Question

1. a. KL Airlines paid an annual dividend of $1.18 a share last month. The company is planning on paying $1.50, $1.75, and $1.80 a share over the next 3 years, respectively. After that, the dividend will be constant at $1.50 per share per year. What is the market price of this stock if the market rate of return is 10.5 percent?

b.ABC Ltd. plans to pay a yearly dividend of $0.50 over the next 10 years. After which the company’s yearly dividend will remain constant at $0.75. Determine the current price of the stock, if the required rate of return in the market is 10%?

Answer 1

Both the parts of the question ask us to use the Dividend discount model, also called Gordon's growth model, which states that Price of a stock is the sum of the present values of all the future dividends to be received.

a. Given that, D1 = 1.50 ; D2 = 1.75 ; D3 = 1.80 ; D4 = 1.50

Thereafter, dividends will remain constant at $1.50 per share per year. Hence, Growth Rate on dividends after 4th year, g = 0

R = Cost of Capital = 10.5%

P0 = Price of stock today = Sum of PV of all the future dividend payments

=> P0 = D1 / (1+R)¹ + D2 / (1+R)² + D3 / (1+R)³ + P3 / (1+R)³

P3 = D4 / (R - g) ..........................[ D4 / (R-g) means the capitalisation of the dividends to an amount, which when applied with R will give the result as D4.

But, the P3 calculated above is the price of the stock in year 3. So, we will discount the price of the stock in year 3 to get the present value of price of the stock in Year 3. Hence, P3 / (1+R)³

P3 = D4 / (R - g) = 1.50 / (10.50% - 0) = 14.28

Now, Let's calculate the Price of stock today, that is, P0.

=> P0 = D1 / (1+R)¹ + D2 / (1+R)² + D3 / (1+R)³ + P3 / (1+R)³

=> P0 = 1.50 / (1+10.50%)¹ + 1.75 / (1+10.50%)² + 1.80 / (1+10.50%)³ + 14.28 / (1+10.50%)³

We can do the calculations using a calculator or excel.

=> P0 = 14.708 = 14.71 (approx.)

The market price of this stock today is $14.71.

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b.

This is again a similar question.

The dividend over next 10 years = $0.50

Dividend from 11th year onwards, till perpetuity = $0.75

So, D11 = 0.75

Growth rate of dividends from 11th year, g = 0 because the dividends will remain constant.

Cost of Equity, R = 10% = 0.10

So, again,

Step 1:we will first calculate the price of stock in the 10th year,P10, based on the expected dividends from 11th year onwards.

Step 2: we will compute the Present value of P10 using R as the discounting Rate.

Step 3: We will find the Present value of all the dividends in the first 10 years, using the Present Value Interest Factor of Annuity (PVIFA) using R as the discounting Rate

Step 4: We will add the results of Step 2 and Step 3 because Price of a stock is the sum of the present values of all the future dividends to be received.

The steps are performed as below:

Step 1:  P10 = D11 / (R - g) = 0.75 / (0.10 - 0) = 7.50

P10 is the price of stock in the 10th year.

Step 2: PV of P10 = P10 / (1+R)¹⁰ = 7.50 / (1+0.10)¹⁰ = $2.89

Step 3: PV of all dividends in first 10 years = 0.50 x PVIFA (10%, 10 years)

PVIFA = (1 - (1 + r)^-n) / r = (1 - (1 + 0.10)^-10) / 0.10 = 6.144567

PV of all dividends in first 10 years = 0.50 x 6.144567 = $3.07

Step 4: P0 = PV of all dividends in first 10 years + PV of price of stock in the 10th year = 3.07 + 2.89 = 5.96

So, current price of the stock is $5.96.