Question

Part 1: Dallas Star Inc.'s stock has a 40% chance of producing a 5% return, and a 60% chance of producing a 12% return. What is the firm's expected rate of return? What is the firm's Standard Deviation? What is the firm's Coefficient of Variation?

Part 2: Calculate the required rate of return for Dallas Star Inc., assuming that (1) investors expect a 1.5% rate of inflation in the future, (2) the real risk-free rate is 2.0%, (3) expected market return is 8% and (4) the firm has a beta of 1.5. (Hint: You need to find out market risk premium first.)

Answer 1

1)

Expected return = sum of (probability of state * return of state)

= 0.4*0.05 + 0.6*0.12

= 9.2%

E(X^2) =  sum of (probability of state * return of state^2)

= 0.4*0.05^2 + 0.6 * 0.12^2

= 0.00964

variance = E(X^2) - (E(X))^2

= 0.00964 - (0.092)^2

= 0.001176

Standard deviation = sqrt(variance)

= sqrt(0.001176)

= 3.43%

coefficient of variation= 0.0343/0.092

= 0.3728

2)

Required return

= risk free rate + inflation + beta * market risk premium

= 0.02 + 0.015 + 1.5 * (0.08-0.02)

= 12.5%