Question

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'

Answer 1

Given that Dividend for the last year (D0) = $ 3.40

Now, given that next Year (Year 1) there will be no growth therefore Dividedn for the next year = $ 3.40

Now, Growth Rate for Year 2 and Year 3 = 5%.

Therefore Dividend for the year 2 = $ 3.4 x (1 + Growth Rate)

Dividend for Year 2 (D2) = 3.4 (1.05) = $ 3.57

Now, Dividend for Year 3 (D3) = D2 x (1+G)

Dividend for Year 3 (D3) = 3.57 (1.05) = $ 3.7485

Now In year 4 Growth Rate of Dividend = 15%.

Therefore Dividend of Year 4 (D4) = D3 x (1+0.15)

Dividend for year 4 (D4) = $ 3.7485 x (1.15) = $ 4.310775

Now Growth rate of dividend after year 4 = 10%

Therefore Dividend for the year 5 = D4 x (1+0.10)

Dividend for the year 5 = $ 4.310775 *1.10 = $ 4.7418525

Therefore the value of cash dividend at the end of each year are as follows:-

	Year 1	Year 2	Year 3	Year 4	Year 5
Dividend	3.40	3.57	3.7485	4.310775	4.741853
Growth Rate	0%	5%	5%	15%	10%

Now Let us compute the present values of Dividend computed Above. To claculate the present value we use the below formula

Present Value = Dividend Amount/ (1+ R) ^n where R is the discount Rate and n is the no. of years.

We have Discount Rate given = 12% so let us compute the present values of the dividends

	Year 1	Year 2	Year 3	Year 4	Year 5
Dividend (A)	3.40	3.57	3.7485	4.310775	4.741853
Growth Rate	0%	5%	5%	15%	10%
Discount Factors @ 12% (B)	0.892857	0.797194	0.71178	0.635518	0.567427
Derivation of Discount Factors (B)	=1/1.12	=1/1.12^2	=1/1.12^3	=1/1.12^4	=1/1.12^5
Present Value (AxB)	3.04	2.85	2.67	2.74	2.69

Now, given that from year 5 the growth rate of dividend is 10%.

Therfore the Value of Stock at the end of Year 5 = Dividend for the year 5 x (1+G)/ (R - G) where G is the Growth Rate is 10 % and R is 12%

Therefore the Value of stock at the end of initial growth phase year 5= 4.741853 *(1+0.10)/(0.12-0.10) = $ 260.8019.

Now, Value of Stock = Sum of the PV of Dividend as computed above + PV of Stock value at the end of year 5 as computed above.

Value of Stock = $ 13.98 + $ 260.8019 / (1.12)^5

Value of Stock = $13.98 + $147.986

Value of Stock = $161.97