Question

Leverage:
Fixed costs and the break-even point:
Firm ABC expects to earn $210,000 next years after taxes. Sales will be $4 mil. The firm produces desks used in colleges. These desks sell for $200 each and have a variable cost per unit of $150. The firm’s tax rate is 30%.
a. What are the firm’s fixed costs expected to be next year?
b. Calculate the firm’s break-even point in both units and dollars.
Leverage analysis:
You have developed the following analytical income statement for your corporation. It represents the most recent year’s operations, which ended yesterday. You are now asked to answer the following questions:
Sales $20 mil.
Variables costs 12 mil.
Fixed costs 5 mil.
EBIT 3 mil.
Interest expense 1 mil.
EBT 2 mil.
Taxes (50%) 1 mil.
Net Income 1 mil.
a. At this level of output, what’s the degree of operating leverage?
b. What’s the degree of financial leverage?
c. What’s the degree of combined leverage?
d. What’s the firm’s break-even point in sales dollars?
e. If sales should increase by 30%, by what percent would earnings before taxes (and net income) increase?
f. Prepare an analytical income statement that verifies the calculations from part (e).

Please provide all work for the problem, not just the answer so it can be modeled for other questions, thank you :)

Answer 1

Leverage

Projected Profits After Tax (PAT) = $210,000

Projected Sales = $4,000,000

Selling Price of Desks= $200

Variable Cost (VC) of Desks= $150

Tax rate= 30%

Calculations

a.) What are the firm’s fixed costs expected to be next year?

Profit Before Tax= ($210,000*100)/70    = $300,000

(As tax rate mentioned 30% hence PAT is 70%, And Profit Before Tax would be 100%)

Fixed Cost= Sales- VC- PBT

Contribution Per Unit= Sales Per Unit - VC per unit

Particular $ Units Price per unit Sales $4,000,000 20,000 $200 Variable Cost $3,000,000 20,000 $150 PAT $210,000 20,000 PBT $300,000 20,000 Contribution Per Unit(sales-VC) $50 Fixed Cost $700,000

Fixed Cost= $700,000

b. Calculate the firm’s break-even point (BEP) in both units and dollars.

Contribution Per Unit(sales-VC) = $50

BEP in Units= FC/Contribution per unit =$700,000/$50 =14000 Units

ABC was at BEP while selling 14000 units of the Desks, whereas projected sales are 20,000 units, anyways he is at profit stage of the operations.

BEP in Dollers= BEP in Units* Sales Price = 14000*$200 = $2,800,000

Leverage Analysis

Sales= $20,000,000

Variables costs =$12,000,000
Fixed costs = $5,000,000
EBIT= $3,000,000
Interest expense = $1,000,000
EBT (Also,EBIT- Interest)= $2,000,000     
Taxes (50%) =$1,000,000
Net Income = $1,000,000
a. At this level of output, what’s the degree of operating leverage (DOL)?

Formulas

DOL= % change in EBIT/ % change in sales OR Contribution margin/ Net operating income

Contribution= Sales - VC= $20m- $12M = $8M

NOI=$3 M

DOL= $8M/ $3M = 2.66

b. What’s the degree of financial leverage (DFL)?

DFL= EBIT/ (EBIT- Interest)

       = $3,000,000/ $2,000,000     

       = 1.5

c. What’s the degree of combined leverage?

DCL= DOL + DFL = 2.66+1.5 = 4.16

d. What’s the firm’s break-even point in sales dollars?

BEP($) = FC/Contribution margin ratio

Contribution margin= $8M

Contribution margin ration= (Contribution / sales)*100 = ($8M/$20M)*100= 40%

        BEP($)    =          $5,000,000/ 0.40 =$12.5 M

e. If sales should increase by 30%, by what percent would earnings before taxes (and net income) increase?

Expected increase in sales im NOI= 30%*2.66 = 79.8%

Expected increase in net operating income($)= $3M*79.8% = $2,394,000

OR EBIT= $2,394,000

EBT= $2,394,000-$1,000,000 (If same interest charged) = $1,394,000

% increase in EBT= (New EBT-Old EBT)/Old EBT

                             ( $2,394,000- $2,000,000)/$2,000,000= 19.7%