Question

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

Year	DPS
2019	$1.93
2018	$1.7
2017	$1.58
2016	$1.44
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 14.49%.

Scenario #2 – Expand: Dividend in 2021 is expected to be $2.17 per share, which will grow at an annual rate of 14.42% 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 16.65%.

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

Answer 1

SCENARIO 1:
Historic growth rate in dividends = (1.93/1.32)^(1/4) -1 =	9.96%
PV per share = 1.93*1.0996/(0.1449-0.0996) =	$            46.85
SCENARIO 2:
The PV is calculated in the table below:
Year	Dividend	PVIF at 16.65%	PV at 16.65%
2019	$            1.930
2020 [9.96% growth rate]	$            2.122	0.85727	$              1.82
2021 [given]	$            2.170	0.73490	$              1.59
2022 [14.42% growth rate]	$            2.483	0.65616	$              1.63
2023 [14.42% growth rate]	$            2.841	0.58586	$              1.66
Sum of PV of dividends of years 2020 to 2023			$              6.71
Continuing value of dividends at 2023 EOY = 2.841*1.0996/(0.1665-0.0996) =				$         46.6960
PV of continuing value = 46.696*0.58586 =			$            27.36
Price of the stock today =6.71+27.36 =			$            34.06
DOLLAR DIFFERENCE IN PV [Scenario #1-Scenario #2] = 46.85-34.06 =			$            12.79