, and we require a return of 13 percent on this project.

Calculate the base-case operating cash flow and NPV.

If we use sales of 100,000 units, how much would the NPV be?

What is the sensitivity of NPV to changes in the sales figure?

Answer 1

Particulars	Annual cash flow
Initial Investment	924000.00
Sales Units	87600.00
Selling price per unit	34.55
Variable cost per unit	-20.80
Contribution margin per unit	13.75
Total contribution	1204500.00
Less: Fixed costs	-756000.00
Less: Depreciation	-231000.00
Net income before tax	217500.00
Less: tax @ 35%	-76125.00
Net income	141375.00
Add: Depreciation	231000.00
Operating cash flow	372375.00

Operating cash flow = 372375

NPV = PV of annual cash flows - Initial investment

NPV = 372375 * (1 - (1 + 13%)^-4)/0.13 - 924000

= 183618.76

If Sales units = 100000 then Operating cash flow =

Particulars	Annual cash flow
Initial Investment	924000.00
Sales Units	100000.00
Selling price per unit	34.55
Variable cost per unit	-20.80
Contribution margin per unit	13.75
Total contribution	1375000.00
Less: Fixed costs	-756000.00
Less: Depreciation	-231000.00
Net income before tax	388000.00
Less: tax @ 35%	-135800.00
Net income	252200.00
Add: Depreciation	231000.00
Operating cash flow	483200.00

Operating cash flow = 483200

NPV = PV of annual cash flows - Initial investment

NPV = 483200 * (1 - (1 + 13%)^-4)/0.13 - 924000

= 513264.54

Sensitivity = Change in NPV / Change in sales figure

Change in NPV = (513264.54 - 183618.76) = 329645.78

Change In sales = (100000 - 87600) * 34.55 = 428420

Sensitivity to dollar sales = 329645.78 / 428420 = 0.77