Valuation of Shares — Preference, Ordinary Formulae [Worked Examples]
by Jack Bodeley on October 07, 2021
Valuation of Shares is ...
Classification of Shares
Shares are generally classified into two:
- Preference shares
- Ordinary or equity shares
Valuation of Preference Shares
Preference are further classified into:
- Redeemable preference shares
- Irredeemable preference shares
Valuation of Redeemable Preference Shares
The value of redeemable preference shares is the present value of dividends plus interest plus the present value of maturity value.
Formulae
$$P_0 = \left[\sum^{n}_{t=1}\frac{Div_t}{(1 + K_p)^t}\right]+\frac{P_n}{(1 + K_p)^n}$$
$$or;$$
$$P_0 = \left[\frac{Div_1}{(1 + K_p)^1}+\frac{Div_2}{(1 + K_p)^2}+...\frac{Div_n}{(1 + K_p)^n}\right]+\frac{P_n}{(1 + K_p)^n}$$
Where;
- $P_0$ — Preference shares value
- $Div_t$ — Preference dividends in year $t$
- $P_n$ — Terminal value of preference shares
- $K_p$ — Cost of preference shares
Valuation of Irredeemable Preference Shares
Irredeemable preference shares do not carry a terminal value. To arrive at a value, we discount the expected dividends into infinity.
Formula
$$P_0 = \frac{Div}{K_p}$$
Valuation of Ordinary of Equity Shares
The techniques used in the valuation of bonds will also be applied here—with a few modifications.
Worked Examples
Example 1.1
Suppose an investor is considering the purchase of 3-year, 10% £100 par value preference shares. If the redemption value of the preference shares is £115 and the required rate of return is 12%, what should he pay for the shares now?
Solution 1.1
$$P_0 = \left[\frac{10}{(1 + .12)^1}+\frac{10}{(1 + .12)^2}+\frac{10}{(1 + .12)^n}\right]+\frac{115}{(1 + .12)^3}$$
$$P_0 \approx 24.0183 + 81.8547 \approx £105.87$$
Example 1.2
Assume an investor is interested in £100 irredeemable preference shares of a company which pays a dividend of £15. If the required rate of return on these shares is 10%, what is their value today?
Solution 1.2
$$P_0 = \frac{15}{.1} = £150$$