Question

In practice, a common way to value a share of stock when a company pays dividends is to value the dividends over the next five years or so, then find the “terminal” stock price using a benchmark PE ratio. Suppose a company just paid a dividend of $1.15. The dividends are expected to grow at 10 percent over the next five years. The company has a payout ratio of 40 percent and a benchmark PE of 19. The required return is 11 percent.

a.	What is the target stock price in five years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What is the stock price today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Solution :-

Last paid Dividend ( D0 ) = $1.15

Growth for next Five years = 10%

Therefore Dividend in Year 5 ( D5 ) = $1.15 * ( 1 + 0.10 )⁵ = $1.15 * 1.6105 = $1.852

Now Payout ratio Year 5 = 40%

Now EPS in Year 5 = Dividend in Year 5 / Payout Ratio = $1.852 / 0.40 = $4.63

Now PE = 19

MPS / EPS = 19

MPS = 19 * EPS

MPS = 19 * $4.6302 = $87.974

Therefore target stock Price in Year 5 = $87.974

(b)

Stock Price today = Present Value of dividend of 5 years

D1 = $1.15 * ( 1 + 0.10 ) = $1.265

D2 = $1.265 * ( 1 + 0.10 ) = $1.3915

D3 = $1.3915 * ( 1 + 0.10 ) = $1.531

D4 = $1.531 * ( 1 + 0.10 ) = $1.684

D5 = $1.684 * ( 1 + 0.10 ) = $1.852

Now Share Price = [ $1.265 / ( 1 + 0.11 ) ] + [ $1.3915 / ( 1 + 0.11)² ] + [ $1.531 / ( 1 + 0.11)³ ] + [ $1.684 / ( 1 + 0.11)⁴​​​​​​​ ] + [ $1.852 / ( 1 + 0.11)⁵​​​​​​​ ] + [ $87.974 / ( 1 + 0.11)⁵​​​​​​​ ]

= $57.805

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