Question

Consider the following information which relates to dividends per share (DPS) for a given company:

Year	DPS
2019	$1.92
2018	$1.73
2017	$1.51
2016	$1.39
2015	$1.32

Today, we are in 2020. Management is in the process of deciding whether to expand or not to expand the firm’s branches. Below, is a set of inputs associated with each scenario:

Scenario #1 – Do Not Expand: Dividend by the end of 2020 is expected to grow at the historical annual growth rate for the period 2015−2019, which is currently undetermined. This period adds up to four years based upon starting at time zero. Once determined, this rate is expected to continue in the future. Under this scenario, the required return on common stock is 14.36%.

Scenario #2 – Expand: Dividend in 2021 is expected to be $2.13 per share, which will grow at an annual rate of 14.12% for two years (2022 and 2023), and then, the divided would grow at the same unknown rate in the first scenario from 2024 thereafter. Under this scenario, the required return on common stock is 17.58%.

Required: What is the dollar difference in the present value per share of common stock between both scenarios?

Answer 1

Scenario 1 The table below explains the scenario

Year	Dividend	Dividend Growth	Terminal Value	Cash flows
2015	1.32			1.32
2016	1.39			1.39
2017	1.51			1.51
2018	1.73			1.73
2019	1.92	9.82%		1.92
2020	2.11	9.82%	51.01	53.11
PV of Stock		$46.44
Required Return	14.36%

The annual grow rate till 2019 is calculated using CAGR formula

CAGR = (Ending Value / Beginning Value)^(1/periods in between) -1

Here CAGR = (1.92/1.32)^(1/4) -1 = 9.82% (There are 4 periods between 2015 - 2019)

Thus 2020 dividend = 1.92 x (1+ 9.82%) = $ 2.11

The terminal value is calculated using the formula = D0 x (1+ g)/ (k-g)

Where D0 = Base Year dividend

g = the perpetual growth rate

k= Discount rate or Cost of capital or required return

Here D₀ = $2.11 (Dividend in 2020)

g = 9.82% (the perpetual growth rate)

K = 14.36%

Terminal Value = 2.11 x (1+9.82%)/ (14.36% - 9.82%) = $51.01

PV of all future dividends can be calculated using NPV function

where PV of stock = NPV(14.36%, (2.11+51.01)) = $46.44

Scenario 2 Can be explained as per the table below

Year	Dividend	Dividend Growth	Terminal Value	Cash flows
2015	1.32			1.32
2016	1.39			1.39
2017	1.51			1.51
2018	1.73			1.73
2019	1.92	9.82%		1.92
2020	2.11	9.82%		2.11
2021	2.13	1.02%		2.13
2022	2.43	14.12%		2.43
2023	2.77	14.12%		2.77
2024	3.05	9.82%	43.11	46.16
PV of Stock		$26.82
Required Return	17.58%

2020 Dividend is found using the CAGR formula explained above

2021 is given as 2.13, & 2022, 2023 & 2024 are derived using growth rates of 14.12%, 14.12% & 9.82% respectively

The terminal growth rate is again 9.82%

Required Return = 17.58%

Terminal Value of Dividend = 3.01 x (1+9.82%) / (17.58% - 9.82%) = $43.11

The Present Value of stock is found using NPV function.

The discount rate = 17.58% and we find NPV of all dividends from 2020 onward

Pv of the stock = NPV = (17.58%, (2.11,2.13,2.43,2.77,46.16) = $26.82

The difference in PV in scenario 1 & scenario 2 = $46.44 - $ 26.82 = $19.62