Question

Finance 4310 Homework Problem Given the following information about Stock A: P. = $62.75 BA= 1.3 D = $2.20 paid at end of year K = 11% annual R = 5% annual a. Estimate the price of stock A at the end of the year b. Suppose that Stock a is combined with two other stocks as follows: Stock Proportion Beta 0.25 0.40 0.35 1.3 0.9 1.1 What is the beta of the portfolio of three stocks?

Answer 1

Cost of equity= R(f)+ β{E(m)-R(f)}

•             R(f) = Risk-Free Rate of Return

•             β = Beta of the stock

•             E(m) = Market Rate of Return

•             [E(m)-R(f)] = equity risk premium

R(f)= 5%

B= 1.3

E(m)= 11%

Cost of equity = 0.05+ 1.3(0.11-0.05)

= 0.05 + 1.3* 0.06

= 0.05+ 0.078

= 0.128 or 12.8%

Cost of equity = (DPS/MPS)+g

DPS= Dividend per share. MPS= Market price per share, g= growth rate of dividend

So growth g= Cost – Pps/MPS

= 0.128- 2.20/62.75

= 00.128-0.035

G = 0.0929 or 9.29%

Value of stock = D1 / (k - g)

where:

D1 = next year's expected annual dividend per share

k = the investor's discount rate or required rate of return,

g = the expected dividend growth rate

Value = 2.20(1+0.0929) / (0.128-0.0929)

= 2.404/0.0351

= 68.49

Price of stock = $68.49

b.

beta of portfolio = Beta of A*weight of A + beta of B*weight of b+ beta of C * weight of c

= 0.25*1.3 +0.40*0.9+0.35*1.1

= 1.07