Fin 370, Problem 1

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Problem #1, Chapter 20
1. Firm A has $10,000 in assets entirely financed with equity. Firm B also has $10,000 in assets, but these assets are financed by $5,000 in debt (with a 10 percent rate of interest) and $5,000 in equity. Both firms sell 10,000 units of output at $2.50 per unit. The variable costs of production are $1, and fixed production costs are $12,000. (To ease the calculation, assume no income tax.)
a. What is the operating income (EBIT) for both firms?
Units sold*price per unit = Sales = 10000*2.5=25000
Units sold*Variable cost = Variable cost = 10000*1=10000
Fixed cost = 12000
Sales – Cost= EBIT=25000-10000-12000=3000 for both Firm A and Firm B
b. What are the earnings after interest?
Calculate interest and subtract it from EBIT to get earnings after interest.
Firm A: Interest=0; Earnings after interest=3000
Firm B: Interest= 5000*10%=500; 3000 – 500 = 2500; Earnings after interest=2500

c. If sales increase by 10 percent to 11,000 units, by what percentage will each firm's earnings after interest income increase? To answer the question, determine the earnings after taxed and compute the percentage increase in these earnings from the answers you derived in part b.
Units sold*price per unit = Sales = 11000*2.5=27500
Units sold*Variable cost = Variable cost = 11000*1=11000
Fixed cost = 12000
Sales – Cost = EBIT=27500-11000-12000=4500 for both Firm A and Firm B

Firm A: Interest=0 Earnings after tax=4500
Firm B: Interest= 5000*10%=500; 4500-500 = 4000; Earnings after tax = 4000

Percentage of increase equals difference in EBIT/EBIT in question a
Firm A = (4500-3000)/3000 = 50%
Firm B = (4000-2500)/2500 = 60%

d. Why are the percentage changes different?
The reason for the difference in percentage increase is the difference in interest. Even with a higher sales total, Firm A will have a lesser increase because there is no interest to deduct, which only changes the total by the units sold. Firm B, on the other hand, has

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