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310 Corporate Finance BRILLIANT’S

Where, P = the current price of the share
o
D = the dividend expected to be paid at the end of year
1
K = the required rate of return
r
If dividends are expected to grow at a ¶{X {S>{dS>oÝS> Ho$ EH$ pñWa aoQ> na ~‹T>Zo H$s g§^mdZm
constant rate, equation would be reduced to: h¡, V~ ’$m°‘y©bm {ZåZ{b{IV hmoJm:

D 1
P 
o
K  G
r
Where, G = growth rate.
In equilibrium, the expected and required Bp³d{b{~«¶‘ ‘|, Ano{jV VWm [a³dm¶S>© aoQ> Am°’$
rates of return must be equal, so we can solve K [aQ>Z© g‘mZ hmoZm Mm{hE, Vm{H$ h‘ Bp³dQ>r na [aQ>Z© aoQ>
r
to obtain the required rate of return on equity: kmV H$aZo Ho$ {bE K gm°ëd H$a gH|$:
r
D 1
K   expected
r
P o
To illustrate this, consider a firm expected Bgo g‘PmZo Ho$ {bE ‘mZm {H$ EH$ ’$‘© H$mo AmZo dmbo
to earn ` 24 a share and to pay a ` 12 dividend df© ‘| EH$ eo¶a na ` 24 AZ© hmoZo VWm ` 12 H$m
during the coming year. The company's {S>{dS>oÝS> no H$aZo H$s g§^mdZm h¡& H§$nZr H$s A{Zª½g,
earnings, dividends and share prices have all {S>{dS>oÝS>g VWm eo¶a àmBgog g^r EH$ df© ‘| 12% ~‹T>
been growing at about 12% a year, this growth
rate is expected to continue indefinitely. If the OmVr h¢, ¶h J«moW aoQ> AmJo ^r Omar ahZo H$s g§^mdZm h¡&
current price of the equity share is ` 100, then, ¶{X Bp³dQ>r eo¶a H$s H$a§Q> àmBg ` 100 h¡, V~ K H$s
K would be estimated as follows: JUZm {ZåZ{b{IV àH$ma go H$s OmEJr:
12
K   12%  24%
r
100
If the firm refrains from meeting invest- ¶{X ’$‘© BÝdoñQ>‘|Q> Zht H$aVr h¡ VWm AnZr g^r
ment and pays all its earnings in dividends, it A{Zª½g H$mo {S>{dS>oÝS> Ho$ ê$n ‘| no H$aVr h¡ V~ Cgo AnZr
will cut its growth rate to zero. However, the J«moW aoQ> Oramo VH$ KQ>mZr hmoJr& hmbm§{H$ Bggo eo¶a H$s
price of the share will not fall, because investors H$s‘V Zht {JaoJr ³¶m|{H$ BÝdoñQ>g© H$mo A~ ^r AnZo eo¶g©
still get the required 24% rate of return on their na 24% H$m Ano{jV [aQ>Z© aoQ> {‘boJm&
shares.

24
K   0 24%
r
100
If a firm earns required rate of return K ¶{X ’$‘© Ano{jV [aQ>Z© aoQ> K AZ© H$aVr h¡ VWm dh
and it decides to retain earnings and invest A{Zª½g H$mo [aQ>oZ H$aZo VWm Cgo AnZo Am°naoeÝg ‘|
them in its operations, its current share price BÝdoñQ> H$aZo H$m {ZU©¶ boVr h¡ CgH$s H$a§Q> eo¶a àmBg
will not change as a result of this financing and CgH$s ’$m¶Z|qgJ VWm BÝdoñQ>‘|Q> Ho$ n[aUm‘ñdê$n Zht
investment. However, if it earns less than K the ~XboJr& hmbm§{H$ ¶{X dh K go H$‘ AZ© H$aVr h¡ V~