The returns of a common stock consist of cash dividends and capital gains that are highly uncertain. The uncertainty associated with returns
from common stock makes the valuation of common stock difficult.
Generally returns on preferred stocks and bonds are fixed and predictable, whereas the returns on common stock are variable depending on the performance of the enterprise. Notwithstanding the variability of returns on common stocks, the expected returns in forms of dividends and capital gains are the major variables employed in common stock valuation.
Since common stocks have no maturity date, unlike bonds, we begin by assuming a one– year holding period. This can be determined by using the following formula.
Ke = E(D1) + (E(P1) – Po) Po
Where Ke = Cost of common/equity stock
E(D1) = Expected dividend per share in period 1 E(P1) = Expected market price per share in period 1 Po = current market price of share.
Example One
Assuming that Mohammed Plc’s common stock has an expected dividend per share, E(D), of N6, the current price of a share (Po) is N65, and the expected price at the end of the year, E(P1), is N73, determine the expected return on the share, (Ke), for a one – year holding period.
Ke = E(D1) + (E(P1) – Po) Po
Ke = N6 + (N73 – N65)= 0.2154 = 21.54%
N65
This implies that the expected return on the security holding for one – year period, (ke) is 21.54%. Therefore, depending on the investor’s required rate of return (IRR), if Ke > RRR, he should go for this investment and vice versa.
Equation above can be used to determine current price of the share if we are given investor’s forecast of dividend and price, and the expected return of other equally risky shares. Thus,
Po = ED1 + E(P1) 1 + Ke
The above formula is achieved by making current price (Po ) the subject of the fomula.
Example Two
Assuming that Mohammed Plc’s shares in the above example one is= E (P1) = N73 and E(D1) = N6. If the expected returns for securities in the same risk class, as Mohammed Plc are 21.54 percent, determine current price of the share.
Solution
Po = N6 + N73 = N79 = N65
(1 + .2154) 1.2156
Whenever the estimated value of the share, which is the intrinsic value, is greater than the actual market price, the share is said to be undervalued, investors will want to buy more of the shares. For instance if the market of price of Mohammed Plc share is less than N55, which is calculated value, investors would like to buy more of the shares of Mohammed Plc, and vice versa.
If the holding period is for a longer period more than one year, as it is with most investor, then equation can be expressed as follows:
)
E(Dt) = Expected dividend at the end of period t Ke = Expected return on a share or cost of equity E(Pn) = Market price expected to prevail at period n.
Po = Current market price
∑
= n t 1= Sum of the discounted dividends from period 1 to n Ke will be assumed constant in a multi period model.
Example Three
Assuming that Mohammed Plc shares in the above example expected dividend after a year, E(D1), is N6, and it is expected to grow at a rate of 10 percent per annum, the expected dividend after two years, E(D2), will be N6 (1.10) = N6.60; after three years. N6.0 (1.10)2 = N7.26 and so on. Assume that the expected return on the share is 24 percent, whereas the expected price of the share at the end of 5 year is N75, calculate the current market price of the share.
Solution
The value of dividends in N16.09 and value of the price at the end of five years is N25.58.
If the holding is infinite (∝) i.e., n approaches to infinity, the present value of the future price will approach zero. Thus, the price of a share today is the present value of an infinite stream of dividends.
∞
The above equation relies on dividends as its foundation as such it is called Dividend Capitalization Model. If common stock dividends do not grow over time but remain constant, that is E(D1) – E(D2) = --- E(D∝), then equation will become:
Po = E(D) Ke Example Four
Zaco Inc. is currently paying N8.0 dividend per share. This level of dividends is expected to be maintained into the future. If the capitalization rate, i.e. cost of equity is 16 percent, determine the current market price per share.
Solution
Po = N8.0 = N50
0.16
However, if dividends are expected to grow, but at a constant rate, the equation will become.
Do = dividend at time zero (that is a current dividend).
g = constant growth rate of dividend
If Ke is greater than g (a reasonable assumption since a dividend growth rate which is always greater than the capitalization rate would imply an infinite stock value), the equation can be expressed as follow:
Po = E(D1) Ke - g
Where: ED1 = the expected dividend per share at time 1.
The above equation is the perpetual growth model in which the relationship between Ke and g is assumed to be constant and perpetual.
To obtain the investor’s required rate of return, Ke, we can rearrange equation as follows:
Ke = E(D1) + g Ke – g Example Five
Assuming the Mohammed Plc has recently paid N7.5 each dividends and it is expected to grow at an 8 percent rate per annum forever, the dividend per share expected at t = 1 is N7.5 (1.08). If the market capitalization rate is 20 percent; determine the present value of the share.
Solution:
Po = N8.10 = N67.50
.20 - .08
For most companies in the mature stage of their life cycle, the perpetual growth model is often reasonable.