Explain the difference between redeemable and irredeemable preference shares and calculate the value of the preference share under different scenarios.

Okay, let's continue with Question 3 and Question 4.

QUESTION THREE

a) Explain the difference between redeemable and irredeemable preference shares and how this difference affects (8 marks)

Redeemable preference shares have a specified maturity date, meaning the company repurchases them at a predetermined price, similar to debt. Irredeemable preference shares, conversely, have no maturity date and remain outstanding indefinitely, functioning as a perpetual security. This distinction significantly impacts their valuation; redeemable shares are valued like bonds, considering both periodic dividends and the final principal repayment, while irredeemable shares are valued as a perpetuity based solely on their constant dividend stream. Consequently, redeemable shares offer investors greater certainty of capital repayment, reducing capital risk compared to irredeemable shares, which carry the risk of never having the principal returned by the company.

b) Calculate the value of the preference share under the following scenarios (12 marks)

Given:
Face Value (FV) = GH¢100
Dividend rate = 10%
Required rate of return ($r_p$) = 11%

First, calculate the annual preference dividend ($D_p$):

$$D_p = \text{GH}\cent 100 \times 0.10 = \text{GH}\cent 10$$

i) If the share has a maturity period of 6 years

Step 1: Identify the given values for a redeemable preference share.
$D_p = \text{GH}\cent 10$
$r_p = 0.11$
$\text{FV} = \text{GH}\cent 100$
$n = 6$ years

Step 2: Calculate the present value of the annual dividends.

$$\text{PV (Dividends)} = D_p \times \left[ \frac{1 - (1+r_p)^{-n}}{r_p} \right]$$ $$\text{PV (Dividends)} = \text{GH}\cent 10 \times \left[ \frac{1 - (1+0.11)^{-6}}{0.11} \right]$$ $$\text{PV (Dividends)} = \text{GH}\cent 10 \times \left[ \frac{1 - 0.53464}{0.11} \right]$$ $$\text{PV (Dividends)} = \text{GH}\cent 10 \times 4.2305$$ $$\text{PV (Dividends)} = \text{GH}\cent 42.305$$

Step 3: Calculate the present value of the face value (redemption amount).

$$\text{PV (Face Value)} = \frac{\text{FV}}{(1+r_p)^n}$$ $$\text{PV (Face Value)} = \frac{\text{GH}\cent 100}{(1+0.11)^6}$$ $$\text{PV (Face Value)} = \frac{\text{GH}\cent 100}{1.87041}$$ $$\text{PV (Face Value)} = \text{GH}\cent 53.464$$

Step 4: Sum the present values to find the intrinsic value ($P_0$).

$$P_0 = \text{PV (Dividends)} + \text{PV (Face Value)}$$ $$P_0 = \text{GH}\cent 42.305 + \text{GH}\cent 53.464$$ $$P_0 = \boxed{\text{GH}\cent \textbf{95.769}}$$

ii) If the share has no maturity date

Step 1: Identify the given values for an irredeemable preference share.
$D_p = \text{GH}\cent 10$
$r_p = 0.11$

Step 2: Calculate the intrinsic value ($P_0$) using the perpetuity formula.

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