Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
9th Edition
ISBN: 9781259277214
Author: Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Bradford D Jordan Professor
Publisher: McGraw-Hill Education
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Chapter 3, Problem 45QP

Internal and Sustainable Growth Rates. Best Buy reported the following numbers (in millions) for the years ending February 1, 2014, and January 31, 2015. What are the internal and sustainable growth rates? What are the internal and sustainable growth rates using ROE × b and (ROA × b) and the end of period equity (assets)? What are the growth rates if you use the beginning of period equity in this equation? Why aren’t the growth rates the same? What is your best estimate of the internal and sustainable growth rates?

  2014 2015
Net income   $ 1,233
Dividends   251
Total assets $14,013 15,256
Total equity 3,986 4,995
Expert Solution & Answer
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Summary Introduction

To discuss: The internal growth rate and sustainable growth rate and calculate the rates, growth rate by using the starting of period equity, the reason for the similar growth rates and the best estimate the internal and sustainable growth rates.

Introduction:

The rate of internal growth is the highest growth rate which can be achieved without any kind of external financing. The rate of sustainable growth is the highest growth rate which can be achieved without external equity financing.

Answer to Problem 45QP

The ROA in the beginning is 8.80% and in the end is 8.08% respectively. The ROE in the beginning is 30.93% and the ROE in the end is 24.68%.

Explanation of Solution

Given information:

The net income of Company B for the year 2015 is $1,233. The dividend in the year 2015 is 251. The total assets for the year 2014 and 2015 are $14,013 and $15,256 respectively. The total equity for 2014 and 2015 are $3,986 and $4,995 respectively.

Formula to compute the ROA in the beginning:

ROABegin=Net incomeTotal assets

Compute the ROA in the beginning:

ROABegin=Net incomeTotal assets in 2014=$1,233$14,013=0.0880 or 8.80%

Hence, the ROA in the beginning is 8.80%.

Compute the ROA in the end:

ROAEnd=Net incomeTotal assets in 2015=$1,233$15,256=0.0808 or 8.08%

Hence, the ROA in the end is 8.08%.

Formula to compute the ROE using the starting period equity:

ROEBegin=Net incomeTotal equity

Compute the ROE using the starting period equity:

ROEBegin=Net incomeTotal equity in 2014=$1,233$3,986=0.3093 or 30.93%

Hence, the ROE in the beginning is 30.93%.

Compute the ROE using the end of period equity:

ROEEnd=Net incomeTotal equity in 2015=$1,233$4,995=0.2468 or 24.68%

Hence, the ROE in the end is 24.68%.

Formula to compute the retention ratio:

b=1DividendsNet income

Compute the retention ratio:

b=1DividendsNet income=1$251$1,233=0.7964 or 79.64%

Hence, the retention ratio is 79.64%.

Formula to compute the internal growth rate:

Internal growth rate=[(ROA)(b)1(ROA)(b)]

Where,

ROA denotes the return on assets.

b denotes the retention or plowback ratio.

Calculate the internal growth rate:

Internal growth rate=[(ROA)(b)1(ROA)(b)]=[0.0808(0.7964)10.0808(0.7964)]=0.0688 or 6.88%

Hence, the internal growth rate is 6.88%.

Formula to calculate the sustainable growth rate:

Sustainable growth rate=ROE×b1ROE×b

Where,

ROE denotes the return on equity.

b denotes the retention or plowback ratio.

Compute the sustainable growth rate:

Sustainable growth rate=ROE×b1ROE×b=0.2088×0.796410.2088×0.5737=0.2447 or 24.47%

Hence, the sustainable growth rate is 24.47%.

Formula to compute the internal growth rate using ROA at the end:

Internal growth rate=ROAEND×b

Compute the internal growth rate using ROA at the end:

Internal growth rate=ROAEND×b=0.0808×0.7964=0.0644or 6.44%

Hence, the internal growth rate is 6.44%.

Formula to compute the sustainable growth rate using ROE at the end:

Sustainable growth rate=ROEEND×b

Compute the sustainable growth rate using ROE at the end:

Sustainable growth rate=ROEEND×b=0.2468×0.7964=0.1966or 19.66%

Hence, the sustainable growth rate is 19.66%.

Formula to compute the internal growth rate using ROA at the beginning:

Internal growth rate=ROABegin×b

Compute the internal growth rate using ROA at the beginning:

Internal growth rate=ROABegin×b=0.0880×0.7964=0.0701or 7.01%

Hence, the internal growth rate is 7.01%.

Formula to compute the sustainable growth rate using ROE at the beginning:

Sustainable growth rate=ROEBegin×b

Compute the sustainable growth rate using ROE at the beginning:

Sustainable growth rate=ROEBegin×b=0.3093×0.7964=0.2464 or 24.64%

Hence, the sustainable growth rate is 24.64%.

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Chapter 3 Solutions

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)

Ch. 3.4 - Why is the sustainable growth rate likely to be...Ch. 3.5 - Prob. 3.5ACQCh. 3.5 - Prob. 3.5BCQCh. 3.5 - Prob. 3.5CCQCh. 3.5 - Prob. 3.5DCQCh. 3 - Section 3.1A common-size balance sheet expresses...Ch. 3 - What are the categories of traditional financial...Ch. 3 - Prob. 3.3CCh. 3 - Prob. 3.4CCh. 3 - Prob. 3.5CCh. 3 - Current Ratio. What effect would the following...Ch. 3 - Current Ratio and Quick Ratio. In recent years,...Ch. 3 - Prob. 3CTCRCh. 3 - Financial Ratios. Fully explain the kind of...Ch. 3 - Standardized Financial Statements. What types of...Ch. 3 - Prob. 6CTCRCh. 3 - Prob. 7CTCRCh. 3 - Prob. 8CTCRCh. 3 - Industry-Specific Ratios. So-called same-store...Ch. 3 - Industry-Specific Ratios. There are many ways of...Ch. 3 - Prob. 11CTCRCh. 3 - Financial Statement Analysis. In the previous...Ch. 3 - Prob. 1QPCh. 3 - Calculating Profitability Ratios. Aguilera, Inc.,...Ch. 3 - Calculating the Average Collection Period. Ordonez...Ch. 3 - Calculating Inventory Turnover. Bobaflex...Ch. 3 - Calculating Leverage Ratios. Fincher, Inc., has a...Ch. 3 - Calculating Market Value Ratios. Rossdale, Inc.,...Ch. 3 - Prob. 7QPCh. 3 - DuPont Identity. Jiminy Cricket Removal has a...Ch. 3 - Calculating Average Payables Period. For the past...Ch. 3 - Equity Multiplier and Return on Equity. Shelton...Ch. 3 - Internal Growth. If Williams, Inc., has an ROA of...Ch. 3 - Sustainable Growth. If the Crash Davis Driving...Ch. 3 - Sustainable Growth. Based on the following...Ch. 3 - Prob. 14QPCh. 3 - Prob. 15QPCh. 3 - Calculating Financial Ratios. Based on the balance...Ch. 3 - DuPont Identity. Suppose that the Bethesda Mining...Ch. 3 - Prob. 18QPCh. 3 - Return on Assets. Beckinsale, Inc., has a profit...Ch. 3 - Calculating Internal Growth. The most recent...Ch. 3 - Calculating Sustainable Growth. For Shinoda...Ch. 3 - Total Asset Turnover. Kalebs Karate Supply had a...Ch. 3 - Return on Equity. Carroll, Inc., has a total debt...Ch. 3 - Market Value Ratios. Ames, Inc., has a current...Ch. 3 - Prob. 25QPCh. 3 - Enterprise ValueEBITDA Multiple. The market value...Ch. 3 - Prob. 27QPCh. 3 - Ratios and Fixed Assets. The Smathers Company has...Ch. 3 - Prob. 29QPCh. 3 - Prob. 30QPCh. 3 - Prob. 31QPCh. 3 - Calculating the Times Interest Earned Ratio. For...Ch. 3 - Return on Assets. A fire has destroyed a large...Ch. 3 - Prob. 34QPCh. 3 - SMOLIRA GOLF. INC. 2016 Income Statement Sales...Ch. 3 - Prob. 36QPCh. 3 - Market Value Ratios. Smolira Golf has 10,000...Ch. 3 - Interpreting Financial Ratios. After calculating...Ch. 3 - Growth and Profit Margin. Fulkerson Manufacturing...Ch. 3 - Market Value Ratios. Abercrombie Fitch and...Ch. 3 - Growth and Assets. A firm wishes to maintain an...Ch. 3 - Prob. 42QPCh. 3 - Prob. 43QPCh. 3 - Constraints on Growth. High Flyer, Inc., wishes to...Ch. 3 - Internal and Sustainable Growth Rates. Best Buy...Ch. 3 - Expanded DuPont Identity. Hershey Co. reported the...Ch. 3 - Ratios and Financial Planning at SS Air, Inc....Ch. 3 - Prob. 2CCCh. 3 - Prob. 3CCCh. 3 - Ratios and Financial Planning at SS Air, Inc....
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