Bretton, Inc., just paid a dividend of $3.15 on its stock. The growth rate in dividends is expected to be a constant 5 percent per year, indefinitely. Investors require a return of 13 percent on the stock for the first three years, a rate of return of 11 percent for the next three years, and then a return of 9 percent thereafter. What is the current share price for the stock?

The price of share of the Bretton Inc in the given question shall be the present value of all the dividends associated with this share in the future years.

Present value of year 1 dividend=3.31(1+13%)^-1=$2.93

(3.15*1.05)

Present value of year 2 dividend=3.48(1+13%)^-2=$2.73

(3.31*1.05)

Present value of year 3 dividend=3.65(1+13%)^-3=$2.53

(3.48*1.05)

Present value of year 4 dividend=3.83(1+11%)^-4=$2.52

(3.65*1.05)

Present value of year 5 dividend=4.02(1+11%)^-5=$2.39

(3.83*1.05)

Present value of year 6 dividend=4.22(1+11%)^-6=$2.26

(4.02*1.05)

Present value of all the cash flows after 6 year=$59.22

[4.22(1+5%)/(9%-5%)]*(1+11%)^-6

Price of share $74.58

amcool amcool · Answer 2 · 2021-11-24T21:11:37+01:00

See the attached photo for the calculation of present values (PV) of dividends for year 1 to 8.

From the attached photo, we have:

Previous year dividend in year 1 = Dividend just paid = $3.15

Total of PV of dividends from year 1 to year 8 = $15.48744740759770

Year 8 dividend = $3.69363860947266

Therefore, we have:

Year 9 dividend = Year 8 dividend * (100% + Perpetual dividend growth rate) = $3.69363860947266 * (100% + 5%) = $3.87832053994629

Price at year 8 = Year 9 dividend / (Rate of return in year 8 - Perpetual dividend growth rate) = $3.87832053994629 / (9% - 5%) = $96.9580134986573

PV of price at year 8 = Price at year 8 / (100% + Required return in year 8)^Number of years = $96.9580134986573 (100% + 9%)^8 = $48.6599575190332

Therefore, we have:

Current share price for the stock = Total of PV of dividends from year 1 to year 8 + PV of price at year 8 = $15.48744740759770 + $48.6599575190332 = $64.15

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