Question

Nonconstant Growth Stock Valuation

Reizenstein Technologies (RT) has just developed a solar panel capable of generating 200% more electricity than any solar panel currently on the market. As a result, RT is expected to experience a 14% annual growth rate for the next 5 years. By the end of 5 years, other firms will have developed comparable technology, and RT's growth rate will slow to 8% per year indefinitely. Stockholders require a return of 14% on RT's stock. The most recent annual dividend (D₀), which was paid yesterday, was $1.30 per share.

1. Calculate RT's expected dividends for t = 1, t = 2, t = 3, t = 4, and t = 5. Do not round intermediate calculations. Round your answers to the nearest cent.

   D₁ = $

   D₂ = $

   D₃ = $

   D₄ = $

   D₅ = $

2. Calculate the estimated intrinsic value of the stock today,  . Proceed by finding the present value of the dividends expected at t = 1, t = 2, t = 3, t = 4, and t = 5 plus the present value of the stock price that should exist at t = 5,  . The  stock price can be found by using the constant growth equation. Note that to find  you use the dividend expected at t = 6, which is 8% greater than the t = 5 dividend. Round your answer to the nearest cent. Do not round your intermediate computations.
   $  
   
3. Calculate the expected dividend yield (D₁/  ), the capital gains yield expected during the first year, and the expected total return (dividend yield plus capital gains yield) during the first year. (Assume that  = P₀, and recognize that the capital gains yield is equal to the total return minus the dividend yield.). Round your answers to two decimal places. Do not round your intermediate computations.

   Expected dividend yield	%
   Capital gains yield	%
   Expected total return	%

   
   Also calculate these same three yields for t = 5 (e.g., D₆/  ). Round your answers to two decimal places. Do not round your intermediate computations.

   Expected dividend yield	%
   Capital gains yield	%
   Expected total return	%

Answer 1

Part (a)
Calculation of Dividend paid every year
Last paid dividend (D0) =					1.3
Next 5 years growth rate in dividend is 14% a year and 8 % per year thereafter
To calculate D1 to D5, growth rate of 14% is added. To calculate D6, Growth rate of 8% is added to D5.
D1 = D0 + (D0 * growth rate)
(D0 = 1.30)			1.482000
D2 = D1 + (D1 * growth rate)			1.689480
D3 = D2 + (D2 * growth rate)			1.926007
D4 = D3 + (D3 * growth rate)			2.195648
D5 = D4 + (D4 * growth rate)			2.503039
	(round off)
D1 =	$1.48
D2 =	$1.69
D3 =	$1.93
D4 =	$2.20
D5 =	$2.50
Part (b)
D6 = D5 + (D5 * growth rate)
= 2.503039 + (2.503039 * 0.08)			2.703282
Required rate of return (Ke) =			14 % or	0.14
Growth rate from 6 year =			8% or	0.08
Present value of stock at end of 5th year (P5) = D6 / (Ke - g)
	= 2.703282 / (0.14 - 0.08)
P5 =	45.0547
Intrinsic value of Stock is total of discounted or present value of Dividend upto 5 th year and Present value at the end of 5th year.
Year				P.V.F. @ 14%	Present Value
1	D1	1.482000		0.877193	$1.3000
2	D2	1.689480		0.769468	$1.3000
3	D3	1.926007		0.674972	$1.3000
4	D4	2.195648		0.592080	$1.3000
5	D5	2.503039		0.519369	$1.3000
5	P5	45.054701		0.519369	$23.4000
	P0				$29.9000
So, Intrinsic value of Stock is $ 29.90 today (round off up to 2 decimal places)
Part (C )
D1 =	1.482000
P0 =	$29.9000
Expected Dividend Yield = D1 / P0 * 100
	1.482000	/ 29.90 * 100
	4.956522	or 4.96%
First we shall calculate P0 for calculation of capital gains yield.
At end of year 1 (t = 1), Dividend expected next year shall be $ 1.689480 and so on. And Present value at the end of 4th year shall be 45.0547
		P.V.F.@14%		Present value
D1	1.689480	0.877193		1.482
D2	1.926007	0.769468		1.482
D3	2.195648	0.674972		1.482
D4	2.503039	0.59208		1.482
P4	45.054701	0.59208		26.676
			P1 =	32.604
So, Present value at end of Year 1 (P1) shall be $32.604.
Capital gains expected during first year = ( P1 - P0 ) / P0 * 100
	(32.604 - 29.90 ) / 29.90 * 100
	9.043478	or 9.04%
Total return = ( D1 + P1 - P0 ) / P0 * 100
	(1.4820 + 32.604 - 29.90 ) / 29.90 * 100
	14.000000
So, Expected dividend yield is			4.96	%
Capital gains yield is			9.04	%
Expected Total return is			14.00	%
Part (d)
D6 =	2.703282
P5=	$45.0547
Expected Dividend Yield at (t =5) = D6 / P5 * 100
	2.703282	/ 45.0547 * 100
	6.000000	or 6.00%
First we shall calculate P6 for calculation of capital gains yield.
Growth rate is 8%
So, Dividend expected next year = 2.703282 + (2.703282 * 0.08)
2.919545
P6 = D7 / (ke -g)
= 2.919545 / (0.14 - 0.08)
48.65908
So, Present value at end of Year 6 (P6) shall be $48.65908.
Capital gains expected during fifth year = ( P6 - P5 ) / P5 * 100
	(48.65908 - 45.0547 ) / 45.0547 * 10
	8.000000	or 8.00%
Total return = ( D6 + P6 - P5 ) / P5 * 100
	2.703282 + 48.65908 - 45.0547 ) / 45.0547 * 100
	14.000000	or 14%
So, Expected dividend yield is			6.00	%
Capital gains yield is			8.00	%
Expected Total return is			14.00	%