Question

Thirsty Cactus Corp. just paid a dividend of $1.30 per share. The dividends are expected to grow at 40 percent for the next 8 years and then level off to a 8 percent growth rate indefinitely.

    

Required :

If the required return is 14 percent, what is the price of the stock today?

$150.27

$147.27

$3.67

$153.28

$121.06

Answer 1

Before we start the calculations, let's understand the underlying Gordan growth dividend discount model for calculating the share price. As per this model:

Price per share, P = Present value of all the expected future dividend payments = PV of dividends over horizon period + PV of terminal value of the dividend

Here, it's a two stage growth model.

In stage 1: The dividends are growing at a rate of g₁ = 40% from year 1 to year 8

In stage 2: the perpetual growth rate in dividend beyond year 8 and in perpetuity is g₂ = 8%

Hence,

$P = \frac{D_{1}}{1 + K_{e}} + \frac{D_{2}}{(1 + K_{e})^{2}} + \frac{D_{3}}{(1 + K_{e})^{3}} + .......+ \frac{D_{8}}{(1 + K_{e})^{8}} + \frac{TV}{(1+K_{e})^{8}}$

where,

Where, P = Price per share

g₁ = dividend growth rate in stage 1 = 40%

D₀ = Last year's annual dividend = $ 1.30 / share

D₁ = Expected dividend next year = D₀ x (1 + g₁) = $ 1.82

D₂ = D₁ x (1 + g₁); D₃ = D₂ x (1 + g₁) = D₁ x (1 + g₁)² and so on...

K_e = Cost of equity or required return by the shareholder = 14%

g₂ = perpetual growth rate in dividend in stage 2 = 8%

TV = Terminal value of all the future dividends beyond year 8, at the end of year 8 and is mathematically given by

$TV = \frac{D_{9}}{K_{e} - g_{2}} = \frac{D_{8}\times (1 + g_{2})}{K_{e} - g_{2}}$

The results are now summarised in the table below:

Year	N	0	1	2	3	4	5	6	7	8
Dividend	D	1.30	1.82	2.55	3.57	4.99	6.99	9.79	13.70	19.19
Y-o-y growth	g1		40%	40%	40%	40%	40%	40%	40%	40%
Perpetual growth rate	g2	8%
Cost of equity	Ke	14%
Terminal value, TV at the end of year 8	D8 x (1 + g2) / (Ke-ge)									345
PV factor	(1+Ke)-N		0.8772	0.7695	0.6750	0.5921	0.5194	0.4556	0.3996	0.3506
PV of future dividends	D x PV factors		1.60	1.96	2.41	2.96	3.63	4.46	5.48	6.73
PV of TV	TV x PV factor of year 8									121.06
Price per share	Sum of PV of all future dividends and PV of TV	150.27

Hence the correct answer is first option $ 150.27