Question

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 $570,000 per year. The required return on the project is 9 percent, and the relevant tax rate is 21 percent a. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within 10 percent. What are the upper and lower bounds for these projections? What is the base-case NPV? What are the best-case and worst-case scenarios? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round your NPV answers to 2 decimal places, e.g., 32.16. Round your other answers to the nearest whole number, e.g. 32.) Scenario Unit Sales Variable Cost Fixed Costs NPV Base 570,000$ 513,000 220 $ 11,750 252,299.32 10,575 12,925 Best 242 1,460,965.91 Worst 198 627,000 -824,047.40 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.) 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.) C.

Answer 1

a). Base case NPV calculation table:

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

If the sales number, variable cost and fixed cost are varied by +/- 10%, the scenario table will be:

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: All tables for the scenario analysis cannot be pasted here due to the answer limit but they can be found by changing the relevant numbers in the NPV table.

b). Sensitivity of base-case NPV to changes in fixed cost: If fixed cost falls by 10% then NPV rises to 1,460,965.91

Sensitivity of NPV to change in fixed cost = (change in NPV/change in fixed cost)

= (252,299.32-1,460,965.91)/(570,000-513,000) = 2,120.47% or 21.20 times (ignore the -ive sign as we are measuring 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