# 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.

## Answer and Explanation:

(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

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