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Bonga currently has a portfolio of ordinary shares representing several different companies. Bonga considers it to be a well-balanced investment portfolio, but he wants to reduce the overall risk of the portfolio a bit more by including ordinary shares from Titan Mining Corporation. The following information on Titan Mining Corporation is available: For the period 2017 to 2020, the company paid the following dividends per year respectively: R3,14; R3,55; R3,89; and R3,95. The 2021 dividend is expected to increase by the average growth rate of the dividends between 2017 and 2020, and the dividend will increase by 10% per year indefinitely from 2022 onwards. Bonga requires a return of 15% on his investment portfolio and is not prepared to pay more than R52,00 per ordinary share of Titan Mining Corporation.Calculate the current price of Titan Mining Corporation’s ordinary share.

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Answer to a math question Bonga currently has a portfolio of ordinary shares representing several different companies. Bonga considers it to be a well-balanced investment portfolio, but he wants to reduce the overall risk of the portfolio a bit more by including ordinary shares from Titan Mining Corporation. The following information on Titan Mining Corporation is available: For the period 2017 to 2020, the company paid the following dividends per year respectively: R3,14; R3,55; R3,89; and R3,95. The 2021 dividend is expected to increase by the average growth rate of the dividends between 2017 and 2020, and the dividend will increase by 10% per year indefinitely from 2022 onwards. Bonga requires a return of 15% on his investment portfolio and is not prepared to pay more than R52,00 per ordinary share of Titan Mining Corporation.Calculate the current price of Titan Mining Corporation’s ordinary share.

Expert avatar
Seamus
4.9
98 Answers
"To calculate the current price of Titan Mining Corporation's ordinary share, we can use the Dividend Discount Model (DDM), which is particularly useful for companies that pay dividends regularly. The formula for the price of a stock in this model is:

P = \frac{D_1}{r - g}

where:
- P is the current price of the stock.
- D_1 is the expected dividend next year.
- r is the required rate of return.
- g is the expected growth rate of dividends.

### Step 1: Calculate the Average Growth Rate from 2017 to 2020

The growth rates for each year are as follows:
- From 2017 to 2018: 13.06%
- From 2018 to 2019: 9.58%
- From 2019 to 2020: 1.54%

The average annual growth rate over the period from 2017 to 2020 is approximately 8.06%.

### Step 2: Calculate D_1 for 2021

Given the average growth rate obtained in Step 1, the dividend for 2021 ( D_1 ) is calculated using:
D_1 = \text{Dividend}_{2020} \times (1 + \text{average growth rate})

### Step 3: Calculate the Price of the Stock Using DDM

Using a required return r = 0.15 (15%) and a growth rate g = 0.10 (10%) from 2022 onwards, the price of the stock is calculated as:
P = \frac{D_1}{0.15 - 0.10}

### Calculation Details

- Dividend for 2021 ( D_1 ): R4.27
- Price of the Stock Using DDM: Approximately R85.37

\boxed{Current \ price = R85.37}"

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