Question

Milwaukee Telecom (MT) just paid a dividend (D0) of $2.44 per share; future dividends are expected to grow 3% per year indefinitely. The firm’s stock is not publicly traded but data from comparable firms shows an average beta of 1.28; these firms had average debt-equity ratios of 51 and an average tax rate of 28%. MT has a debt-equity ratio of 82 and a tax rate of 32%. The current yield on 10-year U.S. Treasury bonds is 2.8%, and the expected return on the S&P 500 is 11.6%. What would be the firm’s current cost of common stock?

Answer 1

Unlevered beta of Comparable firms = Levered Beta * Equity / [ Equity+ Debt ( 1 - Tax )

= 1.28 * [ 1 / 1 + 0.51 ( 1 - 0.28 ) ]

= 1.28 * [ 1 / ( 1 + 0.51 * 0.72 )

= 1.28 * [ 1 / 1 + 0.3672 ]

= 1.28 * 1 / 1.3672

= 0.9362

Levered Beta of MT = Unlevered Beta * [ E + D( 1 - T ) ] / E

= 0.9362 * [ 1 + 0.82 ( 1 - 0.32 ) ] / 1

= 0.9362 * [ 1 + 0.82 * 0.68 ] / 1

= 0.9362 * [ 1 + 0.5576 ] / 1

= 0.9362 * 1.5576

= 1.4583

CAPM Ret = Rf + Beta ( Rm - Rf )

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

Particulars	Amount
Risk Free Rate	2.8%
Market Return	11.6%
Beta	1.4583
Risk Premium ( Rm - Rf)	8.80%

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 )
= 2.8 % + 1.4583 ( 8.8 % )
= 2.8 % + ( 12.83 % )
= 15.63 %

Rf = Risk Free rate

Stock Price :
The price is a reflection of the company's value – what the public is willing to pay for a piece of the company. It is nothing but present value of cash flows ( Div & Sale Price of Stock at future date) from it.

P = D1 / [ Ke - g ]
D1 - Div after 1 Year
P0 - Price Today
Ke - Required Ret
g - Growth rate

Particulars	Amount
D0	$   2.44
Growth rate	3.00%
Ke	15.63%

Price of Stock is nothing but PV of CFs from it.
Price = D1 / [ Ke - g ]
D1 = D0 ( 1 + g )
= $ 2.44 ( 1 + 0.03 )
= $ 2.44 ( 1.03 )
= $ 2.51

Price = D1 / [ Ke - g ]
= $ 2.51 / [ 15.63 % - 3 % ]
= $ 2.51 / [ 12.63 % ]
= $ 19.9

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