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

1. The accounting break-even point is:-

Particular	Amount
Projected Sales	71000 units
Sale price	$                  49
Variable cost	$                  33
Contribution per unit	$                  16
Fixed cost
given	$       765,000
Depreciation(864000/8)	$       108,000
Total fixed cost	$       873,000

Break even point in units	54563
(Fixed cost/ contribution per unit)

2. The degree of operating leverage at the accounting break-even point is:-

For calculation of DOL, it is assumed that OCF is equal to depreciation. So, the DOL at the accounting breakeven is :

DOL = 1+ (Fixed cost/ OCF)

= 1+ (765,000 / 108,000)

DOL= 8.08

3.The base-case cash flow and NPV is:

Particular	Amount
Projected Sales in units	71000
Sale price	$                 49
Variable cost	$                 33
Contribution per unit	$                 16
Contribution in $	1136000
Less: Fixed cost	$      765,000
Income	$      371,000
Less: Tax@35%	$      129,850
Income after tax	$      241,150
Add: Tax on depreciation	$         37,800
Total cash flow	$      278,950

So, we will calculate NPV now. There is no salvage value, so NPV is:

Particular	Year	Amount	Annuity Discount @10%	PV
Cost of the project	0	-864000	1	-864000
Cash InFlow	1 to 8	278950	5.335	1488198.25
NPV(Cash Inflow- Outflow)				624198.25

4. The sensitivity of NPV to changes in the sales figure is:-

For calculation of sensitivity of the NPV to changes in the quantity sold, it is important to calculate NPV at a different quantity say 68000

Cash Flow will be

Particular	Amount
Projected Sales in units	68000
Sale price	$                 49
Variable cost	$                 33
Contribution per unit	$                 16
Contribution in $	1088000
Less: Fixed cost	$      765,000
Income	$      323,000
Less: Tax@35%	$      113,050
Income after tax	$      209,950
Add: Tax on depreciation	$         37,800
Total cash flow	$      247,750

NPV new =

Particular	Year	Amount	Annuity Discount @10%	PV
Cost of the project	0	-864000	1	-864000
Cash InFlow	1 to 8	247750	5.335	1321746.25
NPV(Cash Inflow- Outflow)				457746.25

So change in NPV for every unit change in sales

= (624,198.25-457746.25)/ (71,000-68,000)

= $ 55.483

If sales were to drop by 1000 units, then NPV would drop by ;

NPV drop = $ 55.483 (1000) = $55484

5.The sensitivity of OCF to changes in the variable cost figure is:-

For calculation of sensitive OCF is to change in variable cost, Calculating OCF at different assumed variable cost of $ 30.

So using tax shield approach,

Cash flow at a VC of $30 is = [ (P-V)Q - FC] (1-T) +TD

Particular	Amount
Projected Sales in units	68000
Sale price	$                 49
Variable cost	$                 30
Contribution per unit	$                 19
Contribution in $	1292000
Less: Fixed cost	$      765,000
Income	$      527,000
Less: Tax@35%	$      184,450
Income after tax	$      342,550
Add: Tax on depreciation	$         37,800
Total cash flow	$      380,350

So, the sensitivity in OCF for a $3change in variable costs is:

= ($278,950 - $380,350) / ($33-$30)

= - $33800

Therefore for every variable costs decrease by $3 , OCF would increase by $33800