# You want to buy Burrito Inc. stock. They pay annual dividends, with the next dividend of $0.45... ## Question: You want to buy Burrito Inc. stock. They pay annual dividends, with the next dividend of$0.45 per share being paid later today. You believe that, during the next 10 years, their annual dividends will grow by 45% APR, compounded annually. But after 10 years, their annual dividends will grow more slowly... only at 4% APR compounded annually.

Burrito Inc. has a beta of 1.78. The risk-free rate of return is 3%, and the average risk premium is 6%. What should be the price of a share of Burrito stock?

## Dividend Discount Model (DDM):

The dividend discount model is a model used to value shares of stock which is based on an idea a share of stock is worth the present value of dividends anticipated to occur in the future. DDM discounts future dividends at a given rate of return on a company's stock.

First, we will calculate the return on the stock using the CAPM formula which is given below:

{eq}R= R_{f} + \beta \times (R_{m} - R_{f}) {/eq}, where:

• {eq}R {/eq} = return on stock
• {eq}R_{f} {/eq} = risk-free rate
• {eq}\beta {/eq} = beta of the stock
• {eq}R_{m} {/eq} = expected return on the market
• {eq}(R_{m} - R_{f}) {/eq} = market risk premium

{eq}R= 3\% + 1.78 \times 6\% = 13.68\% {/eq}

The price of the stock is the sum of dividends discounted at the given rate of return on stock. We know that dividends will grow at a rate of 45% annually for the first 10 years. Then the growth rate will decrease to 4%. Assuming that this growth rate will continue forever, we can use the Gordon growth model to find the value of the growing stream of dividends starting from the dividend at year 11. The dividends for the first ten years can be discounted using a simple present value formula. Hence, the calculation should look like this:

{eq}Price = 0.45 + \dfrac{0.45 \times (1+0.45)^{1}}{(1+0.1368)^{1}} + \dfrac{0.45 \times (1+0.45)^{2}}{(1+0.1368)^{2}} + \dfrac{0.45 \times (1+0.45)^{3}}{(1+0.1368)^{3}} + \dfrac{0.45 \times (1+0.45)^{4}}{(1+0.1368)^{4}} + \dfrac{0.45 \times (1+0.45)^{5}}{(1+0.1368)^{5}} + \dfrac{0.45 \times (1+0.45)^{6}}{(1+0.1368)^{6}} + \\ + \dfrac{0.45 \times (1+0.45)^{7}}{(1+0.1368)^{7}} + \dfrac{0.45 \times (1+0.45)^{8}}{(1+0.1368)^{8}} + \dfrac{0.45 \times (1+0.45)^{9}}{(1+0.1368)^{9}} + \dfrac{0.45 \times (1+0.45)^{10}}{(1+0.1368)^{10}} + \dfrac{0.45 \times (1+0.45)^{10} \times (1+0.04)}{0.1368 - 0.04} \times \dfrac{1}{(1+0.1368)^{10}} {/eq}

{eq}Price = \$77.22 {/eq} The answer is: the price of a share of Burrito stock is$77.22. 