what happens to a firm that reinvests its earnings at a rate equal to the firms required return?

The Fundamental Determinants of Growth

With both historical and analyst estimates, growth is an exogenous variable that affects value only is divorced from the operating details of the house. The soundest way of incorporating growth into value is to brand it endogenous, i.e., to make it a part of how much a firm reinvests for future growth and the quality of its reinvestment. We volition begin past considering the relationship between fundamentals and growth in equity income, and then move on to look at the determinants of growth in operating income.

Growth In Equity Earnings

When estimating cash flows to equity, nosotros usually begin with estimates of net income, if nosotros are valuing equity in the aggregate, or earnings per share, if nosotros are valuing equity per share. In this section, we will begin past presenting the fundamentals that make up one's mind expected growth in earnings per share and so movement on to consider a more than expanded version of the model that looks at growth in net income.

Growth in Earnings Per Share

The simplest relationship determining growth is one based upon the retention ratio (per centum of earnings retained in the firm) and the return on disinterestedness on its projects. Firms that have higher retentiveness ratios and earn higher returns on disinterestedness should have much higher growth rates in earnings per share than firms that do not share these characteristics. To establish this, note that

where,

gt = Growth Rate in Internet Income

NIt = Net Income in yr t

Given the definition of render on equity, the net income in year t-1 can be written as:

where,

ROEt-1 = Return on equity in year t-1

The net income in year t tin can be written as:

Bold that the render on disinterestedness is unchanged, i.e., ROEt = ROEt-1 =ROE,

where b is the retention ratio. Note that the firm is not being allowed to raise equity past issuing new shares. Consequently, the growth rate in internet income and the growth rate in earnings per share are the same in this formulation.

Growth in Net Income

If nosotros relax the supposition that the only source of equity is retained earnings, the growth in net income can be different from the growth in earnings per share. Intuitively, notation that a business firm tin can grow internet income significantly past issuing new equity to fund new projects while earnings per share stagnates. To derive the relationship betwixt net income growth and fundamentals, nosotros need a measure out of how investment that goes beyond retained earnings. One way to obtain such a measure is to approximate directly how much equity the firm reinvests back into its businesses in the grade of cyberspace upper-case letter expenditures and investments in working capital.

Disinterestedness reinvested in business = (Capital letter Expenditures � Depreciation + Change in Working Capital � (New Debt Issued � Debt Repaid))

Dividing this number by the net income gives us a much broader measure out of the equity reinvestment rate:

Disinterestedness Reinvestment Rate =

Unlike the retention ratio, this number can exist well in excess of 100% because firms can heighten new equity. The expected growth in net income can then be written as:

Expected Growth in Net Income =

Determinants of Return on Disinterestedness

Both earnings per share and cyberspace income growth are affected past the return on equity of a house. The return on equity is affected by the leverage decisions of the firm. In the broadest terms, increasing leverage will lead to a higher return on equity if the pre-interest, after-tax return on capital letter exceeds the later on-tax involvement rate paid on debt. This is captured in the following formulation of return on equity:

where,

t = Tax rate on ordinary income

The derivation is simple [1] . Using this expanded version of ROE, the growth charge per unit tin exist written every bit:

The advantage of this formulation is that information technology allows explicitly for changes in leverage and the consequent effects on growth.

Average and Marginal Returns

The return on equity is conventionally measured past dividing the cyberspace income in the nigh contempo yr past the book value of equity at the stop of the previous year. Consequently, the return on equity measures both the quality of both older projects that take been on the books for a substantial period and new projects from more than recent periods. Since older investments represent a significant portion of the earnings, the average returns may not shift substantially for larger firms that are facing a decline in returns on new investments, either because of market saturation or competition. In other words, poor returns on new projects volition accept a lagged effect on the measured returns. In valuation, it is the returns that firms are making on their newer investments that convey the most data about a quality of a firm�south projects. To measure these returns, we could compute a marginal render on equity by dividing the change in net income in the about recent twelvemonth by the alter in book value of equity in the prior year:

Marginal Return on Equity =

For case, Reliance Industries reported net income of Rs 24033 million in 2000 on volume value of equity of Rs 123693 million in 1999, resulting in an average return on disinterestedness of 19.43%:

Average Return on Equity = 24033/123693 = 19.43%

The marginal return on equity is computed below:

Change in net income from 1999 to 2000 = 24033- 17037 = Rs 6996 million

Change in Book value of equity from 1998 to 1999 = 123693 � 104006 = Rs 19,687 one thousand thousand

Marginal Render on Disinterestedness = 6996/19687 = 35.54%

The Effects of Changing Return on Disinterestedness

Then far in this section, we have operated on the assumption that the render on equity remains unchanged over time. If we relax this assumption, we innovate a new component to growth � the event of changing return on equity on existing investment over time. Consider, for example, a firm that has a book value of equity of $100 1000000 and a return on disinterestedness of ten%. If this firm improves its return on equity to eleven%, information technology will post an earnings growth rate of 10% even if it does non reinvest any money. This additional growth tin be written as a office of the alter in the return on disinterestedness.

Improver to Expected Growth Rate =

where ROE_t is the render on disinterestedness in catamenia t. This volition exist in addition to the primal growth charge per unit computed as the product of the return on disinterestedness in period t and the retention ratio.

Total Expected Growth Rate =

While increasing return on disinterestedness will generate a spurt in the growth rate in the period of the improvement, a pass up in the return on disinterestedness will create a more than proportional drop in the growth rate in the period of the decline.

Information technology is worth differentiating at this point betwixt returns on equity on new investments and returns on equity on existing investments. The additional growth that we are estimating above comes not from improving returns on new investments but by changing the render on existing investments. For lack of a better term, you could consider information technology �efficiency generated growth�.

Growth in Operating Income

Simply equally equity income growth is determined by the equity reinvested back into the business organisation and the render made on that equity investment, you can relate growth in operating income to total reinvestment made into the firm and the return earned on upper-case letter invested.

You lot will consider three separate scenarios, and examine how to estimate growth in each, in this section. The outset is when a firm is earning a high return on capital that it expects to sustain over time. The second is when a firm is earning a positive return on capital that is expected to increase over time. The third is the most general scenario, where a firm expects operating margins to change over time, sometimes from negative values to positive levels.

A. Stable Render on Capital Scenario

When a firm has a stable return on capital, its expected growth in operating income is a product of the reinvestment rate, i.e., the proportion of the later-tax operating income that is invested in net capital expenditures and not-greenbacks working capital, and the quality of these reinvestments, measured equally the return on the upper-case letter invested.

Expected Growth_EBIT = Reinvestment Rate * Render on Capital

where,

Render on Capital =

In making these estimates, you use the adjusted operating income and reinvestment values that you computed in Chapter 4. Both measures should be forrad looking and the return on capital should represent the expected return on capital on future investments. In the rest of this section, you consider how all-time to estimate the reinvestment rate and the return on majuscule.

Reinvestment Charge per unit

The reinvestment rate measures how much a firm is plowing back to generate time to come growth. The reinvestment charge per unit is ofttimes measured using the most recent financial statements for the firm. Although this is a adept identify to start, it is not necessarily the best gauge of the future reinvestment rate. A firm�southward reinvestment rate can ebb and period, especially in firms that invest in relatively few, big projects or acquisitions. For these firms, looking at an average reinvestment rate over fourth dimension may be a amend measure out of the hereafter. In addition, every bit firms grow and mature, their reinvestment needs (and rates) tend to subtract. For firms that have expanded significantly over the last few years, the historical reinvestment rate is likely to be higher than the expected future reinvestment rate. For these firms, industry averages for reinvestment rates may provide a amend indication of the future than using numbers from the past. Finally, it is important that you keep treating R&D expenses and operating charter expenses consistently. The R&D expenses, in particular, need to be categorized as part of upper-case letter expenditures for purposes of measuring the reinvestment rate.

Return on Capital

The return on capital is often based upon the firm'southward return on existing investments, where the volume value of uppercase is assumed to measure out the capital letter invested in these investments. Implicitly, you presume that the current accounting return on capital is a skilful mensurate of the truthful returns earned on existing investments and that this render is a good proxy for returns that will be made on futurity investments. This supposition, of grade, is open up to question for the following reasons.

� The book value of capital might non exist a skillful measure of the capital invested in existing investments, since it reflects the historical cost of these assets and accounting decisions on depreciation. When the book value understates the uppercase invested, the render on capital volition be overstated; when book value overstates the capital invested, the return on uppercase will be understated. This problem is exacerbated if the book value of upper-case letter is not adapted to reflect the value of the inquiry asset or the capital letter value of operating leases.

� The operating income, like the book value of majuscule, is an accounting measure of the earnings made by a firm during a menstruum. All the problems in using unadjusted operating income described in Affiliate four continue to use.

� Even if the operating income and book value of uppercase are measured correctly, the render on upper-case letter on existing investments may non exist equal to the marginal return on uppercase that the firm expects to make on new investments, especially as you go farther into the time to come.

Given these concerns, you should consider not only a business firm�s current return on capital, but any trends in this return every bit well every bit the manufacture average return on capital. If the current return on uppercase for a firm is significantly higher than the industry average, the forecasted return on capital should be set up lower than the current render to reflect the erosion that is likely to occur as competition responds.

Finally, any firm that earns a return on majuscule greater than its cost of capital is earning an excess render. The excess returns are the result of a firm�southward competitive advantages or barriers to entry into the industry. High excess returns locked in for very long periods imply that this firm has a permanent competitive advantage.

Negative Reinvestment Rates: Causes and Consequences

The reinvestment rate for a firm tin can exist negative if its depreciation exceeds its majuscule expenditures or if the working capital declines essentially during the course of the twelvemonth. For virtually firms, this negative reinvestment rate will be a temporary phenomenon reflecting lumpy uppercase expenditures or volatile working capital. For these firms, the current year�s reinvestment rate (which is negative) tin exist replaced with an average reinvestment rate over the last few years. (This is what we did for Embraer in the Illustration above.) For some firms, though, the negative reinvestment rate may be a reflection of the policies of the firms and how we bargain with it will depend upon why the house is embarking on this path:

� Firms that have over invested in capital letter equipment or working capital letter in the past may exist able to live off past investment for a number of years, reinvesting little and generating higher greenbacks flows for that period. If this is the case, we should non utilise the negative reinvestment charge per unit in forecasts and estimate growth based upon improvements in return on majuscule. Once the firm has reached the point where it is efficiently using its resources, though, nosotros should change the reinvestment rate to reflect industry averages.

� The more than farthermost scenario is a firm that has decided to liquidate itself over time, by not replacing assets equally they become run downwards and by drawing down working uppercase. In this case, the expected growth should exist estimated using the negative reinvestment charge per unit. Not surprisingly, this will lead to a negative expected growth charge per unit and declining earnings over time.

B. Positive and Changing Return on Uppercase Scenario

The assay in the previous section is based upon the supposition that the return on capital letter remains stable over time. If the return on capital changes over time, the expected growth rate for the firm volition accept a 2d component, which will increase the growth rate if the render on capital increases and decrease the growth rate if the return on uppercase decreases.

Expected Growth Rate =

For case, a firm that sees its return on uppercase improves from ten% to 11% while maintaining a reinvestment charge per unit of 40% will have an expected growth rate of:

Expected Growth Rate =

In effect, the comeback in the return on uppercase increases the earnings on existing avails and this improvement translates into an boosted growth of ten% for the firm.

Marginal and Boilerplate Returns on Capital

So far, you have looked at the return on upper-case letter every bit the measure that determines render. In reality, however, there are two measures of returns on capital. One is the return earned by firm collectively on all of its investments, which you ascertain as the boilerplate return on upper-case letter. The other is the return earned by a firm on only the new investments it makes in a year, which is the marginal return on upper-case letter.

Changes in the marginal render on upper-case letter do not create a second-order upshot and the value of the firm is a product of the marginal return on upper-case letter and the reinvestment charge per unit. Changes in the average return on capital, notwithstanding, will event in the additional impact on growth chronicled to a higher place.

Candidates for Irresolute Average Return on Capital

What types of firms are likely to run across their return on majuscule change over time? 1 category would include firms with poor returns on capital that improve their operating efficiency and margins, and consequently their return on capital. In these firms, the expected growth rate will exist much higher than the product of the reinvestment charge per unit and the return on capital. In fact, since the return on capital on these firms is unremarkably depression before the plow-around, small-scale changes in the return on majuscule translate into large changes in the growth rate. Thus, an increase in the return on capital on existing avails of 1% to 2% doubles the earnings (resulting in a growth rate of 100%).

The other category would include firms that have very loftier returns on capital on their existing investments but are likely to see these returns slip every bit contest enters the business organisation, not only on new investments but also on existing investments.

C. Negative Return on Uppercase Scenario

The 3rd and about difficult scenario for estimating growth is when a firm is losing coin and has a negative return on majuscule. Since the firm is losing coin, the reinvestment rate is too likely to be negative. To guess growth in these firms, y'all have to motility up the income argument and first project growth in revenues. Next, you utilize the house�s expected operating margin in future years to estimate the operating income in those years. If the expected margin in time to come years is positive, the expected operating income will likewise turn positive, allowing us to apply traditional valuation approaches in valuing these firms. You as well estimate how much the firm has to reinvest to generate acquirement growth, by linking revenues to the capital invested in the firm.

Growth in Revenues

Many high growth firms, while reporting losses, also show large increases in revenues from catamenia to period. The first step in forecasting greenbacks flows is forecasting revenues in future years, usually past forecasting a growth rate in revenues each catamenia. In making these estimates, there are five points to keep in listen.

� The rate of growth in revenues volition decrease as the firm�s revenues increase. Thus, a ten-fold increment in revenues is entirely feasible for a firm with revenues of $ii one thousand thousand simply unlikely for a firm with revenues of $2 billion.

� Compounded growth rates in revenues over time can seem depression, merely appearances are deceptive. A compounded growth charge per unit in revenues of 40% over x years volition result in a 40-fold increase in revenues over the menses.

� While growth rates in revenues may be the mechanism that you use to forecast future revenues, y'all practice have to keep track of the dollar revenues to ensure that they are reasonable, given the size of the overall market that the firm operates in. If the projected revenues for a business firm ten years out would requite it a 90% or 100% share (or greater) of the overall market in a competitive market place place, yous conspicuously should reassess the revenue growth charge per unit.

� Assumptions about acquirement growth and operating margins have to be internally consistent. Firms can post higher growth rates in revenues by adopting more than aggressive pricing strategies but the higher revenue growth will and then be accompanied by lower margins.

• In coming upwardly with an estimate of revenue growth, you accept to make a number of subjective judgments nigh the nature of contest, the capacity of the firm that you are valuing to handle the acquirement growth and the marketing capabilities of the business firm.

Operating Margin Forecasts

Before considering how all-time to estimate the operating margins, permit usa begin with an assessment of where many high growth firms, early in the life cycle, stand up when the valuation begins. They usually have depression revenues and negative operating margins. If revenue growth translates low revenues into high revenues and operating margins stay negative, these firms will non only be worth zero merely are unlikely to survive. For firms to be valuable, the higher revenues somewhen take to deliver positive earnings. In a valuation model, this translates into positive operating margins in the future. A key input in valuing a high growth firm then is the operating margin you would expect it to have as information technology matures.

In estimating this margin, you should begin by looking at the business organization that the firm is in. While many new firms claim to be pioneers in their businesses and some believe that they have no competitors, it is more likely that they are the beginning to detect a new fashion of delivering a production or service that was delivered through other channels before. Thus, Amazon might have been one of the first firms to sell books online, but Barnes and Noble and Borders preceded them as book retailers. In fact, one tin consider online retailers as logical successors to catalog retailers such as L.Fifty. Edible bean or Lillian Vernon. Similarly, Yahoo! might have been 1 of the first (and about successful) internet portals but they are following the atomic number 82 of newspapers that have used content and features to attract readers and used their readership to attract advertising. Using the average operating margin of competitors in the concern may strike some as conservative. Later on all, they would point out, Amazon can hold less inventory than Borders and does non have the brunt of carrying the operating leases that Barnes and Noble does (on its stores) and should, therefore, be more efficient nigh generating its revenues and subsequently earnings. This may be true but it is unlikely that the operating margins for internet retailers tin can be persistently higher than their brick-and-mortar counterparts. If they were, yous would look to run across a migration of traditional retailers to online retailing and increased competition among online retailers on price and products driving the margin down.

While the margin for the business in which a firm operates provides a target value, there are yet two other estimation problems that yous demand to confront. Given that the operating margins in the early stages of the life cycle are negative, you commencement have to consider how the margin will improve from current levels to the target values. Generally, the improvements in margins will be greatest in the before years (at least in per centum terms) so taper off as the firm approaches maturity. The second issue is 1 that arises when talking about revenue growth. Firms may be able to post higher revenue growth with lower margins but the trade off has to be considered. While firms generally desire both college acquirement growth and higher margin, the margin and acquirement growth assumptions take to be consequent.

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Source: https://pages.stern.nyu.edu/~adamodar/New_Home_Page/valquestions/growth.htm