Question

You are considering a new product launch. The project will cost $1,282,500, have a five-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 410 units per year; price per unit will be $20,300, variable cost per unit will be $16,800, and fixed costs will be $339,000 per year. The required return on the project is 15 percent, and the relevant tax rate is 30 percent. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10 percent.

What are the best-case and worst-case NPVs with these projections?

What is the sensitivity of your base-case NPV to changes in fixed costs?

Answer 1

The NPV of project is given by,

NPV= ? {After-Tax Cash Flow / (1+r)^t} - Initial Investment

or for multi period cash flow

NPV = (initial investment) + CF1 / ((1+r)1) + CF2 / ((1+r)^2)..........CFn / ((1+r)^n-1)

Base case scenario
Cost of capital	15%
Initial investment	($1,282,500)
Depreciation per year	($256,500)	Straight line depreciation since no salvage value at the end of yr 5
Year 1 cash flow
	Units	Price / Cost per unit	Total
sales revenue	$410	$20,300	$8,323,000
Variable cost	$410	$16,800	($6,888,000)
Fixed cost			($339,000)
Depreciation			($256,500)
OperATING INCOME			$839,500
Taxes (30%)			($251,850)
After tax cash flow			$587,650
Year 2 cash flow			$587,650
Year 3 cash flow			$587,650
Year 4 cash flow			$587,650
Year 5 cash flow			$587,650
Putting the values in the formulas given above
NPV			$687,394

Cash flow are same for all the years since there is no change in units price or units sold as given in questions

Now for Best case scenario, the number of unit sales increase by 10%, variable cost per unit decreases by 10 %, and fixed cost per year also decreases by 10%.

Best case
	Units	Price / Cost per unit	Total
sales revenue	$451	$20,300	$9,155,300
Variable cost	$451	$15,120	($6,819,120)
Fixed cost			($305,100)
Depreciation			($256,500)
OperATING INCOME			$1,774,580
Taxes (30%)			($532,374)
After tax cash flow			$1,242,206
Year 2 cash flow			$1,242,206
Year 3 cash flow			$1,242,206
Year 4 cash flow			$1,242,206
Year 5 cash flow			$1,242,206
NPV			$2,881,567

For the worst case the number of unit sales decreases by 10%, variable cost per unit increases by 10 %, and fixed cost per year also increases by 10%.

Worst
	Units	Price / Cost per unit	Total
sales revenue	$369	$20,300	$7,490,700
Variable cost	$369	$18,480	($6,819,120)
Fixed cost			($372,900)
Depreciation			($256,500)
OperATING INCOME			$42,180
Taxes (30%)			($12,654)
After tax cash flow			$29,526
Year 2 cash flow			$29,526
Year 3 cash flow			$29,526
Year 4 cash flow			$29,526
Year 5 cash flow			$29,526
NPV			($1,183,524)

For checking the sensitivity increase or decrease the fixed cost amount by 5 or 10 % and recalculate the NPV.

For eg - in this case, for every 10% increase or decrease in fixed cost, the NPV decrease or increases by 12% respectively.