Question

We are evaluating a project that costs $768,000, has a six-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 57,000 units per year. Price per unit is $60, variable cost per unit is $35, and fixed costs are $770,000 per year. The tax rate is 35 percent, and we require a return of 15 percent on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent. Calculate the best-case and worst-case NPV figures. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places, e.g., 32.16.) NPV Best-case $ Worst-case $

Answer 1

• Suppose the units sold, price, variable & fixed costs increase by 10%

then, unit sold = 57000 * 1.10 = 62700

Price per unit = $60 * 1.10 = $66

Variable Cost per unit = $35 * 1.10 = $38.5

Fixed Costs = $770000 * 1.10 = $847000

Step 1 : Initial Investment

= $768000

Step 2 : Depreciation

= $768000 / 6 = $128000

Step 3 : Recurring Cash Inflows after tax

Particulars	Amount (in $)
Sales (62700 * 66)	4138200
Less: Variable Cost (62700 * 38.5)	-2413950
Less : Fixed Costs	-847000
Less: Depreciation	-128000
Profit Before Tax	749250
Less: Tax @ 35%	-262237.5
Net Profit After Tax	487012.5
Add : Depreciation	128000
Cash Flow After Tax	615012.5

Step 4 : Finding the Net Present Value

NPV = Present Value of cash inflows - Present Value of Cash Outflows

= (Cash Flow after tax * Present value interest factor annuity @ 15% for 6 years) - Present Value of Cash Outflows

= ($615012.5 * 3.7844827) - $ 768000

= $ 2327504.16275 - $768000

= $ 1559504.16

• Suppose the units sold, price, variable & fixed costs decrease by 10%

then, unit sold = 57000 * 0.9 = 51300

Price per unit = $60 * 0.9 = $54

Variable Cost per unit = $35 * 0.9 = $31.5

Fixed Costs = $770000 * 0.9= $693000

Step 1 : Initial Investment

= $768000

Step 2 : Depreciation

= $768000 / 6 = $128000

Step 3 : Recurring Cash Inflows after tax

Particulars	Amount (in $)
Sales (51300 * 54)	2770200
Less: Variable Cost (51300 * 31.5)	-1615950
Less : Fixed Costs	-693000
Less: Depreciation	-128000
Profit Before Tax	333250
Less: Tax @ 35%	-116637.5
Net Profit After Tax	216612.5
Add : Depreciation	128000
Cash Flow After Tax	344612.5

Step 4 : Finding the Net Present Value

NPV = Present Value of cash inflows - Present Value of Cash Outflows

= (Cash Flow after tax * Present value interest factor annuity @ 15% for 6 years) - Present Value of Cash Outflows

= ($344612.5 * 3.7844827) - $ 768000

= $ 1304180 - $768000

= $ 536180.04

Thus the best case NPV is $ 1559504.16 while the worst case NPV is $ 536180.04