Question

Stewart Industries expects to pay a $3.00 per share dividend on its common stock at the end of the year. The dividend is expected to grow 25% a year until t=3 after which time the dividend is expected to grow at a constant rate of 5% a year. The stock’s beta is 1.2, the risk free rate of interest (R_f) is 6% and the rate of return on the market (R_m) is 11%. Use the CAPM equation to find the required rate of return: R_s = R_f + (R_m-R_f)*beta.

What is the company’s current stock price?

1. $60.00
2. $55.75
3. $59.05
4. $45.60
5. $70.00
6. $77.90

The dividend yield and capital gains yield at the end of year 1 are:

1. 5.08%; 6.92%
2. 6.00%; 6.00%
3. 6.12%; 5.88%
4. 5.80%; 6.90%
5. 12%; 10%
6. 5.9%; 2%

Answer 1

Stewart Industries expects to pay a $3.00 per share dividend on its common stock at the end of the year. The dividend is expected to grow 25% a year until t=3 after which time the dividend is expected to grow at a constant rate of 5% a year. The stock’s beta is 1.2, the risk free rate of interest (R_f) is 6% and the rate of return on the market (R_m) is 11%. Use the CAPM equation to find the required rate of return: R_s = R_f + (R_m-R_f)*beta.

- Expected Dividend to be paid at the end of year 1(D1) = $3.00

Dividend growth rate for next 2 years(g) = 25%

Dividend Growth rate thereafter(g1) = 5%

As per CAPM,

R_f = Risk free Return = 6%                                                    

R_m = Market return = 11%

Beta of Stock = 1.2

Required Rate of Return = 6% + 1.2(11%-6%)

= 12%

So, Required Rate of Return(Ke) = 12%

Calculating the Current Stock Price:-

P0 = 2.6786 + 2.9895 + 3.3365 + 50.0470

P0 = $59.05

So, Company's Current price is $59.05

Option C

- Now, Calculating Price of Stock at year end 1 for Capital Gain Yield purpose.

P1 = 3.3482 + 3.7368 + 56.0527

P1 = $63.14

- Formula for Capital Gain Yield:-

Capital Gain Yield = (P1 - P0)/P0

Capital Gain Yield for year end 1 = ($63.14-$59.05)/$59.05

= 6.92%

- Formula for Dividend Yield:-

Dividend Yield = (D1)/P0

Dividend Yield for year end 1 = ($3)/$59.05

= 5.08%

Option A

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