You have forecast the annual dividends for XYZ company on December 31, 2017. The

Question

You have forecast the annual dividends for XYZ company on December 31, 2017. The estimated Cost of Equity (using CAPM) is 7.5%. The perpetuity growth rate (beginning in 2024 is assumed to be 4% per year. Below, I have provided a table with your forecasts of future dividends.

1. Your task is to estimate the price per share on 12/31/2017 using the discounted dividends model. Round to the nearest penny.

2. You were previously asked to value the shares of XYZ using the discounted dividends model with an assumed cost of equity = 7.5% and a perpetuity growth rate of 3%. What would the change in share price be is the perpetuity growth rate increased to 4% per year in perpetuity. Again, here are your forecast details.

Terminal 1 2 3 4 5 6 Value Perpetuity Dividends-Based Valuation 2017 2018 2019 2020 2021 2022 2023 2024 Forecast Dividends Paid to Common Shareholders Millions)        3,687        3,507                3,629                3,835                3,885                4,602         4,717 shares outstanding (millions)     1,544.00

Explanation / Answer

Dividend Discount model
a) Calculating the Price per share with 4% growth rate, cost of equity is 7.5%.

Present value of all the dividend plus the present value of terminal
Present value = D1/(1+r) + D2/1+r)2+..... Dn/(1+r)n

Terminal value = PV of perpetual dividends 7th year k-g)
where k = cost of equity =7% and g = constant growth rate = 4%

= $4717/(7.5% - 4%) = $134771.43
Since the PV calculated above is at the end of 6th year (i.e. start of stable growth phase), it must be discounted back 6 years as follows:
= 134771.43/(1.075)6 = $87326.70

Present value of all dividends + Present value of terminal value
= 17945.39+87326.70
= $105272.09

Price or value per share in 2017 = 105272.09/1544
   = $68.18

b) If we change the perpetuity growth rate to 3%.

Terminal value would be = $4717/(7.5% - 3%) = $104822.22
Since the PV calculated above is at the end of 6th year (i.e. start of stable growth phase), it must be discounted back 6 years as follows:
= 104822.22/(1.075)6 = $67920.77

Total Present value = $17945.39+67920.77
   = $85866.16

Value/ price per share = 85866.16/1544

= $55.61

Change in price per share = $68.18 - 55.61

   = $12.57

Year Dividend PV at t =0 Formula 2018 3687 3429.77 3687/(1+0.075) 2019 3507 3034.72 3507/(1+0.075)^2 2020 3629 2921.20 3629/(1+0.075)^3 2021 3835 2871.65 3835/(1+0.075)^4 2022 3885 2706.13 3885/(1+0.075)^5 2023 4602 2981.92 4602/(1+0.075)^6 Sum = 17945.39

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