Question

We are evaluating a project that costs $864,000, has an eight-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 71,000 units per year. Price per unit is $49, variable cost per unit is $33, and fixed costs are $765,000 per year. The tax rate is 35%, and we require a 10% return on this project.

a-1. Calculate the accounting break-even point. (Round the final answer to 2 decimal places.)

Break even point             units

a-2. What is the degree of operating leverage at the accounting break-even point? (Round the final answer to 3 decimal places.)

DOL            

b-1. Calculate the base-case cash flow and NPV. (Round the final NPV answers to 2 decimal places. Omit $ sign in your response.)

Cash flow	$  %
ΔNPV/ΔQ	$  %

b-2. What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations. Round the final answer to 3 decimal places. Omit $ sign in your response.)

ΔNPV/ΔQ           $

c. What is the sensitivity of OCF to changes in the variable cost figure? (Negative answers should be indicated by a minus sign. Omit $ sign in your response.)

ΔOCF/ΔVC           $

Answer 1

a1)   Depreciation per year = project costs/ life time of project = 864,000/8

= $108,000

Accounting break-even point =( fixed costs + depreciation) / (selling price– variable costs)

= (765,000 + 108000) / (49-33)

= 873000/16

= 54,563 units (rounded)

A2) Degree of operating leverage = (1+ fixed cost)/ operating cash flows

=(1 + 765000)/108000

= 8.083

B1). Base-case cash flows = [[{(Selling price – Variable cost) x Quantity} – Fixed Costs] x (1-Tax rate)] + (Tax rate x depreciation)

= [[{(49 -33) x71000}-765000] x (1-0.35) +(0.35x108000)]

= 241150 +37800

= $278,950

Present value of cash flows = Cash flows x [{1-1/(1+r)^t}/r]

= 278950 x [{1-1/(1+0.10)^8}/0.10]

= $278,950 x 5.3349

= $1,488,170.36

NPV = {Present value of cash inflows) – (initial cost of project)NPV = $1488170.36 -864000

NPV = $624,170.36

B2). If the sales would drop by 500 units then the NPV is dropped by $27,741.48

C)

To find out how sensitive OCF is to a change in variable costs, we will take variable cost of $34.

Let us calculate change in OCF on increase of variable cost by $1

ΔOCF = (33-34 ) *71000* (1 - tax rate) = - $46150

ΔOCF / ΔVC = - $46150