Question

You are considering a new product launch. The project will cost $830,000, have a 4-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 220 units per year; price per unit will be $16,425, variable cost per unit will be $11,350, and fixed costs will be $560,000 per year. The required return on the project is 9 percent and the relevant tax rate is 25 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. a. What are the best-case and worst-case NPVs with these projections? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) b. What is the base-case NPV? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) What is the sensitivity of your base-case NPV to changes in fixed costs? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Best-case NPV Worst-case NPV Base case NPV ANPVIAFC c.

Answer 1

Initial cash outlay =$830,000

Annual Depreciation = $830,000/4= $207,500

The best case scenario will be when unit sales are +10%, variable cost and fixed cost are -10%

The worst case scenario will be when unit sales are -10%, variable cost and fixed cost are +10%

The Best case, worst case and Base case scenario for cash flows of year 1-4 are presented below

		BASE	Best	Worst
	SALES (units)	220	242	198
	Price/Unit	16425	16425	16425
	Variable cost/unit	11350	10215	12485
	Sales ($)	3613500	3974850	3252150
Less	Variable Cost ($)	2497000	2472030	2472030
Less	Fixed cost ($)	560000	504000	616000
Less	Depreciation	207500	207500	207500
	Profit before tax	349000	791320	-43380
	Tax	87250	197830	-10845
	Profit after tax	261750	593490	-32535
	Cash flow	469250	800990	174965

a) Best Case NPV = -830,000+ 800990/1.09+ 800990/1.09² + ...+800990/1.09⁴

= -830000+734853.21 +674177.26 +.....+567441.51

= $1,764,983.22

b) Worst Case NPV = -830,000+ 174965/1.09+ 174965/1.09² + ...+174965/1.09⁴

= -830000+160518.35 +147264.54 +.....+123949.62

= - $263,162.41

c)  Base Case NPV = -830,000+ 469250/1.09+ 469250/1.09² + ...+469250/1.09⁴

= -830000+430504.59 +394958.34 +.....+332428.53

= $690,238.55

d) In the base case, if fixed costs increase by 1% ,i.e. from 560,000 to $565,600, the annual cashflows are :

		BASE
	SALES (units)	220
	Price/Unit	16425
	Variable cost/unit	11350
	Sales ($)	3613500
Less	Variable Cost ($)	2497000
Less	Fixed cost ($)	565600
Less	Depreciation	207500
	Profit before tax	343400
	Tax	85850
	Profit after tax	257550
	Cash flow	465050

Base Case NPV = -830,000+ 465050/1.09+ 465050/1.09² + ...+465050/1.09⁴

= -830000+426651.38 +391423.28 +.....+329453.14

= $676,631.73

So, Change in NPV = ( 676631.73- 690238.55)/690238.55 = -.01971

Change in Fixed cost = (565600-560000)/560000= 0.01

So, Sensitivity = -0.01971/0.01 = -1.971