
a)
To calculate: The EPS (earnings per share) under the three scenarios before the debt issue and the changes in EPS while the economy expands a recession.
Introduction:
The EPS is the part of the profit of a firm that is allocated to every outstanding share of common stock. It indicates the profitability of the company.
a)

Answer to Problem 2QP
The EPS under the recession, normal, and expansion periods are $1.74, $2.49, and $2.99 respectively and the percentage of change in EPS is -30% and +20 for the recession and expansion periods respectively.
Explanation of Solution
Given information:
Company P has no debt outstanding and its market value is $180,000. The EBIT (earnings before interest and taxes) are expected to be $23,000 at normal economic conditions. If the economy condition is strong, then EBIT will increase to 20% and if the economy enters into recession, then it will decrease to 30%. The tax rate of the company is 35%.
Formula to calculate taxes:
Compute taxes for three periods:
Hence, the tax during recession is $5,635.
Hence, the tax during the normal period is $8,050.
Hence, the tax during expansion is $9,660.
Formula to calculate the NI (net income):
Compute NI for three periods:
Hence, the NI during recession is $10,465.
Hence, the NI during normal period is $14,950.
Hence, the NI during expansion period is $17,940.
Formula to calculate EPS:
Compute EPS:
Hence, the EPS during recession period is $1.74.
Hence, the EPS during normal period is $2.49.
Hence, the EPS during expansion period is $2.99.
Table showing the income statement for the three possible periods of economy with the EPS and percentage change in EPS:
Recession | Normal | Expansion | |
EBIT | $16,100 | $23,000 | $27,600 |
Interest | 0 | 0 | 0 |
Taxes | 5,635 | 8,050 | 9,660 |
NI | $10,465 | $14,950 | $17,940 |
EPS | $1.74 | $2.49 | $2.99 |
%EPS | –30 | NIL | +20 |
Note:
It is given that during the recession period, the EBIT will decrease to 35% and during the expansion period, EBIT will increase to 25%.
b)
To calculate: The EPS under the three scenarios before the debt issue and the changes in EPS while the economy expands a recession by assuming that the firm undergoes the planned recapitalization.
Introduction:
The EPS is the part of the profit of a firm that is allocated to every outstanding share of common stock. It indicates the profitability of the company.
b)

Answer to Problem 2QP
After recapitalization, the EPS under the recession, normal, and expansion periods are $2.02, $3.30, and $4.15 respectively and the percentage of change in EPS is -38.79% and +25.76 for the recession and expansion periods respectively.
Explanation of Solution
Given information:
The company is considering the debt issue of $75,000 with the rate of interest at 7%. At present, outstanding shares of $6,000 exist.
Formula to calculate the share price:
Compute the share price:
Hence, the price of the share is $30.
Formula to calculate the repurchased shares:
Compute the repurchased shares:
Hence, the repurchased shares are $2,500.
Formula to calculate the payment of interest:
Compute the payment of interest:
Hence, the payment of interest is $5,250.
Formula to calculate taxes:
Compute taxes for the three periods:
Hence, the tax during recession is $3,797.5.
Hence, the tax during normal period is $6,212.5.
Hence, the tax during expansion period is $7,822.5.
Formula to calculate the NI:
Compute NI for three periods:
Hence, the NI during recession is $6,143.
Hence, the NI during normal period is $11,537.5.
Hence, the NI during expansion period is $14,527.5.
Formula to calculate EPS:
Compute EPS:
Hence, the EPS at recession period is $2.02.
Hence, the EPS at normal period is $3.30.
Hence, the EPS at expansion period is $4.15.
Note: After recapitalization, $2,500 was recovered from the total outstanding shares of $6,000. Now, the shares outstanding is $6,000-$2,500=$3,500.
Formula to calculate the percentage change in EPS:
Compute the percentage change in EPS for recession period:
Hence, the percentage change in EPS for recession period is -$38.79.
Compute the percentage change in EPS for expansion period:
Hence, the percentage change is EPS for expansion period is 25.76.
Table showing the income statement for the three possible periods of economy under the planned recapitalization with the EPS and percentage change in EPS:
Recession | Normal | Expansion | |
EBIT | $16,100 | $23,000 | $27,600 |
Interest | 5,250 | 5,250 | 5,250 |
Taxes | 3,797.5 | 6,212.5 | 7,822.5 |
NI | $7,052.5 | $11,537.5 | $14,527.5 |
EPS | $2.02 | $3.30 | $4.15 |
%EPS | –38.79 | NIL | +25.76 |
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Chapter 16 Solutions
Fundamentals of Corporate Finance Standard Edition
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