CrunchingAlphaα

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:

  1. Preference shares
  2. Ordinary or equity shares

Valuation of Preference Shares

Preference are further classified into:

  1. Redeemable preference shares
  2. 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

$$P_0 = \frac{15}{.1} = £150$$