Question

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

Year	DPS
2019	$1.93
2018	$1.68
2017	$1.58
2016	$1.36
2015	$1.33

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 14.32%.

Scenario #2 – Expand: Dividend in 2021 is expected to be $2.19 per share, which will grow at an annual rate of 13.19% 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 17.07%.

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

$Answer

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

Dear Reader

Solution:

Growth rate of dividend using compounded annual growth rate (CAGR).

Formula : [Ending value/Beginning Value]^1/n -1

               = [1.93/1.33]^1/4-1

                = 9.75%

Scenario 1

Share price = D₁/(K_e-g)

Where D₁ = Expected Dividend

          K_e = Required return

          g= growth rate

Price = [1.93 * (1.0975)²] / (0.1432-0.0975) :- Since 1.93 is 2019 dividend and we need 2021 dividend

         = $ 50.87

Scenario 2

Price using dividend discount model

Price = [2.19/(1.1707) ] + [(2.19*1.1319)/(1.1707)²] + [(2.19*1.1319²)/(1.1707)³] + [(2.19*1.1319²*1.0975)/(1.1707)³ (0.1707-0.0975)]

         = $ 31.65

Difference between present values

= 50.87 - 31.65

= $ 19.22

I sincerely apologize you for the wrong answer earlier. Please look at the new solution and do let us know for any concern.

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Note - The corrected solution is not because of negative rating. It is my duty to solve right one.