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In: Finance

Develop a valuation model for a common stock assuming that a company just paid a dividend of $1.75 per share.

Develop a valuation model for a common stock assuming that a company just paid a dividend of $1.75 per share. It’s assumed that the dividend will grow at a constant rate of 6% per year forever. The risk-free rate is 6% with an expected return on the market of 12% and a beta of 1.1. Show each step in generating the resulting valuation.

Expert Solution

Stock Price : Price of any security is present value of future cash flows it, that are discounted at specified discount rate.

Stock Price = D1 / [ Ke - g ]

D1 = D0 ( 1 +g )

D1 - Div after 1 Year

P0 = Price Today

Ke - required Ret

g - Growth Rate.

Required RetCalculation:

Required Ret = Rf + Beta ( Rm - Rf )

Rf = Risk free ret
Rm = Market ret
Rm - Rf = Risk Premium
Beta = Systematic Risk

Particulars	Amount
Risk Free Rate	6.000%
Market Return	12.000%
Beta	1.1000
Risk Premium ( Rm - Rf)	6.00%

Beta Specifies Systematic Risk. Systematic risk specifies the How many times security return will deviate to market changes. SML return considers the risk premium for Systematic risk alone.Where as CML return considers risk premium for Total risk. Beta of market is "1".

SML Return = Rf + Beta ( Rm - Rf )
= 6 % + 1.1 ( 6 % )
= 6 % + ( 6.6 % )
= 12.6 %

Rf = Risk Free Rate

Stock Price:

Particulars	Amount
D0	$ 1.75
Growth rate	6.00%
Ke	12.60%

Price of Stock is nothing but PV of CFs from it.
Price = D1 / [ Ke - g ]
D1 = D0 ( 1 + g )
= $ 1.75 ( 1 + 0.06 )
= $ 1.75 ( 1.06 )
= $ 1.86

Price = D1 / [ Ke - g ]
= $ 1.86 / [ 12.6 % - 6 % ]
= $ 1.86 / [ 6.6 % ]
= $ 28.11

Where
D0 = Just Paid Div
D1 = Expected Div after 1 Year
P0 = Price Today
Ke = Required Ret
g = Growth Rate

Price of stock Today is $ 28.11

jeff jeffy answered 2 years ago

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