# An analyst uses a two-stage variable growth model to estimate the value of Old Maid Company's...

## Question:

An analyst uses a two-stage variable growth model to estimate the value of Old Maid Company's common stock. The most recent annual dividend paid by the company was $3 per share. The analyst expects dividends to increase 8% per year for the next 3 years and then drop to 4% starting in year 4 and remain stable for the foreseeable future. The required rate of return used for the analysis is 10%.

(a) What are the expected dividends for the next 4 years?

(b) What is the value of the stock attributable to the first 3 years of dividends?

(c) What is the value of the stock at the end of year 3?

(d) What is the value of the stock attributable to years 4 and beyond?

(e) What is the total value of the stock?

## Horizon Value:

In the dividend growth model, horizon value is a concept that arises when the dividend of a stock has non-constant growth rate. Specifically, dividends will have time-varying growth rates followed by a perpetual constant growth rate.

## Answer and Explanation:

(a) The expected dividend for the next four years are:

- year 1: 3 *(1 + 8%) = 3.24
- year 2: 3.12 *(1 + 8%) = 3.50
- year 3: 3.25 *(1 + 8%) = 3.78
- year 4: 3.37 *(1 + 8%) = 4.08

(b) The value of the stock attributable to the first 3 years of dividend is the present value of the next three years of dividends, i.e.,

- {eq}\dfrac{3.24}{(1 + 10\%)} + \dfrac{3.50}{(1 + 10\%)^2} + \dfrac{3.78}{(1 + 10\%)^3} = 8.67 {/eq}

(c) We can use the dividend growth model to compute the value of the stock at the end of year 3:

- price = next dividend / (required return - dividend growth rate)
- price = 4.08 / (10% - 4%)
- price = 68

(d) The value of the stock attributable to years 4 and beyond is the present value of the stock price at the end of year 3, i.e.,

- {eq}\dfrac{68}{(1 + 10\%)^3} = 51.09 {/eq}

(e) The price of the stock today is:

- {eq}8.67 + 51.09 = 59.76 {/eq}

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