Question

You are considering a new product launch. The project will cost $2,300,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 310 units per year; price per unit will be $19,200, variable cost per unit will be $13,700, and fixed costs will be $700,000 per year. The required return on the project is 9 percent, and the relevant tax rate is 24 percent.

  

a.	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 upper and lower bounds for these projections? What is the base-case NPV? What are the best-case and worst-case scenarios?

Evaluate 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.)
c.	What is the cash break-even level of output for this project (ignoring taxes)? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
d-1.	What is the accounting break-even level of output for this project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
d-2.	What is the degree of operating leverage at the accounting break-even point? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)

Answer 1

a). Best case and worst case projections:

	Best	Base	Worst
%change	10%	0%	-10%
Unit sales	341	310	279
Variable cost	12,330	13,700	15,070
Fixed cost	630,000	700,000	770,000

Lower and upper bounds:

	Lower bound	Upper bound
Unit sales	279	341
Variable cost	12,330	15,070
Fixed cost	630,000	770,000

Base case NPV:

Formula	Year (n)	0	1	2	3	4
	Initial cost (IC)	(2,300,000)
	Units sold/year (u)		310	310	310	310
	Price/unit (p)		19,200	19,200	19,200	19,200
	Variable cost/unit (vc)		13,700	13,700	13,700	13,700
(u*p)	Revenue ('R)		5,952,000	5,952,000	5,952,000	5,952,000
(u*vc)	Variable cost (VC)		4,247,000	4,247,000	4,247,000	4,247,000
	Fixed cost (FC)		700,000	700,000	700,000	700,000
(-IC/4)	Depreciation (D)		575,000	575,000	575,000	575,000
(R-VC-FC-D)	EBIT		430,000	430,000	430,000	430,000
(24%*EBIT)	Tax @ 24%		103,200	103,200	103,200	103,200
	Net income (NI)		326,800	326,800	326,800	326,800
	Add: depreciation (D)		575,000	575,000	575,000	575,000
(NI+D)	Operating Cash Flow (OCF)		901,800	901,800	901,800	901,800
(IC + OCF)	Free Cash Flow (FCF)	(2,300,000)	901,800	901,800	901,800	901,800
1/(1+d)^n	Discount factor @9%	1.000	0.917	0.842	0.772	0.708
(FCF*Discount factor)	PV of FCF	(2,300,000.00)	827,339.45	759,027.02	696,355.06	638,857.86
Sum of all PVs	NPV	621,579.39

Best-case NPV (using best case numbers from the 1st table) = 2,363,995.33

Worst-case NPV (using worst case numbers from the 1st table) = -911,698.39

(Note: NPV tables for the scenario analysis cannot be posted due to the answer word limit.)

b). Sensitivity of NPV to fixed costs:

Fixed cost	6,30,000	7,00,000
NPV	7,93,932.48	6,21,579.39
Change in fixed cost	70,000
Change in NPV	(1,72,353.10)
NPV/fixed cost	-2.46

Sensitivity of NPV to fixed cost = -2.46

c). Cash break-even point = Fixed cost/(Price per unit - Variable cost per unit) = 700,000/(19,200-13,700) = 127.27

Cash break-even level NPV = -1,852,918.66

d-1). Accountin break-even point = (Fixed cost + depreciation)/(Price per unit - Variable cost per unit)

= (700,000 + 575,000)/(19,200-13,700) = 231.82

Accounting break-even level NPV = -437,161.07

d-2). Degree of operating leverage = 1 + Fixed cost/Depreciation

= 1 + (700,000/575,000) = 2.217