ESSENTIALS CORPORATE FINANCE + CNCT A.
ESSENTIALS CORPORATE FINANCE + CNCT A.
9th Edition
ISBN: 9781259968723
Author: Ross
Publisher: MCG CUSTOM
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Chapter 13, Problem 3QP

a)

Summary Introduction

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.

Introduction:

The ROE (Return on equity) is a profitability measure that computes the amount of dollar a firm creates with every dollar of shareholders equity.

a)

Expert Solution
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Explanation of Solution

Given information:

Company K has no debt outstanding and its market value is $194,775. The EBIT (Earnings before interest and taxes) are expected to be $13,800 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 35%. The company has the market to book value ratio of 1.0%.

Formula to calculate the ROE:

ROE=NI (Net income)Market value

Compute the ROE:

ROE at recession period=NI (Net income)Market value=$8,970$194,775=0.0461 or 4.61%

Hence, the ROE during recession period is 4.61.

ROE at normal period=NI (Net income)Market value=$13,800$194,775=0.0709 or 7.09%

Hence, the ROE during normal period is 7.09%.

ROE at expansion period=NI (Net income)Market value=$16,560$194,775=0.0850 or 8.50%

Hence, the ROE during expansion period is 8.50%.

Formula to calculate the percentage change in ROE:

Percentage change in ROE=Changes in ROEROE at normal period×100

Compute the percentage change in ROE for recession period:

Percentage change in ROE=Changes in ROEROE at normal period×100=0.04610.07090.0709×100=35%

Hence, the percentage change in ROE for recession period is -$35.

Compute the percentage change in ROE for expansion period:

Percentage change in ROE=Changes in ROEROE at normal period×100=$0.0850$0.0709$0.0709×100=+20

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 4.61% 7.09% 8.50%
%ΔROE –35% 0 20%

b)

Summary Introduction

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 assuming that the company goes through a proposed recapitalization.

Introduction:

The ROE (Return on equity) is a profitability measure that computes the amount of dollar a firm creates with every dollar of shareholders equity.

b)

Expert Solution
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Explanation of Solution

Given information:

The company is considering the debt issue of $39,750 with the rate of interest @6%. At present, the outstanding shares of $7,350 exist.

Formula to calculate the share price:

Share price=Equity Shares outstanding

Compute the share price:

Share price=Equity Shares outstanding=$194,7757,350=$26.5

Hence, the price of the share is $26.5.

Formula to calculate the repurchased shares:

Shares repurchased=Debt issuedShare price

Compute the repurchased shares:

Shares repurchased=Debt issuedShare price=$39,750$26.5=$1,500

Hence, the repurchased shares are $1,500.

Formula to calculate the payment of interest:

Interest payment=Debt issued× Rate of interest

Compute the payment of interest:

Interest payment=Debt issued× Rate of interest=$39,750×0.06=$2,385

Hence, the payment of interest is $2,385.

Table showing the income statement for the three possible periods of economy under the planned recapitalization:

  Recession Normal Expansion
EBIT $8,970 $13,800 $16,560
Interest 2,385 2,385 2,385
NI $6,585 $11,415 $14,175

Note:

  • The net income is computed by subtracting the interest from the EBIT.

Formula to calculate the equity:

Equity=Market valueDebt amount

Compute the equity:

Equity=Market valueDebt amount=$194,775$39,750=$155,025

Hence, the equity is $155,025.

Formula to calculate the ROE:

ROE=NI (Net income)Equity

Compute ROE:

ROE at recession period=NI (Net income)Equity=$6,585$155,025=0.0425 or4.25%

Hence, the ROE during recession period is 0.0425.

ROE at normal period=NI (Net income)Equity=$11,415$155,025=0.0736 or 7.36%

Hence, the ROE during normal period is 0.0736.

ROE at expansion period=NI (Net income)Equity=$14,175$155,025=0.0914or 9.14%

Hence, the ROE during expansion period is 0.0914.

Formula to calculate the percentage change in ROE:

Percentage change in ROE=Changes in ROEROE at normal period×100

Compute the percentage change in ROE for recession period:

Percentage change in ROE=Changes in ROEROE at normal period×100=$0.0425$0.0736$0.0736×100=42.31%

Hence, the percentage change in ROE for recession period is -$42.31.

Compute the percentage change in ROE for expansion period:

Percentage change in ROE=Changes in ROEROE at normal period×100=$0.0914$0.0736$0.0736×100=+24.18

Hence, the percentage change in ROE for expansion period is +24.18.

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 4.25% 7.36% 9.14%
%ΔROE –42.31% 0 +24.18%

c)

Summary Introduction

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 @35%.

Introduction:

The ROE (Return on equity) is a profitability measure that computes the amount of dollar a firm creates with every dollar of shareholders equity.

c)

Expert Solution
Check Mark

Explanation of Solution

Given information:

Company K has no debt outstanding and its market value is $194,775. The EBIT (Earnings before interest and taxes) are expected to be $13,800 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 35%. The company has the market to book value ratio of 1.0%.

If a firm maintains its present capital structure with the corporate taxes, then the ROE is as follows:

Formula to calculate the taxes:

Taxes=EBIT×Tax rate

Compute the taxes for three periods:

Tax during recession=EBIT×Tax rate=$8,970×0.35=$3,139.5

Hence, the tax during recession is $3,139.5.

Tax during normal=EBIT×Tax rate=$13,800×0.35=$4,830

Hence, the tax during normal period is $4,830.

Tax during expansion=EBIT×Tax rate=$16,560×0.35=$5,796

Hence, the tax during expansion is $5,796.

Formula to calculate the NI (Net Income):

NI=EBITTaxes

Compute NI for three periods:

NI during recession period=EBITTaxes=$8,970$3,139.5=$5,830.5

Hence, the net income during recession is $8,872.

NI during normal period=EBITTaxes=$13,8004,830=$8,970

Hence, the net income during normal period is $8,970.

NI during expansion period=EBITTaxes=$16,5605,796=$10,764

Hence, the net income during expansion period is $10,764.

Table showing the income statement for the three possible periods of economy with the EPS and percentage change in EPS:

  Recession Normal Expansion
EBIT $8,970 $13,800 $7,590
Interest 0 0 0
Taxes 3,139.5 4,830 5,796
NI $5,830.5 $8,970 $10,764
 

Note:

  • The net income is computed by subtracting the interest and taxes from the EBIT.

Formula to calculate the ROE:

ROE=NI (Net income)Market value

Compute ROE:

ROE at recession period=NI (Net income)Market value=$5,830.5$194,775=2.99%

Hence, the ROE during recession period is 2.99%.

ROE at normal period=NI (Net income)Market value=$8,970$194,775=4.61%

Hence, the ROE during recession period is 4.61%.

ROE at expansion period=NI (Net income)Market value=$10,764$194,775=5.53%

Hence, the ROE during expansion period is 5.53%.

Formula to calculate the percentage change in ROE:

Percentage change in ROE=Changes in ROEROE at normal period×100

Compute the percentage change in ROE for recession period:

Percentage change in ROE=Changes in ROEROE at normal period×100=$0.029934539$0.046053138$0.046053138×100=35

Hence, the percentage change in ROE for recession period is -$35.

Compute the percentage change in ROE for expansion period:

Percentage change in ROE=Changes in ROEROE at normal period×100=$0.055263765$0.046053138$0.046053138×100=+20

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 2.99% 4.61% 5.53%
%ΔROE –35% 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:

Interest payment=Debt issued× Rate of interest

Compute the payment of interest:

Interest payment=Debt issued× Rate of interest=$39,750×0.06=$2,385

Hence, the payment of interest is $2,385.

Formula to calculate the taxes:

Taxes=(EBITInterest)×Tax rate

Compute the taxes for the three periods:

Tax during recession period=(EBITInterest)×Tax rate=(8,9702,385)×0.35=$2,304.75

Hence, the tax during recession period is $2,304.75.

Tax during normal period=(EBITInterest)×Tax rate=(13,8002,385)×0.35=$3,995.25

Hence, the tax during normal period is $3,995.25.

Tax during expansion period=(EBITInterest)×Tax rate=(16,5602,385)×0.35=$4,961.25

Hence, the tax during expansion period is $4,961.25.

Formula to calculate the NI (Net Income):

NI=EBITTaxes

Compute NI for three periods:

NI during recession=EBITInterestTaxes=$8,970$2,385$2,304.75=$4,280.25

Hence, the net income during recession is $4,280.25.

NI during normal=EBITInterestTaxes=$13,800$2,385$3,995.25=$7,419.75

Hence, the net income during normal period is $7,419.75.

NI during expansion=EBITInterestTaxes=$16,560$2,385$4,961.25=$9,213.75

Hence, the net income during expansion period is $9,213.75

Table showing the income statement for the three possible periods of economy under the planned recapitalization:

  Recession Normal Expansion
EBIT $8,970 $13,800 $16,560
Interest $2,385 $2,385 $2,385
Taxes $2,304.75 $3,995.25 $4,961.25
NI $4,280.25 $7,419.75 $9,213.75

Formula to calculate the ROE:

ROE=NI (Net income)Equity

Compute the ROE:

ROE at recession period=NI (Net income)Equity=$4,280.25$155,025=2.76%

Hence, the ROE during recession period is 2.76%.

ROE at normal period=NI (Net income)Equity=$7,419.75$155,025=4.79%

Hence, the ROE during normal period is 4.79%.

ROE at expansion period=NI (Net income)Equity=$9,213.75$155,025=5.94%

Hence, the ROE during expansion period is 5.94%.

Formula to calculate the percentage change in ROE:

Percentage change in ROE=Changes in ROEROE at normal period×100

Compute the percentage change in ROE for recession period:

Percentage change in ROE=Changes in ROEROE at normal period×100=$0.027610062$0.047861635$0.047861635×100=42.31%

Hence, the percentage change in ROE for recession period is -$42.31%.

Compute the percentage change in ROE for expansion period:

Percentage change in ROE=Changes in ROEROE @ normal period×100=$0.059433962$0.047861635$0.047861635×100=+24.18

Hence, the percentage change is ROE for expansion period is +24.18.

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 2.76% 4.79% 5.94%
%ΔROE –42.31% 0 +24.18%

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Chapter 13 Solutions

ESSENTIALS CORPORATE FINANCE + CNCT A.

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