Question

Suppose today you are considering whether to buy Stock Theta, and you want to do some basic analysis before buying the shares. By reading the firm’s most recent Balance Sheet, you find the following information: Net Income is $5,000,000, Total Shareholders’ Equity is $25,000,000, Total Assets is $40,000,000. From other publicly available sources, you further obtain the following information: the most recent earnings per share (EPS) is $3, the dividend payout ratio is 60%, and the firm’s beta is 1.4. The firm’s shareholders just receive the most recent dividends based on the above EPS and payout ratio today. Assume that the risk-free rate is 4%, and the market portfolio return is 16%.

Please answer the following questions:

(Please show your intermediate processes, instead of just a final number for your answers. Only round your final answers to two decimal places.)

(a) what is the return on equity (ROE) and dividends per share for this firm today?

(b) suppose this firm has a constant sustainable growth rate, what is the value of it?

(c) according to CAPM, what is the required rate of return you would expect based on the firm’s beta?

(d) based on the constant growth model and all your calculated results above, what would be the intrinsic value of this stock today? Assume that the dividends will increase at a rate of what you obtained from (b).

(e) Today, if this firm decides to pay out all its earnings as dividends forever and there is no any change in the amount of dividends, what would be the corresponding intrinsic value of this stock? Based on your calculation and results from (d), what would be the present value of growth opportunities (PVGO) for this stock?

Please remember for the essay questions, a simple final statement or numerical answer is not enough, you must show your explanations and any necessary intermediate procedures of calculations.

Answer 1

Answer (a)

Return on Equity = Net Income / Equity Capital

ROE = $ 5000000/25000000

= 20%

Dividend per share = Earnings per share * Payout Ratio

DPS = $3* 60%

DPS = 1.8 per share

Answer (b)

Sustainable growth Rate = Retention Ratio * Return on Equity

= 40%*20%

= 8%

Answer (c)

Rate of Return (Ke) as per CAPM = Rf + (Rm-Rf) *Beta

= 4 +(16-4) * 1.4

= 20.80%

Answer (d)

Instrinsic Value of share as per constant growth = (D1/ Ke-g)

= 1.8*1.08/0.208-0.08

= $ 15.1875

Answer (e)

When there is payout ratio of 100%, then DPS would be equal to EPS, therefore in current case DPS would be $3

Accordingly, there couldn't be any growth rate

So, Intrinsic Value of Share would be = D0/Ke

= 3/0.208

= $ 14.4231

Answer (f)

PVGO = Share Price - EPS/Ke

= 15.1875 - 3/0.208

= 0.7644