Question

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

Year

DPS

2019

$1.91

2018

$1.73

2017

$1.57

2016

$1.43

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 14.15%.

Scenario #2 – Expand: Dividend in 2021 is expected to be $2.15 per share, which will grow at an annual rate of 14.19% 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 16.34%.

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

INPUT YOUR ANSWER AS AN ABSOLUTE VALUE ROUNDED TO 2 DECIMAL PLACES. DO NOT USE POSITIVE/NEGATIVE SIGNS. DO NOT ROUND INTERMEDIATE CALCULATIONS.

Answer 1

Year	DPS	Difference	Growth rate
2015	$                  1.32
2016	$                  1.43	$                 0.11	8%
2017	$                  1.57	$                 0.14	10%
2018	$                  1.73	$                 0.16	10%
2019	$                  1.91	$                 0.18	10%
2020	$                  2.10	$                 0.19	10%
2021	$                  2.31	$                 0.21	10%
2022	$                  2.54	$                 0.23	10%
2023	$                  2.80	$                 0.25	10%
Scenario 1	Do not Expand
Fair Price per share
=	DPS(1+g)
	(Ke-g)
=	2.80(1+0.10)
	(.1415-.10)
=	$               74.22
Note:- Growth rate is the historical growth rate which is take as 10%
Scenario 2	Expand
		PVF @16.34%	PV			Diff
2021	$                  2.15	1	$       2.15				g=14.19%
2022	$                  2.46	0.8595	$       2.11			$       0.31	14%
2023	$                  2.80	0.7388	$       2.07			$       0.35	14%
2024	$                  3.08	0.6351	$       1.96			$       0.28	10%
Terminal Value of 2024=	{1/(1+ke)2}*((DPS)/(ke-g))
	=	0.7388*(3.08/.1634-.10)
	=	$               35.89
Fair Price per share
=	$2.11+$2.07+$1.96+$35.89
=	$               42.03
Difference in Present Value of Shares under two Scenarios=
	=	$74.22 - $42.03
	=	$               32.19

Hope this Solves your query. Feel free to ask any further queries in the comment section