# Stock XYZ earning at time 0: E0 = $2.50, b = 40%, ROE =1 3%, risk-free rate = 3%, expected return... ## Question: Stock XYZ earning at time 0: E0 =$2.50, b = 40%, ROE =1 3%, risk-free rate = 3%, expected return on market portfolio is 9%, the beta of stock XTZ is 1.5 and CAPM is valid.

(1) What is the required rate of return k based on CAPM?

(2) What is D1 of stock XYZ?

(3) What is stock XYZ's P/E ratio?

(4) What is PVGO?

## PVGO:

Present value of growth opportunity (PVGO) measures the part of the value of a stock that is derived from future growth opportunities. This value is the current value of the stock and the hypothetical value if the stock has no growth.

(1) According to CAPM, the required return is:

• required return = risk free rate + beta * market risk premium
• required return = 3% + 1.5 *(9% - 3%)
• required return = 12%

(2) The expected dividend, D1, is the expected earnings per share times the dividend payout ratio. We first compute the growth rate:

• growth rate = ROE * (1 - b)
• growth rate = 13% *(1 - 40%)
• growth rate = 7.8%

Given current earnings per share of 2.5, the next dividend per share is:

• D1 = E0*(1 + g)* b
• D1 = 2.5 *(1 + 7.8%) * 40%
• D1 = 1.078

(3) We can use the dividend growth model to compute the price of the stock as follows:

• price per share = next dividend / (required return - dividend growth rate)
• price per share = 1.078 / (12% - 7.8%)
• price per share = 25.67

The P/E ratio = price per share / earnings per share = 25.67 / 2.5 = 10.27

(4) We can use the following formula to compute PVGO:

• PVGO = current price - earnings per share / required return
• PVGO = 25.67 - 2.5 / 12%
• PVGO = 4.84