Question

We are evaluating a project that costs $560,400, has a six-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 80,000 units per year. Price per unit is $38, variable cost per unit is $24, and fixed costs are $680,000 per year. The tax rate is 22 percent, and we require a return of 10 percent on this project. a-1.Calculate the accounting break-even point. (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) 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.) a- 2. b-1.Calculate the base-case cash flow and NPV. (Do not round intermediate calculations. Round your cash flow answer to the nearest whole number, e.g., 32. Round your NPV answer to 2 decimal places, e.g., 32.16.) b- What is the sensitivity of NPV to changes in the quantity sold? (Do not round 2. intermediate calculations and round your answer to 2 decimal places, e.g.,32.16.) c. What is the sensitivity of OCF to changes in the variable cost figure? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32. a-1. Break-even point a-2. DOL b-1. Cash flow units NPV

Answer 1

Check the explanation

Step-by-step explanation:

Part a-1

Calculate the accounting break-even point

At break-even point the net income is zero

Quantity Q = 80,000

Price per unit P = $38

Unit Variable cost VC = $24

Fixed costs FC = $680,000

Tax rate t = 22%

Net income NI = (Q * (P - VC) - FC)) * (1 - t)

Q = (NI / (1 - t) + FC) / (P - VC)

= FC / (P - VC)

= $680,000 / ($38 - $24)

= 48571.43

Accounting break-even = Q * P

= 48571.43 * $38

= $1,845,714.29

The accounting break-even point is $1,845,714.29

Part a-2

Calculate the degree of operating Leverage at accounting break-even level

Fixed costs = $680,000

Asset Investment = $560,400

Project life = 6 years

Depreciation = Asset Investment / Project life

= $560,400 / 6

= $93,400

At accounting breakeven level the operating cash flow is equal to depreciation

Operating cash flow = Depreciation

= $93,400

Degree of operating Leverage = 1 + Fixed costs / operating cash flow

= 1 + $680,000 / $93,400

= 8.2805

The degree of operating Leverage at accounting break-even level is 8.2805

Part b-1

Calculate the base case Cash flow and NPV

Asset Investment = $560,400

Quantity Q = 80,000

Price per unit P = $38

Unit Variable cost VC = $24

Fixed costs FC = $680,000

Tax rate t = 22%

Required return r = 10%

Project life n = 6 years

Depreciation D = $93,400

PVIFA(r,n) = (1 - (1 + r)^-n)/r

Cash flow = (Q * P - (Q * VC + FC)) * (1 - t) + D * t

= (80,000 * $38 - (80,000 * $24 + $680,000)) * (1 - 22%) + $93,400 * 22%

= $363,748.00

The base case Cash flow is $363,748.00

NPV = Cash flow * PVIFA(10%,6) - Asset Investment

= $363,748.00 * (1 - (1 + 10%)^-6)/10% - $560,400

= $1,023,817.37

The base case NPV is $1,023,817.37

Part b-2

Calculate the sensitivity of NPV to changes in quantity sold

Assume a 10% quantity increase

Base case Quantity Q0 = 80,000

New case Quantity Q1 = Q0 * (1 + 10%)

= 80,000 * (1 + 10%)

= 88,000

Cash flow CF1 = (Q * P - (Q * VC + FC)) * (1 - t) + D * t

= (88,000 * $38 - (88,000 * $24 + $680,000)) * (1 - 22%) + $93,400 * 22%

= $451,108

Base case NPV = $1,023,817.37

NPV1 = CF1 * PVIFA(10%,6) - Asset Investment

= $451,108 * (1 - (1 + 10%)^-6)/10% - $560,400

= $1,404,292.94

∆Q = Q1 - Q0

= 88,000 - 80,000

= 8,000

∆NPV = NPV1 - Base case NPV

= $1,404,292.94 - $1,023,817.37

= $380,475.57

Sensitivity = ∆NPV / ∆Q

= $380,475.57 / 8,000

= $47.56

The sensitivity of NPV to changes in quantity sold is $47.56

Part c

Calculate the sensitivity of OCF to change in variable cost

Assume the variable cost increase by 10%

Base case variable cost VC0 = $24

New case Variable cost VC1 = VC0 * (1 + 10%)

= $24 * (1 + 10%)

= $26.40

Base case cash flow OCF0 = $363,748.00

New case cash flow OCF1 = (Q * P - (Q * VC1 + FC)) * (1 - t) + D * t

= (80,000 * $38 - (80,000 * $26.40 + $680,000)) * (1 - 22%) + $93,400 * 22%

= $213,988.00

∆OCF = OCF1 - OCF0

= $213,988.00 - $363,748.00

= -$149,760.00

∆VC = VC1 - VC0

= $26.40 - $24

= $2.40

Sensitivity = ∆OCF / ∆VC

= -$149,760.00 / $2.40

= -$62,400

The sensitivity of OCF to change in variable cost -$62,400