
a)
To calculate: The
Introduction:
The ROE (return on equity) is the profitability measure that computes the amount of dollars a firm creates with every dollar of a shareholder’s equity.
a)

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 a recession, then it will decrease to 30%. The company has the market to book value ratio of 1.0%.
Formula to calculate the ROE:
Compute ROE:
Hence, the ROE during recession period is 0.0894.
Hence, the ROE during normal period is 0.1278.
Hence, the ROE during expansion period is 0.1533.
Formula to calculate the percentage change in ROE:
Compute the percentage change in ROE for recession period:
Hence, the percentage change in ROE for recession period is -$30.
Compute the percentage change in ROE for expansion period:
Hence, the percentage change is ROE for expansion period is +20.
Table showing the ROE for the three possible periods of economy under the present capital structure with no taxes:
Recession | Normal | Expansion | |
ROE | 0.0894 | 0.1278 | 0.1533 |
%ΔROE | –30 | 0 | 20 |
b)
To calculate: The return on equity for the three economic scenarios before any issue of debt and compute the percentage changes in ROE, assuming that the company goes through a proposed recapitalization.
Introduction:
The ROE (return on equity) is the profitability measure that computes the amount of dollars a firm creates with every dollar of a shareholder’s equity.
b)

Explanation of Solution
Given information:
The company is considering the debt issue of $75,000 with the rate of interest at7%. At present, the 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.
Table showing the income statement for the three possible periods of economy under the planned recapitalization:
Recession | Normal | Expansion | |
EBIT | $16,100 | $23,000 | $27,600 |
Interest | 5,250 | 5,250 | 5,250 |
NI | $10,850 | $17,750 | $22,350 |
Note:
- The NI (net income) is computed by subtracting the interest from the EBIT.
Formula to calculate equity:
Compute the equity:
Hence, the equity is $105,000.
Formula to calculate the ROE:
Compute ROE:
Hence, the ROE during recession period is 0.10.
Hence, the ROE during normal period is 0.22.
Hence, the ROE during expansion period is 0.26.
Formula to calculate the percentage change in ROE:
Compute the percentage change in ROE for recession period:
Hence, the percentage change in ROE for recession period is -$54.55.
Compute the percentage change in ROE for expansion period:
Hence, the percentage change in ROE for expansion period is +18.18.
Table showing the ROE and the percentage changes in ROE for the three possible periods of economy under the present capital structure with no taxes:
Recession | Normal | Expansion | |
ROE | 0.10 | 0.22 | 0.26 |
%ΔROE | –54.55 | 0 | +18.18 |
c)
To calculate: The return on equity for the three economic scenarios before any issue of debt and compute the percentage changes in return on equity with the rate of tax at35%.
Introduction:
The ROE (return on equity) is the profitability measure that computes the amount of dollars a firm creates with every dollar of a shareholder’s equity.
c)

Explanation of Solution
If a firm maintains its present capital structure with the corporate taxes, then the ROE is as follows:
Formula to calculate taxes:
Compute taxes for three periods:
Hence, the tax during recession is $5,635.
Hence, the tax during normal period is $8,050.
Hence, the tax during expansion is $9,660.
Formula to calculate the NI:
Compute NI for three periods:
Hence, the net income during recession is $10,465.
Hence, the net income during normal period is $14,950.
Hence, the net income during expansion period is $17,940.
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 |
Note:
- The NI is computed by subtracting the interest and taxes from the EBIT.
Formula to calculate the ROE:
Compute ROE:
Hence, the ROE during recession period is 0.0894.
Hence, the ROE during recession period is 0.1278.
Hence, the ROE during expansion period is 0.1533.
Formula to calculate the percentage change in ROE:
Compute the percentage change in ROE for recession period:
Hence, the percentage change in ROE for recession period is -$30.
Compute the percentage change in ROE for expansion period:
Hence, the percentage change is ROE for expansion period is +20.
Table showing the ROE and the percentage changes in ROE for the three possible periods of economy under the present capital structure with corporate taxes:
Recession | Normal | Expansion | |
ROE | 0.0894 | 0.1278 | 0.1533 |
%ΔROE | –30 | 0 | +20 |
If a firm undertakes the planned recapitalization with the corporate taxes, then the ROE is as follows:
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 |
Formula to calculate the ROE:
Compute ROE:
Hence, the ROE during recession period is 0.0672.
Hence, the ROE during normal period is 0.1099.
Hence, the ROE during expansion period is 0.1384.
Formula to calculate the percentage change in ROE:
Compute the percentage change in ROE for recession period:
Hence, the percentage change in ROE for recession period is -$38.85.
Compute the percentage change in ROE for expansion period:
Hence, the percentage change is ROE for expansion period is +25.93.
Table showing the ROE and the percentage changes in ROE for the three possible periods of economy under the present capital structure with corporate taxes:
Recession | Normal | Expansion | |
ROE | 0.0672 | 0.1099 | 0.1384 |
%ΔROE | -$38.85 | 0 | +25.93 |
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Chapter 16 Solutions
Fundamentals Of Corporate Finance, Tenth Standard Edition
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