2 lecture 4 and 5 contant g

Lahore School of Economics. MBA II. M.Phil Bus. Admin (Research). Advance Corporate Finance. Winter 2015. Dr. Sohail Zafar.

Lectures 4 and 5

Financial Planning

This lecture focuses on two issues: 1) If 5 corporate policies are kept constant then internally generated growth in

OE , g OE , translates into same growth rate in TA, TL, Sales, NI, EPS, DPS, and finally in share price (Po); 2) projecting

concise financial statements if 5 corporate policies are kept unchanged; and double checking that it is true that all

the above stated financial variables do grow at the same percentage growth rate. The 5 policies that are assumed

to be kept constant are:

1) NI/S ratio, net profit margin showing profitability

2) S/TA ratio, total assets turnover showing productivity of total assets in generating sales

3) TA/OE ratio, financial leverage showing capital structure of the business

4) DPS/EPS ratio, dividend payout ratio showing dividend policy of the business. It is denoted with symbol ’d’.

5) and number of shares outstanding.

The Idea of Constant Growth Rate of OE

If a Co does not issue new shares to raise fresh cash as equity investment by its owners then any growth in its OE is

internally generated through retention of some portion or all of NI by not distributing all the NI of that year as

cash dividends. NI (net Income) is also called PAT or profits after taxes. Such reinvesting a portion of NI of a year’s

in the business causes on the right hand side of balance sheet an increase in its OE; specifically within OE , the RE

(also called reserves) experience an increase. Since balance sheet must balance therefore on the left hand side of

balance sheet total assets experience an increase by the same amount because 2 sides of balance sheet must

always be the same amount. Therefore percentage change in OE is growth in OE, and is shown as gOE:

gOE = increase in OE due to increase in RE / OE Beg

Why OE Beg .

Please note if you deposit 100 rupees in a bank account at the beginning of a year and bank gives at the end of the

year 10 rupees as interest then percentage change in your bank balance is called growth in your bank balance and

can be calculated as:

g bank balance = increase in bank balance / bank balance Beg

g bank balance = 10 / 100

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g bank balance = 0.1 or 10%

same logic was used above to estimate growth in the beginning OE.

Please note that NI for a year can go only 2 places; either it is given out as cash dividends to shareholders, or it

increases the retained earnings balance in the OE portion of the balance sheet. Such increase in RE is called

reinvesting the profits in the business.

So you can visualize fate of NI for a year as given below:

NI = Cash Dividends distributed by a Co to its shareholders + increase in RE

therefore we can shuffle the above equation as:

NI – DIV = increase in RE (DIV is used for cash dividends)

so in place of increase in RE we can insert ( NI – DIV) in the above gOE formula.

gOE = increase in OE due to increase in RE / OE Beg

gOE = (NI - DIV) / OE Beg

Note that you can write:

DIV = NI * d

whereas ‘d’ refers to dividend payout ratio which tells what percentage of NI is given out as cash dividends, and

d = total cash dividends / NI, or if you have per share data you can find :

d = DPS / EPS .

Then growth rate of OE can be written as:

gOE = (NI - DIV)/OE Beg

gOE = {NI – (NI * d)} /OE Beg

gOE =NI (1 - d) / OE Beg. (taking NI as common)

gOE = NI / OE (1 - d). Since NI / OE is ROE so

gOE = ROE (1 – d)

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In certain text books the term (1 - d) is written as ‘ b’ and termed as retention ratio; which tells what %age of NI of

a year was retained and reinvested in the business. Also instead of writing ROE some authors use symbol ‘ r’ ; thus

g = rb

is commonly found in many text books as formula for constant growth rate of a Co.

Strictly speaking this growth rate “g” is a growth rate of only OE and not of other financial variables such as

sales, NI , TA. It is internally generated growth in OE of a business because this growth in OE is attained by

retaining and reinvesting a portion of NI; and is not generated by issuing shares to raise external equity funds.

As assumed earlier that the management wants to keep the capital structure of the co constant at pre-growth

level, that means TA/OE ratio is constant, then TA (total assets) must also grow at the same growth rate at which

OE is growing due to internally generated growth in OE as discussed above. Its logical if both TA and OE are

growing, say at 7%, then to keep the balance sheet balanced, TL must also grow at 7%. Therefore all three

portions of balance sheet would grow at this growth rate. Since growth in liabilities would entail increase in

external debt financing therefore this growth rate cannot be called sustainable growth rate of a business

corporation because, by definition, sustainable growth rate is that growth rate in sales which does not require

raising debt or equity financing externally to finance additional assets needed to support growth in production and

sales. Rather the sustainable growth rate relies only on raising equity internally by reinvesting the profits and also

relies on that increase in liabilities that takes place spontaneously due to larger production and selling operations,

such as increase in accounts payables and salaries payables. Therefore when a company is growing at sustainable

growth rate then financing for the growth in assets is not done by taking debt or by issuing shares.

Later on in this course when calculations are done for sustainable growth rate of a co, then this difference between

constant growth rate financed by internally generated equity and sustainable growth rate of a corporation would

become clear.

As derived above, Internally generated growth (or constant growth) of OE is quantified by :

gOE = ROE (1 - d)

This is the growth rate in OE achieved without resorting to external equity by issuing shares but it does not prohibit

or preclude raising external debt to achieve growth rate in TL. In fact to achieve the same growth rate in TL as

achieved in OE the corporation may have to resort to external debt financing; though no external equity financing

requiring the owners to buy newly issued shares in the business is required for the OE to grow at this growth rate.

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Forecasting Financial Statements If 5 policies are kept Constant

The following discussion would show with the help of assumed data that when 5 major corporate policies are kept

constant at the same level as last year then gOE , as measured by ROE( 1- d), translates into growth rate in share

price, Po , by the end of the year. For example if ROE (1 – d) for a year comes out 10% then TA, TL, Sales, NI, EPS,

DPS, and finally share price would also grow by 10% in that year. For example if share of a co was at 100 rupees at

the beginning of the year, it would be 10% higher , (100 + 10% of 100 = 100 + 10 = 110), at the end of the year in

the stock market if the co keeps its 5 corporate financial policies unchanged from the last year. Such growth rate

in share price is called capital gains yield , and is calculated as :

g Po = (P1 - P0 ) /P0

whereas P0 refers to share price at time zero or now, and P1 refers to share price after one year.

Please be clear that keeping these 5 policies constant means managing the company as well (or as badly) as it was

managed last year. You would agree this is a rather conservative approach towards managing a business because

usually it is improvement in various performance areas that managers attempt to achieve; but under this

framework of constant growth assumption all that is required of managers is to manage the company in the same

manner as it was managed in the previous year without attempting to improve profitability by improving net profit

margin; or without improving asset productivity by increasing total assets turnover; or without increasing financial

leverage ( and therefore financial risk) by increasing equity multiplier ratio (TA/OE ratio); or without trying to

please shareholders by increasing dividend payout ratio; and also without raising fresh cash from shareholders by

issuing shares.

If above stated 5 corporate policies are kept constant then many items of income statement and balance sheet

grow at the same rate as growth in OE, that is,

gOE = gTA = g TL = gS = gNI = gEPS = g DPS= g Po = (P1 - Po )/Po

Let us work with a simple example using concise balance sheets and income statement formats focusing only on

major categories of these statements. Assume that for the last year (the year just ended) a co has the following

income statement and balance sheet.

TA = TL + OE

200 =100 + 100

S = 500m

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NI =10m

d=50%

Its shareholders’ risk adjusted required rate of return, Kc, calculated as: Rf + (Rm - Rf) baeta (Levered) =10%.

Number of shares outstanding =10 million.

We can find its growth of OE by the end of year 0 (the last year)as :

gOE = ROE(1 - d)

gOE =NI/OE* (1- d)

gOE =10/100*(1- 0.5)

gOE =10%(1- 0.5)

gOE =10 % *0.5

gOE =5%

If the management of the co decides to keep the following 5 policies unchanged during the next year then

ultimately growth in its share price (capital gains yield measured as (P1 - P0 ) /P0 ) would also be 5% by the end of

next year (Year 1).

1) dividend payout policy remains unchanged, i.e. d = 0.5

2) Number of shares outstanding remains unchanged at 10m shares; it means during the next year no new shares

would be issued (for cash or as bonus shares) nor old shares would be repurchased by this co.

3) Net profit margin on sales remains unchanged, i.e., NI /S ratio this year is : 10/500 =2% and would remain the

same next year; it implies no change in profitability.

4) Turnover of TA remains unchanged, this year S / TA ratio: 500/200=2.5 times meaning one rupee invested in TA

was helping to generate sales of 2.5 rupees, and it would be 2.5 next year , it means productivity of TA in

generating sales would remain unchanged during the next year.

5) Financial leverage remains unchanged, this year TA /OE ratio: 200/100 = 2 times, and it would be 2 next year as

well, it means capital structure would remain unchanged; and so would be financial risk.

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If the above stated 5 policies won’t change next year, then forecasting the income statement and balance sheet

for the next year is easy: (note the subscript 0 and 1 refer to current year and the next year respectively). The

following is the detail of forecasting various income statement and balance sheet items for the next year:

Therefore next year’s OE would be 5% higher than this year’s OE:

OE1 = OE0( 1 + gOE)

= 100(1 + 0.05) =105 m

As TA /OE last year is 200 /100 = 2 and therefore this equity multiplier (financial leverage) will be same next year ,

so :

TA1 /OE1=2

TA1=2*OE1

TA1=2*105

TA1=210m , and since balance sheet is always balanced therefore you can work out next year’s TL as:

TL1=TA1 - OE1

=210 – 105

=105m

Now you have projected balance sheet for the next year:

TA1 = TL1 + OE1

210 = 105 + 105

Let us work on preparing the forecasted income statement for the next year:

As S / TA was last year 500/200 = 2.5 times, therefore next year this turnover of asset would also be 2.5 times, so:

S1 / TA1 = 2.5

S1 = 2.5* TA1

S1 = 2.5*210

S1 = 525m

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Since last year NI /S was 10 /500 = 2% therefore net profit margin for the next year would also be 2% of sales, so:

NI1 / S1 = 2%

NI1 = 2% * S1

NI1 = 0.02*525

NI1 = 10.5m

Now you have projected (also called budgeted) income statement for the next year in concise form:

S1 - Expenses1 = NI1

525 – expenses = 10.5

Expenses = 525 – 10.5

Expenses = 514.5

Last year’s EPS was: EPS0 = NIo / Shares =10m Rs/10m shares =1 Rs/share, so next year EPS would be:

EPS1 = NI1 / number of Shares outstanding

EPS1 =10.5m Rs/10m (note the number of shares outstanding is same 10 million as last year)

EPS1 =1.05 Rs/ Share

Last year DPSo= EPS0 * d

DPSo =1*0.5

DPSo = 0.5 Rs/ Share (last year’s cash dividend per share)

Next year DPS would be

DPS1 = EPS1*d

DPS1 = 1.05 * 0.5 (note dividend payout ratio, d, is unchanged at 50%)

DPS1 = 0.525 Rs/Sh (next year’s estimated dividend per share)

Let us check the growth rates of various items of income statement and balance sheet when 5 policies were kept

same as last year.

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We already found that gOE = ROE(1 - d) =5%, and that was the starting point of the whole exercise.

gTA = (TA1 - TAo ) /TAo

=( 210 – 200)/200

=5%

gTL= (TL1 - TLo) /TLo

=(105 – 100)/100

=5%

gS = (S1 - So )/So

= (525 – 500) /500

=5%

gNI = (NI1 - NIo) /NIo

= (10.5 – 10) /10

=5%

gEPS = (EPS1 - EPSo) /EPSo

= ( 1.05 - 1.0) /1.0

=5%

g DPS = (DPS 1 - DPS0) /DPSo

= (0.525 - 0.5)/ 0.5

=5%

According to DDM (dividend discount model with constant growth assumptions, also called The Gordon’s Model)

current price depends on future value of cash dividends:

Po = DPS1/ (Kc – g) , whereas P0 is fair market value now at time zero and share price now should be at fair value

under the assumptions of efficient market hypothesis. DPS1 is next year’s cash dividends per share. Inserting data

of this co you get:

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Po = DPS1/ (Kc – g)

Po = 0.525/ (0.1 - 0 .05)

Po =10.5 Rs/ Sh

Similarly price at the end of first year depends on cash dividends of year 2; and if in year 2 the 5 corporate policies

are again kept unchanged then growth rates of these items of balance sheet and income statement would again be

5% resulting in

DPS 2 = DPS1(1 + g)

=0.525(1 + 0.05)

=0.55 Rs/Share

Therefore share price at the end of this year (year one) , P1, is estimated as:

P1 =DPS2/ (Kc – g), P1 is estimated price after one year

P1 = 0.55/(0.1 - 0.05)

P1 =11.02

And thus growth in share price (capital gains yield) from now till the end of the year is estimated as:

g Po= (P1 - Po) /Po

= (11.02 - 10.5) /10.5

=5%

So you have proof that growth rate in OE translates into growth rate of TA, TL, Sales, NI, EPS, DPS, and ultimately

share price in the market. That is,

gOE = gTA = g TL = gS = gNI = gEPS = g DPS= g Po = (P1 - Po )/Po

5% = 5%= 5% = 5% = 5% = 5% = 5% = 5% = (11.02 - 10.5) /10.5

This is a powerful result and allows you to think clearly about mechanism of wealth creation for the owners of a

business corporation. The above shown exercise gives clear indication that corporations that are likely to grow

faster are also likely to make their shareholders wealthy. Now you understand why there is so much talk about

growth rate of businesses: fast growing businesses are likely to make their owners wealthy quickly.

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Percentage of Sales Method of Forecasting Financial Statements

The above analysis proves that while preparing concise projected income statement and balance sheet for the next

year with the assumption of constancy in 5 corporate finance policies, all you need to do is estimate growth rate in

OE as ROE (1 - d); and then apply that growth rate on TA, TL, Sales, NI, EPS, and DPS to estimate next year’s

income statement and balance sheet. It is done below as demonstration:

Projected next year’s TA = TA0 (1 + g) = 200 (1 + 0.05) = 210

Projected next year’s TL = TL0 ( 1 + g) = 100 (1 + 0.05) = 105

Projected next year’s OE = OE0 (1 + g) = 100 (1 + 0.05) = 105

Projected next year’s Sales = S0 ( 1 + g) = 500 (1 + 0.05) = 525

Projected next year’s NI = NI0 (1 + g) = 10 (1 + 0.05) = 10.5 million

Projected next year’s EPS = EPS0 (1 + g) = 1(1 + 0.05) = 1.05 Rupees per share

Projected next year’s DPS = DPS0(1 + g) = 0.5(1 + ).05) = 0.525 Rupees per share

Projected next year’s share price , P1 = P0 (1 + g) = 10.5(1 + 0.05) = 11.025 rupees per share

Another consequence of the assumption of constancy of 5 corporate policies is shown below. The demonstration

given below shows that various items of income statement and balance sheet remain same percentage of sales

next year as these were last year. For example last year’s various items as percentage of sales were:

TA/S = 200/500 = 0.4 or 40%

TL /S = 100/500 = 0.2 or 20%

OE/S = 100/500 = 0.2 = 20%

NI/S = 10/500 = 0.02 or 2%

And next year projected values of various items as percentages of projected sales are also :

TA1/S1 = 210/525 = 0.4 or 40%

TL1 / S1 = 105 / 525 = 0.2 or 20%

OE1 / S1 = 105 / 525 = 0.2 or 20%

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NI1 / S1 = 10.5 /525 = 0.02 or 2%

In most of the text books the assumption of constancy in 5 corporate policies and resulting constant growth rate in

various items of income statement and balance sheet is not elaborately discussed. Simply it is stated that various

items in income statement and balance sheet will be a constant percentage of sales. This method of preparing

financial plan is termed in text books as percentage of sales method of forecasting income statement and balance

sheet. But now you know that underlying the percentage of sales method of preparing projected income

statement and balance sheet is the assumption of constant growth in various items, and the reason for the

assumption of constant growth is assumption of constancy in 5 corporate policies; which in simple language means

“ running the co as well or as badly as it was run last year”.

Here it must be emphasized that the assumption of constancy of 5 major corporate finance policies is, to say the

least, idealistic; because in real life it may not be practical (or even desirable) for the corporate management to

keep the 5 major corporate finance policies exactly at the same level as last year. In fact it is generally considered

the job of top management to improve performance, which means that in real life the corporate top management

is likely to attempt to improve performance in some of these 5 major policy areas.

Next Three Years’ Projected financial statements ( The original example data)

We have already done forecasting of next year (year 1) income statement and balance sheet above, and it is given

here again. Next year Balance sheet was estimated as:

TA1= TL1+OE1

210=105+105

Next year( Year 1) Income statement was estimated as:

S1=525

NI1=10.5

EPS1=1.05m

DPS1= 0.525 Rs

Now let us continue our forecasting exercise for the next 3 years , that is year 2 to year 4 with 5 policies constant

thus growth in OE being 5%.

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Year 2 Forecast

Growth of OE in year 2 would be same as in year 1 because

DPS1 /EPS1 = d1 = 0.525/1.05 = 0.5 or 50% dividend payout end of year 1 which is same as dividend payout last

year; and NI1 /OE1 = 10.5 /105 = 0.1 or 10% is ROE end of year 1. And in the same way in future each year growth

in OE would be 5%.

gOE1 = ROE 1 (1 - d1) = 10% (1 - 0.5) = 5%

OE2 = OE1(1+ g) , OE2 =105(1 + 0.05) = 110.25

TA2/OE2 = 2

So:

TA 2 = OE2 * 2,

TA 2 = 110.25 * 2 = 220.5

TA2 - OE2 = TL2

220.5 - 110.25 = TL2

110.25 = TL2

S2 = S1(1 + g) = 525(1 + 0.05) = 551.25

Or

S2 / TA2 = 2.5, so

S2 = TA2 * 2.5,

S2 = 220.5 * 2.5 = 551.25

NI2 / S2 = 2% so:

NI2 = S2 * 2%

NI2 = 551.25 * 2%

NI2 =11.025

EPS2 = NI2 / number of shares

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EPS2 =11.025/10

EPS2 =1.1 Rs/share

DPS2 = EPS2 * d

=1.1* 0.5

=0.551 Rs

P1 = DPS2/ (Kc - g)

= 0.551/(0.1 - 0.05)

=11.02 Rs/Share

g Po= (P1 - Po) /Po

= ( 11.02 - 10.5) /10.5

=5%

Year 3 Forecast

OE3 = OE2 (1 + g )

= 110.25 (1 + 0.05)

=115.76m Rs

TA3 / OE3= 2

So:

TA 3 = OE3*2

=115.76 * 2

=231.5m Rs

TL3 = TA3 - OE3

=231.5 - 115.76

=115.76m Rs

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S3 / TA3 = 2.5

S3 = 2.5 * TA3

=2.5*231.5

=578.8

NI3 / S3 = 2%

So:

NI3 = S3 * 2%

=578.8 * 2%

=11.57m


=11.57/10

=1.15 Rs/shares

DPS3 = EPS3 * d

=1.15 *0.5

= 0.58 Rs

P2 = DPS3/ (Kc - g) . note: price of any year depend on DPS of the next year.

=0.58/ (0.1 - 0.05)

=11.58 Rs/Share

gP1= (P2 - P1) /P1

= (11.58 - 11.02) /11.02

=5%

Year 4 Forecast

OE4 = OE3 (1 + g )

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= 115.7( 1 + 0.05)

=121.49m Rs

TA4/OE4 = 2

TA4 = OE4 * 2

= 121.49 * 2

= 242.98m Rs

TL4 = TA4 - OE4

= 242.98 - 121.49mRs

= 121.49

S4 / TA4 = 2.5

S4 =2.5 * TA4

= 2.5 * 242 .98

= 607.4

NI4 / S4 = 2%

So:

NI4 = S4 * 2%

= 607.4 * 2%

= 12.14


= 12.14 / 10

=1.214 Rs/shares

DPS4 = EPS4*d

=1.214* 0.5

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= 0.61 Rs

P3 = DPS4 / (Kc – g)

=0.61/(0 .1 - 0.05)

= 12.14 Rs/Share

gP2 = ( P3 - P2) /P2 = (12.14 - 11.58) /11.58

=5% .

Please note this gP2 is estimated growth rate in share price from end of year 2 till end of year 3, that is growth rate

in the price of year 2, P2; it is not growth rate of share price in year 4, rather it is growth rate in share price in year

3. It tells price at the end of year 2 would grow how many percentage points by the end of year 3. It is so because

the mathematics of the PV (present value) of perpetuity requires discounting next year’s perpetual cash flows to

find today’s present value

PVP0 = cash flows 1 / discount rate

therefore DPS at the end of year 4 is discounted to estimate share price at the end of year 3; and percentage

change between price at the end of year 3 and at the end of year 2 is called growth in price in year 3 or capital

gains yield in year 3 which can be used to calculate expected rate of return (Kc) for year 3 from the share of this co.

From this 4- year financial planning exercise, hopefully you have learnt to make concise projected income

statements and balance sheets for the next 4 years. You have also learnt that if 5 major corporate finance policies

are not changed year after year then percentage growth rate in OE due to increase in RE translates into growth

rate in share price in the stock market, that is commonly called capital gains yield. To re-emphasize, the 5 policies

which were kept constant in this 4 year financial forecasting exercise were:

1) NI/S ratio (net profit margin on sales), it is a measure of profitability

2) S/TA ratio (turnover of TA), it is a measure of productivity of assets in generating sales

3) TA/OE ratio (Equity multiplier), it is a measure of financial leverage, and capital structure, and financial risk.

4) Number of Shares outstanding

5) DPS / EPS ratio, it is called dividend payout ratio, it is depicted by ‘d’, and it is a measure of dividend policy.

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As a conservative first step in financial planning it is advisable to attempt to look into financial future of a

corporation by assuming that next year performance in these 5 policy areas would be at least maintained at the

last year’s level; and you would agree that it is not a very demanding or ambitious target for the corporate

management to achieve.

Therefore first step in financial planning for an existing businesses should be to make projected financial

statements of next 4 or 5 years under the assumption that 5 corporate finance policies would remain constant.

As second step , and as part of risk analysis, later on scenarios can be developed to see the impact on income

statement, balance sheet, and on share valuation of changes in different policies. If impact on share value of such

policy changes is tested one by one it is called sensitivity analysis; and when changes in multiple policy variables

simultaneously are tested, it is called scenario analysis. The ultimate tool in this game of checking the impact of

policy changes on income statement, balance sheet, and share value is called simulation analysis. Simulation

Analysis requires use of powerful computer software, all possible ranges of 5 policy variables are combined again

and again; and outcome variables, such as TA, TL, OE, EPS, DPS, expected share price, are estimated from each

policy combination. The result is millions of forecasted income statements, balance sheets, and share values.

Then all of those millions of estimated values of variables of interest, such as expected share price for the next

year, or sales of next year, are put on a graph paper; and this graph usually takes the shape of a normal curve; then

using the related statistical tools applicable to normal curve (mean and standard deviation in case of normal

curve), you can estimate an expected value of next year’s sales or any other variable of interest such as NI, EPS,

Share price, etc; you can also use normal curve of possible share prices thus generated to make probabilistic

statement such as: there is 95% chance that next share price would be between 67 and 103 rupees with expected

value of 85 rupees as most probable price. Or you can make , using normal curve of share price, statement such

as: there is only less than one percent chance that share price would exceed above 119 rupees, and less than one

percent chance that share price would fall below 54 rupees.

Expected Rate of Return For Shareholders

Up till now in the exercise done above for 4 years’ financial planning of this hypothetical company, the growth

rates were estimated for various items of income statement and balance sheets; and projected income statement

and balance sheets in concise form were also made; but an important variable of interest for the shareholders ,

namely the expected rate of return (Kc) was not estimated. You can do that estimation as well because you have

all the required data. You know that expected rate of return for shareholders of a corporation is composed of

expected capital gains yield + expected dividend yield. Expected capital gains yield for each of the next three

years you have worked out already in pages above as (P1 - P0)) / P0 , and it was 5% in each of the next year under

the assumption of policy constancy in 5 policy areas; but expected dividend yield for each year is based upon end

of the year expected cash dividends received by shareholders by virtue of investing in the shares of this company

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at the beginning of the year, so expected dividend yield is : DPS 1/ Po for year one; DPS2 / P1 for year 2, DPS3/ P2 for

year three; let us work those out now

Expected ROR next year (Kc1) = (P1 - P0) / P0 + DPS1 /P0

= (5%) + (0.525 /10.5)

= 5% + 5%

= 10%

Expected ROR for year 2 (Kc2) = (P2 - P1) / P1 + DPS2 /P1

= 5% + (0.551 / 11.02)

= 5% + 5%

= 10%

Expected ROR for year 3 (Kc3) = (P3 - P2) / P2 + DPS3 /P2

= 5% + 0.58 / 11.58

= 5% + 5%

= 10%

Please note that though you have done financial planning exercise for the next 4 years by forecasting the balance

sheet and income statements for the next 4 years under the assumption of policy constancy and resulting growth

rate was also constant at 5 % for most of the important financial variables; but from this projected data you can

estimate expected rate of return for shareholders only for the next three years not for the next 4 years. It is also

interesting that not only share price is expected to grow by 5% each year (capital gains yield) , but also the

dividend yield each year would also be 5%, thus giving a forecast for expected rate of return 10% per year for each

of the next 3 years to the shareholders (that is owners) if 5 major policies are kept unchanged during the next 4

years. Please note that expected Kc came 10% because while doing valuation of share in year 0, 1, 2, 3, and 4, to

estimate P0, P1, P2, and P3, the risk adjusted required rate of return used , Kc, was 10% in the Gordon’s valuation

formula: P0 = DPS1 / (Kc - g).

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It is hoped that you remember from the previous classes that the current share price (P 0) at which risk adjusted

required rate of return calculated as Kc = Rf + (Rm - Rf) Beta (Levered) and expected rate of return calculated as Kc =

DPS1/P0 + (P1 - P0)/ P0 are same is called fair price or theoretically correct price of the share. In this example it is

10% required Kc as well as expected Kc; therefore estimated share price is the fair value of this share.

The above stated analysis and financial forecasting exercise may appear too simple to be believable; but based

upon your knowledge from previous courses in finance area, you can’t help admit that the underlying logic is

sound. And by now you have done hands-on financial planning for the next 4 years for this hypothetical co, albeit

under restrictive conditions of 5 policies being constant year after year. This is an important learning exercise for

you that will hopefully allow you in your practical life to apply this simple tool for estimating the future

performance (income statement) and financial position (balance sheet) of any business corporation in a few

minutes, like an expert physician. For further elaborate diagnosis you can work by employing the sensitivity

analysis, scenario analysis, and simulation analysis as briefly outlined in the previous paragraphs.

Please also note that constant growth example given above shows clearly that shareholders of fast growing

companies are likely to become richer sooner than shareholders of slow growing companies; therefore fast

growing companies are deemed as more valuable in the stock market because their share price is expected to

grow faster, and their shareholders are likely to get richer more quickly. And that is why when you go out looking

for investing in shares you should search for fast growing companies; also as finance manager who is looking for

target companies for friendly mergers and acquisitions or for hostile takeovers, you should look for companies

which have high growth potential. In fact most often quoted reason for the hostile takeovers of companies is poor

performance of their management as depicted by the low or negative growth rate of these companies; and

resulting destruction of shareholders value, because negative growth in share price means owners are becoming

poorer. The management of the acquiring co believes that there is room for improvement in various performance

areas of the target co. They also believe that the incumbent management of target company is so bad that it has

not realized such improvement; while the acquiring co believes it can introduce requisite improvements in target

co after take-over thus unleashing its growth potential which is finally going to result in value creation in the form

higher growth in share price.

For example: A co has paid Rs 3 per share cash dividends, its risk adjusted required rate of return estimated using

CAPM model is 17%, and it is estimated to grow at the constant growth rate of 3% per year for ever, this growth

rate was estimated as ROE (1 - d) under the assumption of constancy of 5 corporate policies.

Required:

Estimate its fair value of share today? Or in other words; at what price it should be trading in the market?

P0 = DPS0(1 + g) / ( Kc - g) = 3 (1 + 0.03) / (0.17 - 0.03) = 3.09 / 0.14 = 22.07 Rs per share.

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Now suppose you do not agree that this co has a growth potential and decide that it is a no growth co, that means

its g = 0%; what would be your estimate of its fair value per share?

P0 = DPS0(1 + g) / ( Kc - g) = 3 (1 + 0) / (0.17 - 0) = 3/0.17 = 17.64 Rs per share.

Lesson: growing companies are more valuable than non-growing companies. Now to extend this logic a bit further,

suppose you, as an analyst, believe this co’s product lines are losing market share to competitors, therefore you

think it is likely to experience negative 3% growth per year in foreseeable future. What is your estimate of its fair

value per share?

P0 = DPS0(1 + g) / ( Kc + g) = 3 (1 + - 0.03) / (0.17 - - 0.03) = 2.91 / 0.2 = 14.55 Rs per share.

Lesson: companies that are likely to shrink in future are less valuable.

The issue of growth would be discussed again and again in this course; especially the issue of constant growth

calculated as ROE (1 - d). Hopefully you would gain a lot more analytical insight when multiple methods of

decomposing the ROE would be discussed in detail in the coming classes. Just to re-emphasize the importance of

growth rate and therefore importance of ROE in the value creation process, just look a few line above at the

equation for fair value, you would notice ‘g” is appearing twice in that equation. Also notice that instead of writing

‘g’ in the equation, you could have written ROE (1 - d); thereby giving you fair value formulation which looks like:

P0=DPS0 [1+ROE (1−d ) ][K c−{ROE (1−d ) }]

ROE has positive influence on current share price while Kc and ‘d’ have negative influence. In simple terms: Higher

DPS next year and higher ROE would lead to higher share price while higher Kc and higher dividend payout rates

would push the share price downward. Though all these 4 drivers of share value are important but throughout this

course more attention would be paid to generating high ROE because out of 5 corporate policies discussed in this

lecture, 3 are constituents of ROE:

ROE = NI/ OE = NI/S * S /TA * TA/OE

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2 lecture 4 and 5 contant g

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