# Valuation of Shares — Preference, Ordinary Formulae [Worked Examples]

by Jack Bodeley on October 07, 2021

## 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

$$P_0 = \frac{15}{.1} = £150$$