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 7% per year indefinitely. Stockholders require a return of 16% on RT's stock. The most recent annual dividend (D₀), which was paid yesterday, was $1.45 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 7% 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

Years	Expected Dividend	PV @ 16%	PV of dividend
0	1.45
1	1.653	0.862069	1.425
2	1.884	0.743163	1.400431034
3	2.148	0.640658	1.376285672
4	2.449	0.552291	1.352556609
5	2.792	0.476113	1.329236667
			6.884
Price at t= 5	16.83699778
Intrinsic Value	42.25

The Expected Dividend formula used here is D₀(1+g) where g =  14%

Present Value Formula = 1/(1+r)^n where r = 16%, n = the respective year

Price at T=5 has been calculated by the formula D₆/(k_e-g) where D₆ = D₅(1+g), k_e is = 16%, g = 7%

Intrinsic Value has been calculated by the formula = Sum of PV of Dividends + (Price at T₅ ) / (1+.16)^5

Expected Dividend Yield(D₁) has the formula = DPS / Market Price * 100

Market Price of Share at T₁ = D₂/ (k_e - g) = 1.884 / (.16-.14) = 94.2

Dividend Yield D1 = 1.653 / 94.2 * 100 = 1.75%

Capital Gain Yield = (P₁ - P₀) / P₀ *100

P1 = 94.2

P0 = D1/(ke- g) = 1.653 / (.16-.14) = 82.65

Capital Gain Yield = (94.2 - 82.65 )/ 82.65 * 100 = 13.974 = 13.97%

Expected Total Return at D1 = 1.75 + 13.97 = 15.72 %

At t = 5

Expected Dividend Yield = D6 / Market Price at T= 5 * 100

D6 = D5(1.07) = 2.987

Market Price = 2.987/(.16-.07) = 33.188

Expected Dividend Yield = 2.987/ 33.188 * 100 = 9 %

Capital Gain Yield =( P6 - P5 ) / P5 *100 =

P6 = 2.987*1.07 / (.16-.07) = 35.521

CGY = (35.521- 33.188) / 33.188 * 100 = 7.029 = 7.03%

Expected Total Return = 7.03%+ 9% = 16.03%