Question

Use the chart to answer the questions

Year    Return

1 2%

2 -6%

3 -1%

4 14%

5 -1%

6 5%

What is the average return on this stock?

What is the standard deviation of the annual returns?

What is the expected return on a stock, given the Beta is 1.2, the risk-free rate is 2% and the Market risk premium is 6%?

What is the most you should pay for a share of common stock that just paid a dividend of $1.68 if rate of return is 10% and you expect dividends to increase at a constant rate of 2%?

Answer 1

1)

Average return on stocks = ( 0.02 - 0.06 - 0.01 + 0.14 - 0.01 + 0.05) / 6

Average return on stocks = 0.13 / 6

Average return on stocks = 0.02167

Variance = [ ( 0.02 - 0.02167)² + ( -0.06 - 0.02167)² + ( -0.01 - 0.02167)² + ( 0.14 - 0.02167)² + ( -0.01 - 0.02167)² + ( 0.05 - 0.02167)²] / 6 - 1

Variance = [ 0.000003 + 0.00667 + 0.001003 + 0.014002 + 0.001003 + 0.000803] / 5

Variance = 0.023484 / 5

Variance = 0.004697

Standard devation is square root of variance

Standard deviation = ( 0.004697)^1/2 = 0.0685 or 6.85%

2)

Expected return on stock using CAPM model = risk free rate + beta ( market risk premium)

Expected return = 0.02 + 1.2 ( 0.06)

Expected return = 0.092 or 9.2%

3)

Price of share = D1 / required rate of return

Price of share = [1.68 ( 1.02) / 0.1]

Price of share = [ 1.7136 / 0.1]

Price of share = $17.136