
Ryan S. answered 02/11/14
Tutor
4.8
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Mathematics and Statistics
The CAPM model says that the return on an asset includes the risk free rate of return plus additional return based on the asset's risk relative to the market.
ra : expected rate of return of asset
rf : risk-free rate of return
rm : expected rate of return of market
β : beta of asset
ra = rf + β(rm - rf
ra = 0.06 + 1.5(0.18 - 0.06) = 0.18
In other words, in an efficient market, investors will demand a return of 18% on this asset.
The return is calculated thus:
P0: Current price of stock
P1: Price of stock after one year
D0: Current dividend = $1
D1: Dividend after one year
(P1 + D1)/P0 - 1 = ra
This is where the problem is not fully clear to me. Does the statement that the earnings are growing annually at 6% mean that the expected P1 is 1.06*P0? I will assume so. Then we have:
1.06(P0 + 1)/P0 - 1 = 0.18
(P0 + 1)/P0 = 1.18/1.06 = 1.1132
0.1132P0 = 1
P0 = 8.83
This means that in an efficient market, an investor will pay $8.83 for a stock with this risk profile whose price and $1 dividend is expected to increase 6% annually in an environment where the risk free rate is 6% and the market rate of return is expected to be 15%.