Question

Suppose the required rate of return on a stock with Beta 1.2 is 18 per cent and risk free rate is 6 per cent. According to the CAPM

a) What is the expected rate of return on the market portfolio?

b) What is the expected rate of return of a zero-beta security?

c) Suppose you select Stock ABC for Rs. 50 and the stock is expected to pay a dividend of rs. 2 next year and is expected to fetch Rs. 53 when sold. The stock has a beta of -0.5. Is the stock fairly priced, overvalued or undervalued?

d) A stock XYZ has Beta 1.5 and one year from now is expected to yield dividend income of Rs. 6. What is the fair price stock XYZ if its growth rate is 10 per cent?

c) Suppose you select

Answer 1

Beta = 1.2

Rf = 6%

Rm = 18%

a) Re = Rf + B(Rm-Rf)

Re = 6 + 1.2(18-6)

Re = 20.4

Expected rate of return = 20.4%

b) When B = 0

Re = Rf + B(Rm-Rf)

Re = 6 + 0(18-6)

Re = 6

Expected rate of return = 6%

c) Actual Return on Stock = Capital gain on sale plus dividend

= (53-50)+2 = 5

Actual return on stock = (5/50*100) = 10%

Return as per CAPM

Re = Rf + B(Rm-Rf)

Re = 6 + -0.5(18-6)

Re = 0

Since the Actual return is greater than the expected return as per CAPM, the security is undervalued.

d) Re as per CAPM = 6 + 1.5(18-6) = 24%

Re = Dividend/Price + Growth Rate

0.24 = 6/Prirce + 0.1

0.14 = 6/Price

Price = 6/0.14

Fair Price of Share = 42.86