Question

Problem 11-19 Project Analysis [LO1, 2, 3, 4]

You are considering a new product launch. The project will cost $1,975,000, have a four-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 $17,700, variable cost per unit will be $11,750, and fixed costs will be $570,000 per year. The required return on the project is 9 percent, and the relevant tax rate is 21 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? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round your NPV answers to 2 decimal places, e.g., 32.16. Round your other answers to the nearest whole number, e.g. 32.)
	Scenario Unit Sales Variable Cost Fixed Costs NPV Base 220 $11,750 $570,000 Best Worst

  

  

b.	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.)

  

	b. ΔNPV/ΔFC c. Cash break-even d-1. Accounting break-even d-2. Degree of operating leverage

Answer 1

a). Base-case NPV:

Formula Year (n) Initial investment (11) Number of units (u) Price per unit (p) Variable cost per unit (vc) Fixed cost (FC) Depreciation (D) up-vc)-FC-D EBIT 21%*EBIT Tax @ 21% EBIT-Tax Net income (NI) Add: depreciation (D) NI+D-11 Free Cash Flow (FCF) 1/(1+9%)^n Discount factor @ 9% FCF*Discount factor PV of FCF Sum of all PVs NPV 0 1 2 3 4 1975000 220 2201 2201 2201 17700 17700 177001 17700 11750 117501 117501 117501 570000 570000570000 570000 4937501 493750 493750| 493750 L 2452501 245250245250 51502.5 51502.5 51502.5 51502.5 193747. 5 193747.5| 193747.5 193747.5 493750| 493750 493750 493750 -1975000 687497.5 687497.5| 687497.5 687497.5 1.000 0.917 0.842 0.772 0.708 -1975000 630731.65 578652.891 530874.21 487040.56 252299.32

Scenario analysis is done by changing the fixed cost, variable cost per unit and unit sales by +/- 10% depending on the best-case scenario or the worst case scenario.

Scenario Base Best Worst Unit Sales Variable Cost Fixed Cost NPV 220 117501570000 252299.32| 242 10575 513000 1460965.91 198 12925 627000 -824047.40

Note: NPV calculation table for each scenario is not uploaded due to the answer word limit but it can be found by varying the relevant numbers in the base-case NPV table.

b). Change in NPV to change in FC can be found by considering the base-case and best-case NPVs and FCs.

Change in NPV to change in FC = (base-case NPV - best-case NPV)/(base-case FC - best-case FC)

= (252,299.32-1,460,965.91)/(570,000-513,000) = 21.20 times or 2,120.47% (ignore negative sign as we are calculating sensitivity.)

c). Cash break-even level = fixed cost/(price per unit - variable cost per unit) = 570,000/(17,700-11,750) = 95.80 units

d-1). Accounting break-even level = (fixed cost + depreciation)/(price per unit - variable cost per unit) = (570,000+493,750)/(17,700-11,750) = 178.78 units

d-2). Degree of operating leverage = 1 + (fixed cost/operating cash flow)

Operating cash flow at 178.78 units = u*(p-vc)-FC = 178.78*(17,700-11,750)-570,000 = 493,750

DOL = 1+ (570,000/493,750) = 2.154