Chapter 19, Problem 4CP

Summary Introduction

(A)

Adequate information:

Components	Quick brush company(in $)	Smile white corporation (in $)
Net Profit	445	4850
Pretax Profit	660	7350
EBIT	660	7700
Sales	7760	119200
Assets	5470	33600
Equity	3720	22700
Dividend per share	0	1.72
Earnings Per Share(EPS)	1.18	2.62

Requirement 1: To calculate and analyze five components that determine Return on Equity(ROE).

Introduction:

Return on Equity measures the financial performance of the company by focusing only on the profitability of equity investments. It is expressed as:

  $\begin{array}{l}\text{Return On Equity = }\frac{\text{Net Income}}{\text{Shareholder's equity}}\hfill \\ \hfill \\ \hfill \\ \hfill \end{array}$

Though in Du-pont system, the return on equity is decomposed into five components. Thus decomposed return on equity is calculated as:

  $\begin{array}{l}\text{Return On Equity = Net profit Pre tax profit EBIT Sales Assets}\hfill \\ \text{ \_\_\_\_\_\_\_\_\_\_ × \_\_\_\_\_\_\_\_\_\_ × \_\_\_\_\_× \_\_\_\_\_ × \_\_\_\_\_\_\_}\hfill \\ \text{ Pretax profit EBIT Sales Assets Equity}\hfill \end{array}$

= Tax burden X Interest burden X Margin X Turnover X Leverage

Explanation of Solution

Calculation of Return on Equity using five components for Quick Brush company and smile white corporation.

  $\begin{array}{cccccc}& & QuickBrush& Company& SmileWhite& Corporation\\ Components& Breakupofcomponents& Calculation\left(In\$\right)& Result& \begin{array}{c}Calculation\left(In\$\right)\end{array}& Result\\ Taxburden& Netprofit/pretaxprof& \left(445/660\right)\times 100& 67.42\%& \left(4850/7350\right)\times 100& 66\%\\ InterestBurden& Pretaxprofit/EBIT& \left(660/660\right)\times 100& 100\%& \left(7350/7700\right)\times 100& 95.45\%\\ Margin& EBIT/sales& \left(660/7760\right)\times 100& 8.5\%& \left(7700/119200\right)\times 100& 6.4\%\\ Turnover& Sales/assets& 7760/5470& 1.41& 119200/33600& 3.54\\ Leverage& Assets/Equity& 5470/3720& 1.47& 33600/22700& 1.48\\ ROE& & & 11.87\%& & 21.12\%\end{array}$

Conclusion

Though the Margin for profits in Quick Brush Company (8.5%) is more than Smile White Corporation(6.4%), but the Return on equity is less in Quick brush company(11.87%) as compared to Smile white corporation(21.12%). Thus Quick Brush company is not profitable from shareholders point. Also the Turnover of assets in Quick brush is also less (1.41) as compared to Smile White Corporation which shows that Quick brush company earns less from its total assets as compared to Smile white corporation.

Summary Introduction

Requirement 2: To calculate and analyze ROE and plowback ratios that determine sustainable growth.

Introduction:

The sustainable growth is the maximum growth rate that a firm can sustain without having to lookout for outside finance. It is multiple of return on equity and retention ratio. It is calculated as:

Sustainable Growth rate = Return on equity * Plowback ratio

Explanation of Solution

Calculation of Sustainable growth

  $\begin{array}{cccccc}& & QuickBrush& Company& SmileWhite& Corporation\\ \begin{array}{l}Componentsof\\ sustainablegrowth\end{array}& \begin{array}{l}Breakupof\\ components\end{array}& \begin{array}{l}Calculation\\ \left(In\$\right)\end{array}& Result& \begin{array}{l}Calculation\\ \left(In\$\right)\end{array}& Result\\ ROE& & & 11.87\%& & 21.12\%\\ Plowbackratio& \begin{array}{l}1-Dividendpayout\\ ratiowheredividend\\ payoutratio=Dividend\\ pershare/earningpershare\end{array}& 1-\left(0/1.18\right)& 1& 1-\left(1.72/2.62\right)& 0.34\\ Sustainablegrowth& & & 11.87\%& & 7.18\%\end{array}$

Conclusion

Since the sustainable growth rate shows the firm's dependency on dividend policy and profitability, thus here the analyst- Janet Ludlow is confident on both the firm's sustainable growth rate.

Summary Introduction

(B)

To explain that the Quick Brush Company is having average annual Earning per share growth rate of 40% in last two years though the Return on Equity is declining in two years.

Introduction:

Earning per share is the portion of a firm's profit allocated to each share of common stock. A firm with high Earning per share ratio means that it is capable of generating high dividends for investors of common stock or it may plow back funds for business growth.

Return on Equity measures the financial performance of the company by focussing only on the profitability of equity investments. It is expressed as:

  $ReturnOnEquity=\frac{NetIncome}{Shareholder\text{'}sequity}$

Answer to Problem 4CP

Quick Brush Company has growing Earning Per Share but declining ROE because it has increased its book value per share over the period of two years.

Explanation of Solution

Quick Brush Company has a declining Return On Equity because it had retained earnings which were perhaps used to issue more share at market price instead of book value. This increased the book value of the firm and thus increasing the shares proportionately. So the earning per share increased while Return on equity declined.