question archive Consider the following information which relates to dividends per share (DPS) for a given company: Year DPS 2019 $9
Consider the following information which relates to dividends per share (DPS) for a given company: Year DPS 2019 $9
Subject:FinancePrice:2.86 Bought3
Consider the following information which relates to dividends per share (DPS) for a given company: Year DPS 2019 $9.2 2018 $1.70 2017 $1.55 2016 $1.40 2015 $3 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 9.9%. Scenario #2 – Expand: Dividend in 2021 is expected to be $9.2 per share, which will grow at an annual rate of 5.9% 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 1.6%. Required: What is the dollar difference in the present value per share of common stock between both scenarios? $Answer (ROUND YOUR ANSWER TO 2 DECIMAL PLACES. FOR EXAMPLE: 17.23)
Purchase A New Answer
Custom new solution created by our subject matter experts
GET A QUOTE
Answer Preview
Answer:
Calcuation of Average Annual Growth rate :
Growth Rate = [(Current Year DPS - Previous Year DPS)/Previous Year DPS] x 100
| Year | Annual Growth Rate |
| 2019 | (9.2-1.7)/1.7 = 441.18% |
| 2018 |
(1.7-1.55) / 1.55 = 9.68% |
| 2017 | (1.55-1.40)/1.40 = 10.71% |
| 2016 | (1.40-3)/3 = -53.33% |
Average growth rate of 4 years is as follows:
(441.18% + 9.68% + 10.71% -53.33%) / 4 = 102.06%
Scenario 1:
Formula for present value per share = Dividend 2019 x (1 + growth rate) / ( cost of equity - average growth rate)%
Dividend 2019 x (1 + growth rate) = 9.2 * (1 + 1.0206)
= $18.5895
Cost of equity (Given) = 9.9%
Average growth rate = 102.06%%
present value per share = [18.5895/ (9.9 - 102.06)%]
= - $ 20.17
Scenario - 2
Dividend 2021 = $9.2
Dividend 2022 = 9.2 x (1.059) = $9.7428
Dividend 2023 = 9.7428x (1.059) = $10.3176
Perpetuity ( value after 2023) = Dividend 2023 x (1 + average Growth rate) / ( Cost of equity - average growth rate)
=10.3176 x (1 + 1.0206)/ (0.016 - 1.0206)
= $ -20.75
Present Value per share = Dividend 2021/1.016 +Dividend 2022/1.016^(2) + Dividend 2023/1.016^(3) + Perpetuity/1.016^(3)
Present Value per share = 9.2/1.016 + 9.7428/1.016 ^(2) + 10.3176/1.016 ^(3) + (-20.75)/1.016 ^(3)
= $ 8.55
Dollar difference in the present value per share of common stock between both scenarios = Scenario 2 - Scenario 1
= $ 8.55 - (- $ 20.17)
= $ 28.72 (final answer)
