Question

We are evaluating a project that costs $874,800, has a nine-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 85,000 units per year. Price per unit is $55, variable cost per unit is $39. and fixed costs are $765,000 per year. The tax rate is 24 percent, and we require a return of 11 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.) a- What is the degree of operating leverege at the accounting break-even point? (Do 2. not round intermediate calculations and round your answer to 3 decimal places e.g., 32.161.) 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 units DOL a-2. b-1. Cash flow NPV b-2. ANPVIAQ AOCF/AVC C.

Answer 1

a1)

Breakeven = Fixed expenses / Contribution per unit

Depreciation per year = 874800/ 9 = $ 97200 per year

Total Fixed Cost = $ 765,000 + $ 97200 per year = $ 8,62,200 per year

Contribution per unit = $ 55- $ 39 = $ 16

So, breakeven = 862200/ 16 = 53887.5 units

a2)

Degree of Operating leverage = Sales - Variable cost / (Sales - variable cost - fixed cost)

So, at accounting break-even unit, operating leverage = 53887.5 ($ 55- $ 39)/ [53887.5 ($ 55- $ 39) - 862200]

= 0

Degree of Operating leverage at accounting break-even units is 0.

b3)

We will use the tax shield approach to calculate the OCF.

The OCF is:

OCF base= [(P – v)Q – FC](1 – tc) + tc D

OCFbase= [($55 – 39)(85,000) – $765,000](0.76) + 0.24($97,200)

OCF base= $475,528

Now we can calculate the NPV using our base-case projections.

There is no salvage value or NWC, so the NPV is:

NPV base= –$874,800 + $475,528 (PVIFA 11%,9)

NPV base= -$874,800 + $ 475,528 x 5.5370 = $1,758,198.536

b2)

To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the NPV at a different quantity. We will use sales of 86,000 units.

OCF at this sales level is = [($55 – 39)(86,000) – $765,000](0.76) + 0.24($97,200)

OCF = $487,688

And the NPV at this sales level is

NPV = –$874,800 + $487,688 (PVIFA 11%,9) = -$874,800 + $ 487,688 x 5.5370 = $1,825,528.46

So, NPV for every unit change in sales is = (1825528.46 - 1758198.54)/ (86000-85000) = $67.33

c)

To find out how sensitive OCF is to a change in variable costs,we will compute the OCF at a variable cost of $40.

So, using the tax shield approach, the OCF at a variable cost of $40 is:

OCF new= [($55 – 40)(85,000) – $765,000](0.76) + 0.24($97,200) = $410928

So, the change in OCF for a $1 change in variable costs is:

(410,928 – 475,528)/(40 - 39) = $ 64,600