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Fundamentals of Financial Manageme...

9th Edition
Eugene F. Brigham + 1 other
ISBN: 9781305635937

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BuyFindarrow_forward

Fundamentals of Financial Manageme...

9th Edition
Eugene F. Brigham + 1 other
ISBN: 9781305635937
Textbook Problem
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FINANCIAL LEVERAGE EFFECTS The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $14 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $4.2 million with a 0.2 probability, $2.8 million with a 0.5 probability, and $700,000 with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios; then evaluate the results:

Debt/Capital Ratio Interest Rate
0%
10 9%
50 11
60 14

Summary Introduction

To identify: The expected return on equity, standard deviation, and coefficient of variance from the given situation.

Introduction:

Return on Equity:

The return, which is generated on the equity that is invested by the stockholders is known as return on equity.

Explanation

The capital ratio at 0% and none interest rate.

Compute the expected return on equity.

State-1

Compute the net income.

Given,

The probability is 0.2.

The EBIT is $4,200,000.

Formula to calculate the net income,

Netincome=(EBITI)×(1T)

Where,

  • EBIT is earning before interest and tax.
  • I is interest.
  • T is tax rate.

Substitute $4,200,000 for EBIT, 0 for I and 0.40 for T.

Netincome=($4,200,0000)×(10.40)=$4,200,000×0.60=$2,520,000

The net income of state 1 is $2,520,000.

Compute the return on equity of state 1.

The net income is $2,520,000. (Calculated above)

The equity is $14,000,000. (Given)

Formula to calculate the return on equity,

Returnonequity=NetincomeEquity×100

Substitute $2,520,000 for net income and $14,000,000 for equity.

Returnonequity=$2,520,000$14,000,000×100=0.18×100=18% (1)

The return on equity of state 1 is 18%.

State-2

Compute the net income.

Given,

The probability is 0.5.

The EBIT is $2,800,000.

Formula to calculate the net income,

Netincome=(EBITI)×(1T)

Where,

  • EBIT is earning before interest and tax.
  • I is interest.
  • T is tax rate.

Substitute $2,800,000 for EBIT, 0 for I and 0.40 for T.

Netincome=($2,800,0000)×(10.40)=$2,800,000×0.60=$1,680,000

The net income of state 2 is $1,680,000.

Compute the return on equity of state 2.

The net income is $1,680,000. (Calculated above)

The equity is $14,000,000. (Given)

Formula to calculate the return on equity,

Returnonequity=NetincomeEquity×100

Substitute $1,680,000 for net income and $14,000,000 for equity.

Returnonequity=$1,680,000$14,000,000×100=0.12×100=12% (2)

The return on equity on state 2 is 12%.

State-3

Compute the net income.

Given,

The probability is 0.3.

The EBIT is $700,000.

Formula to calculate the net income,

Netincome=(EBITI)×(1T)

Where,

  • EBIT is earning before interest and tax.
  • I is interest.
  • T is tax rate.

Substitute $700,000 for EBIT, 0 for I and 0.40 for T.

Netincome=($700,0000)×(10.40)=$700,000×0.60=$420,000

The net income of state 3 is $420,000.

Compute the return on equity of state 3.

The net income is $420,000. (Calculated above)

The equity is $14,000,000. (Given)

Formula to calculate the return on equity,

Returnonequity=NetincomeEquity×100

Substitute $420,000 for net income and $14,000,000 for equity.

Returnonequity=$420,000$14,000,000×100=0.03×100=3% (3)

The return on equity on state 3 is 3%.

Compute the expected return on equity of 3 states.

The return on equity of state 1 is18%. (Calculated in equation (1))

The return on equity of state 2 is 12%. (Calculated in equation (2))

The return on equity of state 3 is 3%. (Calculated in equation (3))

The probability of state 1 is 0.2. (Given)

The probability of state 2 is 0.5. (Given)

The probability of state 3 is 0.3. (Given)

Formula to calculate the expected return on earnings,

Expectedreturnonearnings=Probability×Returnonearnings

Substitute 0.2, 0.5 and 0.3 for probability and 18%, 12% and 3% for return on earnings.

Expectedreturnonearnings=(0.2×18%)+(0.5×12%)+(0.3×3%)=3.60%+6%+0.90%=10.50%

The expected return on earnings is 10.50%.

Compute the standard deviation.

StateProbability

Return on

Equity

(ROE)

Expected

Return on

Equity (EROE)

Deviation

((ROEEROE)^2)×P

10.218%10.50%11.25%
20.512%10.50%1.125%
30.33%10.50%16.88%
 Variance  29.25%

Table (1)

The variance is 29.25%. (Calculated above)

Formula to calculate the standard deviation,

Standarddeviation=Variance

Substitute 29.25% for variance.

Standarddeviation=29.25%=5.408%

The standard deviation is 5.408%.

Compute the coefficient of deviation.

The standard deviation is 5.408%.

The expected return on equity is 10.50%.

Formula to calculate the coefficient of variance,

Coefficientofvariance=StandarddeviationEROE

Where,

  • EORE is expected return on equity.

Substitute 5.408% for standard deviation and 10.25% for EROE.

Coefficientofvariance=5.408%10.50%=0.515

The coefficient of variance is 0.515.

The capital ratio at 10% and interest rateis 9%.

Compute the expected return on equity

Statement to show the computation of return on equity of each state

Table (2)

Compute expected return on equity of 3 states.

The return on equity of state 1 is 19.40%. (Calculated above)

The return on equity of state 2 is 12.73%. (Calculated above)

The return on equity of state 3 is 2.73%. (Calculated above)

The probability of state 1 is 0.2. (Given)

The probability of state 2 is 0.5. (Given)

The probability of state 3 is 0.3. (Given)

Formula to calculate the expected return on earnings,

Expectedreturnonearnings=Probability×Returnonearnings

Substitute 0.2, 0.5 and 0.3 for probability and 19.40%, 12.73% and 2.73% for return on earnings.

Expectedreturnonearnings=(0.2×19.40%)+(0.5×12.73%)+(0.3×2.73%)=3.88%+6.37%+0.82%=11.07%

The expected return on earnings is 11.07%.

Compute the standard deviation

StateProbability

Return on

Equity

(ROE)

Expected

Return on

Equity (EROE)

Deviation

((ROEEROE)^2)×P

10.219.40%11.07%13.88%
20.512.73%11.07%1.378%
30.32.73%11.07%20.87%
 Variance  36.128%

Table 3

The variance is 36.128%. (Calculated above)

Formula to calculate the standard deviation,

Standarddeviation=Variance

Substitute 36.128% for variance.

Standarddeviation=36.128%=6.01%

The standard deviation is 6.01%.

Compute the coefficient of deviation.

The standard deviation is 6.01%.

The expected return on equity is 11.07%.

Formula to calculate the coefficient of variance,

Coefficientofvariance=StandarddeviationEROE

Where,

  • EORE is expected return on equity.

Substitute 6

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