Question

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C&P Trading Inc., is entering into a 3-year remodeling and expansion project. Last year, the company...

  1. C&P Trading Inc., is entering into a 3-year remodeling and expansion project. Last year, the company paid a dividend of $3.40. It expects zero growth in the next year. In years 2 and 3, and 5% growth is expected, and in year 4, and 15% growth. In year 5 and thereafter, growth should be a constant 10% per year. What is the maximum price per share that an investor who requires a return of 12% should pay for Home Place Hotels common stock?(15')
  1. Find the value of the cash dividends at the end of each year. 4'
  2. Find the present value of the dividends expected during the initial growth period.3'
  3. Find the value of the stock at the end of the initial growth period. 4'
  4. Find the value of the stock. (Sum of PV of dividends during initial growth period and PV price of stock at end of growth period) 4'

Solutions

Expert Solution

Let D0,D1,D2,D3 and all be dividends in year 0,1,2,3 and so on

Value of cash dividends is as follows at the end of each year

D0=D1= $3.40

D2 = 3.4*(1.05) = 3.57

D3 = 3.4*(1.05^2) = 3.7485

D4 = D3*1.15 = 3.7485*1.15 = 4.3108

D5 = D4*1.1 = 4.7419

Required return, r is 12%

According to multistage Dividend growth model,

Price of stock, P is given by discounted future dividends

P = D1/(1+r) + D2/(1+r)^2 +D3/(1+r)^3 + D4/(1+r)^4 + D5/[(r-g)*(1+r)^4]

The last part if Gordon growth model value of stock at time 4, (of dividends from year 5 till perpetuity) which is discounted to present

P = 3.4/1.12 + 3.57/(1.12^2) + 3.7485/(1.12^3) + 4.3108/(1.12^4) + 4.7419/[(.12-.10)*(1.12^4)]

P = 3.0357+2.846+2.6681+2.7396+134.5327

P = $ 145.82

Thus, maximum price an investor should pay is $ 145.82. This is the value of stock today.

If we take initial growth period till year 4, the stock price at year 4 end is D5/(r-g)

= 4.7419/(0.12-0.10) = $237.09

If we take initial growth period till year 4, the present value of dividends is

3.4/1.12+ 3.57/(1.12^2) + 3.7485/1.12^3) + 4.3108/1.12^4

= 3.0357+2.846+2.6681+2.7396

= $11.29

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