A firm’s total annual dividend payout is $1 million. Its stock price is $45 per
ID: 2800287 • Letter: A
Question
A firm’s total annual dividend payout is $1 million. Its stock price is $45 per share and it has 17,500,000 shares outstanding. The firm earned $4 million in Net Income last year. This year, the firm expects earnings to grow at 7%, with growth the year after that expected to be 5%, and then in all following years, the firm expects earnings to grow at 3%. The firm plans to hold their dividend payout ratio constant over the coming 20 years and beyond. The risk free rate is 3%, beta for the dividend portion of the firm must be lower than for the entire income stream, and it measured at is 0.65, and the equity risk premium is 7.75%. What is the value of equity for the entire firm using the DIVIDEND DISCOUNT model, using annual dividends as free cash flow?
Explanation / Answer
Requird rate of reurn on the firm's equity using CAPM model
r = risk free rate + beta x risk premium = 3+.65 x 7.75 = 8.0375%
Dividend per share = 1,000,000/17,500,000 =$ .057143 per share
Dividend growth will be inline with the growth in the revenue of the firm
Dividend at the end of the year 1= .057143 x (1.07) = .061143
Dividend at the end of the year 2 =.061143 x (1.05) = .0642
Dividend at the end of the year 3 =.061143 x (1.03) = .066126
Dividend growth is constant thereafter so the value of equity at the end of year 2 according to the Gordan dividend discount model
P2= D3/(r-g) = .066126 / (.080375 - .03 ) = $1.312675
Value of one share today can be found by the discounting all these dividends and value of equity at required rate of return
P0 = .061143 /(1.080375) + (.0642+1.312675)/(1.080375)2
P0 = .056594 + 1.179629 = $1.236223
the value of equity for the entire firm using the DIVIDEND DISCOUNT model =
Number of shares outstanding x share price as per dividend discount model = 17500000 x 1.236223 = $ 21,633,904
The value of share is coming too low as compared to the given stock price of 45 per share. But with these figures this the answer we'll get.
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