Question

You are considering a new product launch. The project will cost $1,900,000, have a 4-year life, and have no salvage value; depreciation is straight-line to 0. Sales are projected at 180 units per year, price per unit will be $23,000; variable cost per unit will be $14,500, and fixed costs will be $530,000 per year. The required return on the project is 15%, and the relevant tax rate is 35%. a. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within +10%. 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? (Negative answers should be indicated by a minus sign. Do not round intermediate calculations. Round the final NPV answers to 2 decimal places. Omit $ sign in your response.) Unit Sales Variable Cost Fixed Costs NPV A A Scenario Base Best Worst A A A A b. Evaluate the sensitivity of your base-case NPV to changes in fixed costs. (Negative answers should be indicated by a minus sign. Do not round intermediate calculations. Round the final answer to 3 decimal places. Omit $ sign in your response.) ANPV/AFC $D c. What is the cash break-even level of output for this project (ignoring taxes)? (Round the final answers to the nearest whole unit.) Cash break-even units d-1. What is the accounting break-even level of output for this project? (Round the final answers to the nearest whole unit.)

Answer 1

a)

Variable Cost is per unit

Refer table below for NPV Calculation Base scenario.

Scenario	Unit Sales	Variable Cost	Fixed Cost	NPV
Base	180	14500	530000	-19283.00
Best	198	13050	477000	473443.44
Worst	162	15950	583000	-459848.99

NPV Calculation

		0	1	2	3	4
1	Cost	-1900000
2	Sales Unit		180	180	180	180
3	Price per Unit		23000	23000	23000	23000
4	Total Sales		4140000	4140000	4140000	4140000
5	Variable Cost per Unit		14500	14500	14500	14500
6	Total Variable Cost		2610000	2610000	2610000	2610000
7	Fixed Cost		530000	530000	530000	530000
8	Depreciation (Cost / Project Life)		475000	475000	475000	475000
9	Profit Before Tax (4 - 6 - 7 - 8)		525000	525000	525000	525000
10	Tax @ 35%		341250	341250	341250	341250
11	PAT		183750	183750	183750	183750
12	Adding back Depreciation		658750	658750	658750	658750
13	Present Value @ 15%	-1900000	572826.1	498109.6	433138.8	376642.5
14	NPV	-19283

Ans b)

At Fixed Cost 530000 NPV is - 19283

If we change in fixed cost by 10%

At Fixed Cost 583000 NPV is - 35413

Change in Fixed Cost 53000

Change in NPV - 16130

= - 16130 / 53000 = - 0.304

Ans c)

Cash Break Even = Fixed Cost Excluding Depreciation / (Sales Price - Variable Cost )

= 530000 / (23000 - 14500) = 62.35= 62 (Rounded off)

Ans d - 1)

Accounting Break Even = Fixed Cost including depreciation / (Sales Price - Variable Cost )

= (530000 + 475000) / (23000 - 14500) = 118.24 = 118 (Rounded off)

Ans d - 2)

Degree of Operating Leverage = % Change in EBIT / % Change in Sales

EBIT if Quantity is 180 = 525000

EBIT if Quantity is 118 = -2000

% Change in Quantity = (180 - 118) / 180 =34.44%

% Change in EBIT = (525000 - (-2000)) / 525000 = 100.38%

Degree of Operating Leverage = 2.91

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