We have the following information for the Valverde company. The stock pays a $1 dividend and it will grow by 12% the first year, 9% the second year and 3% forever after that. The unlevered bheta is 1, D/E is 75/25 and the tax rate is .3. Additionally, we know the treasury bond rate is 0.04 and the ROR of the S&P has been 10%. Required:
Derive the stock price of Valverde.

P0 = $5.99394080634  rounded off to $5.99

Explanation:

The dividend discount model (DDM) can be used to calculate the price of the stock today. DDM calculates the price of a stock based on the present value of the expected future dividends from the stock. The formula for price today under DDM is,

P0 = D1 / (1+r)  +  D2 / (1+r)^2  +  ...  +  Dn / (1+r)^n  +  [(Dn * (1+g) / (r - g)) / (1+r)^n]

Where,

We first need to calculate the levered beta of Valverde.

Levered Beta = Unlevered Beta * [1+ (1-tax rate) * (Debt/Equity)]

Levered Beta = 1 * [(1 + (1 - 0.3) * (75/25)]

Levered Beta = 3.1

We first need to calculate the cost of equity (r) using the CAPM equation. The equation is,

r = risk free rate  +  Levered Beta  *  (Expected return on Market - risk free rate)

We know that the risk free rate is 0.04 or 4%, the beta is 3.1 and the expected return on market is 0.1 or 10%.

r = 0.04  +  3.1  *  (0.1 - 0.04)

r = 0.226 or 22.6%

Now, using the DDM equation, the price of stock will be,

P0 = 1 * (1+0.12) / (1+0.226)  +  1 * (1+0.12) * (1+0.09) / (1+0.226)^2  +  

[(1 * (1+0.12) * (1+0.09) * (1+0.03) / (0.226 - 0.03)) / (1+0.226)^2]

P0 = $5.99394080634  rounded off to $5.99

P0 = $99.2830  rounded off to $99.28

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