Question

2. In Apple’s just-released financial report, it had an earnings per share of E0 = $4. It has also

just paid dividend per share of D0 = $1. The risk-free rate is 0%, Apple stock's beta is 1, and

the expected market return is 10%. Currently, Apple has a stock price of $100. You assume

Apple's dividend grows at a constant rate.

a. What is Apple's ROE implied by the dividend discount model? (That is, you need to use the

dividend discount model to solve Apple’s ROE)

After reading Apple's financial statements, you find that Apple's net income is 9 million and its shareholders' equity is 100 million.

b. What is Apple ROE calculated from its financial statement

c. What is Apple's intrinsic value? Is Apple undervalued or overvalued

d. Assume you are the advisor to Tim Cook, the CEO of Apple, you tell him the stock's intrinsic

value will increase to $40 if he starts now to pay all earnings as dividends. Show him the

calculation.

Answer 1

(a): Stock Price = Expected Dividend Per Share / (Cost of Capital Equity - Dividend Growth Rate )

Cost of Capital Equity using = Risk free rate of return + Beta × (market rate of return – risk free rate of return) => 0 + 1*(10-0) = 10%

Hence, 100 = 1 / (10-Dividend Growth Rate)

Hence, Dividend Growth Rate = 10 - 1/100 = 9.99

Also, Dividend Growth Rate = ROE * Retention Ratio = ROE * 3/4

Hence, ROE = 9.99*4/3 = 13.32%

(b): ROE = Net Income / Shareholders' Equity = 9/100 = 9%

(c): Using ROE from (b) and plugging in formlae for (a), to calculate intrinsic value (Stock Price).

Intrinsic Value = Expected Dividend Per Share / (Cost of Capital Equity - Dividend Growth Rate )

Dividend Growth Rate = ROE * Retention Ratio = 9 * 3/4 = 6.75%

Hence, Intrinsic Value = 1 / (10% - 6.75%) = ~$30.77

Apple stock is OVERVALUED

(d): In this scenario, Retention Ratio = 0 and Expected Dividend Per Share = $4. Hence using formula in (c),

Dividend Growth Rate = ROE * Retention Ratio = 9 * 0 = 0%

Intrinsic Value = Expected Dividend Per Share / (Cost of Capital Equity - Dividend Growth Rate ) = 4 / (10%-0%) = $40

Let me know in case of any issues. Enjoy learning. Good luck!