Question

We are evaluating a project that costs $924,000, has an eight-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 75,000 units per year. Price per unit is $46, variable cost per unit is $31, and fixed costs are $825,000 per year. The tax rate is 35 percent, and we require a 15 percent return 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 tata

Answer 1

Depreciation each year = $924000/8 = $115500

In Best Case Scenario

Quantity and price per unit, will be maximum possible 110% of projected figures (10% positive tolerance) ,

So,for best case,

Quantity = 75000*1.1 = 82500 ,

Price per unit = 46*1.1 = 50.6

Variable cost = 31* 0.9 = 27.9

Fixed cost = 825000*0.9 = 742500

Variable costs and fixed costs will be 90% of projected figures (10% negative tolerance)

So,for worst case,

Quantity = 75000*0.9 = 67500 ,

Price per unit = 46*0.9 = 41.4

Variable cost = 31* 1.1 = 34.1

Fixed cost = 825000*1.1 = 907500

Accordingly , the annual cash flows in the best and worst case are calculated as shown below

		Best Case	Worst Case
Quantity	75000	82500	67500
Price	46	50.6	41.4
Sales	3450000	4174500	2794500
Variable cost/Unit	31	27.9	34.1
Total Variable Cost	2325000	2301750	2301750
Fixed Cost	825000	742500	907500
Profit before Depreciation	300000	1130250	-414750
Depreciation	115500	115500	115500
Profit before Tax	184500	1014750	-530250
Tax	64575	355162.5	-185588
Profit after tax	119925	659587.5	-344663
Cash flows	235425	775087.5	-229163

Hence,

NPV (best case) = -924000 + 775087.5 /1.15+ .... +775087.5/1.15⁸

= - 924000 + 775087.5 /1.15 *{ 1- (1/1.15)⁸} / {1- (1/1.15)}

=-924000 + 775087.5 /0.15 * (1-0.326902)

= -924000 + 3478067

= $2554067

NPV (worst case) = -924000 - 229163 /1.15- .... -229163/1.15⁸

= - 924000 - 229163 /1.15 *{ 1- (1/1.15)⁸} / {1- (1/1.15)}

=-924000 - 229163 /0.15 * (1-0.326902)

= -924000 - 1028328

= - $1952328