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Homework answers / question archive / Consider the following information which relates to dividends per share (DPS) for a given company: Year 2019 2018 DPS $2
Consider the following information which relates to dividends per share (DPS) for a given company: Year 2019 2018 DPS $2.4 $1.70 2017 $1.55 2016 $1.40 2015 $5.8 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 5.5%. Scenario #2 - Expand: Dividend in 2021 is expected to be $2.9 per share, which will grow at an annual rate of 5.4% 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 7.1%. Required: What is the dollar difference in the present value per share of common stock between both scenarios?
Answer:
Present value per share of common stock as per Dividend Growth Model = D1 / (ke – g)
Where D1 = Expected dividend for next year
ke = Cost of equity
g = Growth rate
Calculation of Average Annual growth rate from 2015 to 2019:
2019 = ( 2.4 - 1.7) / 1.7*100 = 41.17%
2018 = (1.7 - 1.55) / 1. 55*100 = 9.67%
2017 = (1.55 - 1.40) / 1. 40*100 = 10.71%
2016 = (1. 40 - 5.8) / 5.8 * 100 = -75.86%
Average growth rate = (41.17% + 9.67% + 10.71% - 75.86%) / 4
= -3.58%
Scenario #1:
Present value per share of common stock = D1 / (ke – g)
Where,
D1 = Dividend of 2019 * (1+g)
= 2.4*(1 - 0.0358)
= $ 2.31
Present value per share of common stock = 2.31 / (5.5 + 3.58) %
= 2.31/ 9.08%
= $ 25.44
Scenario #2:
Present value per share of common stock = [D1 / (1 + r)1] + [D2 / (1 + r)2] + [D3 / (1 + r)3] + [Perpetuity Value / (1 + r)3]
Where, D1 =2.9
D2 = 2.9*(1 + .054) = 3.05
D3 = 3.05*(1+.054) = 3.21
Perpetuity Value = D3 (1+g) / (ke-g)
= 3.21 (1 - 0.0358) / [0.071 - (-0.0358)]
= 3.3292 / 0.1068
= 31.17
Present value per share of common stock = [2.9 / 1.071] + [3.05 / (1.071)^2] + [3.21 / (1.071)^3] + [31.17/ (1.071)^3]
= 2.71 + 2.66+ 2.61+ 25.37
= $ 33.35
Difference in present value per share of common stock is :
=Scenario #2 - Scenario #1
= 33.35 – 25.44
=$7.91 (final answer)
