Question

You are considering a new product launch. The project will cost $2,125,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 240 units per year; price per unit will be $18,900, variable cost per unit will be $12,650, and fixed costs will be $630,000 per year. The required return on the project is 9 percent, and the relevant tax rate is 22 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.)

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.)

Answer 1

Solution and Explanation:

Initial Investment = $2,125,000

Useful Life = 4 years

Annual Depreciation = Initial Investment / Useful Life

Annual Depreciation = $2,125,000 / 4

Annual Depreciation = $531,250

Base Case:

Annual OCF = [(Price per unit - Variable Cost per unit) * Sales Quantity - Fixed Cost] * (1 - Tax Rate) + Tax Rate * Depreciation

Annual OCF = $[(\ 18,900-\ 12,650) * 240-\ 630,000] *(1-0.22)+0.22 * \ 531,250$

Annual OCF = $\ 870,000 * 0.78+0.22 * \ 531,250$

Annual OCF = $795,475

NPV = $-\ 2,125,000+\ 795,475 * \text { PVA of } \ 1(9 \%, 4)$

NPV = $-\ 2,125,000+\ 795,475 * 3.23972$

NPV = $452,116.27

Worst Case:

Annual OCF = [(Price per unit - Variable Cost per unit) * Sales Quantity - Fixed Cost] * (1 - Tax Rate) + Tax Rate * Depreciation

Annual OCF = $[(\ 17,010-\ 13,915) * 216-\ 693,000] *(1-0.22)+0.22 * \ 531,250$

Annual OCF = $-\ 24,480 * 0.78+0.22 * \ 531,250$

Annual OCF = $97,780.60

NPV = -$\ 2,125,000+\ 97,780.60 * \text { PVA of } \ 1(9 \%, 4)$

NPV = $-\ 2,125,000+\ 97,780.60 * 3.23972$

NPV = -$1,808,218.23

Best Case:

Annual OCF = [(Price per unit - Variable Cost per unit) * Sales Quantity - Fixed Cost] * (1 - Tax Rate) + Tax Rate * Depreciation

Annual OCF =$[(\ 20,790-\ 11,385) * 264-\ 567,000] *(1-0.22)+0.22 * \ 531,250$

Annual OCF = $\ 1,915,920 * 0.78+0.22 * \ 531,250$

Annual OCF = $1,611,292.60

NPV = $-\ 2,125,000+\ 1,611,292.60 * \text { PVA of } \ 1(9 \%, 4)$

NPV = -$\ 2,125,000+\ 1,611,292.60 * 3.23972$

NPV = $3,095,136.86

Answer 2

A series of cash flows occurring at different dates is given a net present value. The time interval between now and the cash flow determines the present value of a cash flow.

Solution:-

Initial Investment = $2,125,000

Useful Life = 4 years

Annual Depreciation = Initial Investment / Useful Life

Annual Depreciation = $2,125,000 / 4

Annual Depreciation = $531,250

Base Case:

Annual OCF = [(Price per unit - Variable Cost per unit) * Sales Quantity - Fixed Cost] * (1 - Tax Rate) + Tax Rate * Depreciation

Annual OCF=[(18,900-12,650)*240-630,000]*(1-0.22)+0.22*531.250

Annual OCF=$795,475

NPV=-2,125,000+795,475*PVA of 1(9%, 4)

NPV=-2,125,000+795,475*3.23972

NPV=$452,116.27

Worst Case:

Annual OCF = [(Price per unit - Variable Cost per unit) * Sales Quantity - Fixed Cost] * (1 - Tax Rate) + Tax Rate * Depreciation

Annual OCF=[(17,010-13,915)*216-693,000]*(1-0.22)+0.22*531.250

Annual OCF=$97,780.60

NPV=-2,125,000+97,780.60*PVA of 1(9%,4)

NPV=$1,808,218.23

BEST CASE:

Annual OCF = [(Price per unit - Variable Cost per unit) * Sales Quantity - Fixed Cost] * (1 - Tax Rate) + Tax Rate * Depreciation

Annual OCF=[20,790-11,385)*254-567,000]*(1-0.22)+0.22*531,250

Annual OCF=1,915,920*0.78+0.22*531,250

Annual OCF=$1,611,292.60

NPV=-2,125,000+1,611,292.60*PVA of 1(9%,4)

NPV=$3,095,136.86

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