Question

You are considering an investment in Justus Corporation's stock, which is expected to pay a dividend of $2.75 a share at the end of the year (D₁ = $2.75) and has a beta of 0.9. The risk-free rate is 4.0%, and the market risk premium is 4.5%. Justus currently sells for $42.00 a share, and its dividend is expected to grow at some constant rate, g. Assuming the market is in equilibrium, what does the market believe will be the stock price at the end of 3 years? (That is, what is ?) Do not round intermediate calculations. Round your answer to the nearest cent.

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Computech Corporation is expanding rapidly and currently needs to retain all of its earnings; hence, it does not pay dividends. However, investors expect Computech to begin paying dividends, beginning with a dividend of $1.00 coming 3 years from today. The dividend should grow rapidly - at a rate of 19% per year - during Years 4 and 5, but after Year 5, growth should be a constant 7% per year. If the required return on Computech is 18%, what is the value of the stock today? Do not round intermediate calculations. Round your answer to the nearest cent.

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Answer 1

(A)

Required return as per CAPM = Risk free rate + beta*market risk premium

= 4% + 0.9*4.5%

= 8.05%

Price of share = Expected Dividend/(Required Return - Growth Rate)

42 = 2.75 / (8.05% - growth rate)

8.05% -G = 2.75/42

g = 6.55% - 8.05%

Growth rate (g) = 1.50%

Price after 3 years = Dividend in Year 4/(required Return - Growth rate)

= 2.8756/ (8.05-1.5)

= $43.90

Shwo Calculation

Given:
Risk-free rate (TRF) 4%
Market risk premium (IM - TRF) 4.5%
Stock beta (bg) 0.9
Stock value today (Po) $42
Dividend (D1) $2.75

Now, we know growth rate (g) and required return (rs), we find expected dividends 4 years from now (D4) and then plug the variables to the Gordon Growth Model to solve for price of stock 3 years (P3) from now.

Find D₄

D_{4 =} D₁ * (1 + g_1-4)³

= $2.75 * (1+1.50%)³

= $2.75 * (1+0.015)³

= $2.75 * 1.0456784

= $2.8756

Finally Solve for price of stock 3 year from now (P₃)

P₃ = D₄ / Required rate of return - Growth rate

= $2.8756 /8.05% - 1.50%

= $2.8756 / 6.55%

= $2.8756 / 0.0655

= $43.90

(B)

(1)

Given:
Dividend 3 years from now (D₃) = $1
Nonconstant growth rate (1st 2 years) = 19%
Constant growth rate (g) = 7%
Required rate of return (rs) = 18%

Year 3 dividend = $1.00

Year 4 dividend = $1.00(1 + 19%) = $1.19

Year 5 dividend = $1.19 (1 + 19%) = $1.4161

Year 6 dividend = $1.4161 (1 + 7%) = 1.5152

Value at year 5 = D6 / required rate - growth rate

= $1.5152 / 0.18 -0.07

= $1.5152/ 0.11

= $ 13.7745

(2) Finally, find the price of stock today (Po).

The price of the stock today is equal to the sum of the present value of the dividends (year 3, year 4, and year 5) with the nonconstant growth, plus the present value of the horizon value of $13.7745. In other words, we discount each cash flow to year 0, then find their sum to find the stock price today.

D₃ D₄ D₅ P₅
P0 = ------ + ------ + ----- + -----------
(1+r)³ (1+r)³ ( 1+r)³ (1+r)³

=$1 / (1+0.18)³ + $1.19 / (1+0.18)⁴ + $1.4161 / (1+0.18)⁵ + $ 13.7745 / (1+0.18)⁵

= $1 / 1.6430 + $1.19 / 1.9388 + $1.4161 / 2.2876 + $13.7745 / 2.2876

= $0.6086 + $0.6138 + $0.6190 + $6.0214

= $7.8628

:-   The value of the stock today is $7.86