Question

You are considering a new product launch. The project will cost $4,500,000, have a five-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 750 units per year; price per unit will be $15,500, variable cost per unit will be $12,200, and fixed costs will be $850,000 per year. The required return on the project is 11 percent, and the relevant tax rate is 25 percent. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±12 percent. 1. What are the upper and lower bounds for these projections? What are NPVs for the base-case, the best-case and worst-case scenarios?(20 Points)2. What is the accounting break-even level of output for this project (ignoring taxes)? (5 Points)3. What is the cash break-even level of output for this project (ignoring taxes)? (5 Points)4. What is the financial break-even level of output for this project (ignoring taxes)? (5 Points)5. What is the degree of operating leverage under each scenario?(5 Points)

Answer 1

given variance is + or - 12%,in case of upper bounds we add 12% to base values and in case of lower bounds we deduct 12%

calculation of NPV:

cost of the project = $4,500,000

useful life = 5 years

Depreciation = 4500000 / 5 = 900,000

NOTE: under best case units volume increases by 12% and variable costs,fixed costs decreases by 12%.vice versa in case of worst case scenario.

NPV = PV of cash inflows - initial cash out flow

2)

accounting break even level of output = (Fixed costs + Depreciation) / contribution

contribution = selling price - variable cost

= 15,500 - 12,200 = 3,300

so break even = (850000+900000) / 3300

= 1750000 / 3300 = 530.30 units

3)

cash break even level of output = fixed costs / contribution

= 850000 / 3300 = 257.57 units

4)

usually financial break even = [EAC + FC(1 - tax rate) - D(1-taxrate)] / contribution

where, EAC = Equivalent annual cost ,FC = fixed costs , D = depreciation

here specifically asked to ignore taxes so

financial break even = (EAC + FC -D) / contribution

EAC = initial investment / PVIFA( n = 5 ; r = 11%)

= 4500000 / 3.695897

= 1217566.40

so financial break even = (1217566.40 + 850000 - 900000) / 3300

= 353.81 units

5)

Degree of operating leverage = sale units x contribution / [(sales x contribution) - fixed operating costs)]

operating leverage under base case:

= 750 x 3300 / [(750 x 3300) - 850000]

= 2475000 / 1625000

= 1.523076

under best case:

here fixed costs = 748000

contribution = selling price - variable cost

= 15,500 - 10736

= 4764

sales units = 840

operating leverage = 840 x 4764 / [(840 x 4764) - 748000]

= 4001760 / 3253760

= 1.229887

under worst case:

here fixed costs = 952000

contribution = selling price - variable cost

= 15,500 - 13664

= 1836

sales units = 660

operating leverage = 660 x 1836 / [(660 x 1836) - 952000]

= 1211760 / 259760

= 4.6649214