Question

5. Market Equilibrium: Bingo Inc. has a beta of 0.8, a market price of $30, and recently paid a dividend of $2.00 which is expected to grow at a constant rate of 3%. The risk-free rate is 2% and the market risk premium is 6%.

a. Compute the required rate of return on Bingo stock.

b. Compute the expected return on Bingo stock.

c. Compute the dividend yield and capital gains yield for Bingo’s stock.

d. Is Bingo’s stock in equilibrium? If not, then explain what must happen for Bingo’s stock to be in equilibrium.

Answer 1

a. Compute the required rate of return on Bingo stock.

Formula to calculate Present value of stock with constant dividend growth

P0 = D0 (1+g) / (re –g)

Where

Price P0 = $30

Dividend paid recently D0 = $2.00

Constant Dividend growth rate g = 3% per year

Annual rate of return or required rate of return re =?

Therefore

Stock Price $30 = $2.00 * (1+3%) / (re% - 3%)

Or re = ($2.06/$30) + 3% = 9.87%

Therefore the required rate of return on Bingo stock is 9.87%

b. Compute the expected return on Bingo stock.

Assuming CAPM holds we have following formula

Expected return for Bingo Inc. = risk free rate + β*market risk premium

Where

Risk-free rate = 2%

The market risk premium = 6%

And beta of stock = 0.8

Therefore

Expected return for Bingo Inc. = 2% + 0.8 * 6%

= 2% +4.8% = 6.8%

The expected return for Bingo Inc. is 6.8%.

c. Compute the dividend yield and capital gains yield for Bingo’s stock.

Dividend yield = (Current Expected dividend / current share price) *100

= ($2/$30) *100

= 6.67%

Capital gains yield = [(Stock’s selling price at year end - Stock’s current selling price)/ Stock’s current selling price]*100

Where, Stock’s current selling price P0 = $30.00

Stock’s selling price at year end P1 = $2.06*(1+3%) / (9.87% -3%) = $30.90

Therefore,

Capital gains rate = (P1 –P0) /P0 *100

= ($30.90 - $30.00)/$30.00 * 100

= ($0.90 / $30.00) *100 = 3%

d. Is Bingo’s stock in equilibrium? If not, then explain what must happen for Bingo’s stock to be in equilibrium.

No Bingo’s stock is not in equilibrium. For equilibrium, the required rate of returns should be equal to expected returns of Bingo’s stock. For Bingo’s stock to be in equilibrium the required rate of returns of 9.87% should decrease to equal to expected returns of Bingo’s stock of 6.8%.