You want to find the price per share for ABC Corporation. They paid a dividend o

Question

You want to find the price per share for ABC Corporation. They paid a dividend of $0.06 last year. You think this will grow at 80% every year for the next 11 years, then will drop to a 15% growth rate for the following 12 years, after which it will stabilize to a long-term growth rate of 4%.
To find the discount rate, you will use the CAPM. Use the current 10-year treasury yield for the risk-free rate (Yahoo Finance is one place to find this information, or you can just Google it), assume the market return is 8.5% and that ABC has a beta of 1.74.
What is the most you would be willing to pay for a share of ABC?
(Hint: Do this using the year by year analysis, for at least 200 years.)

Do it on Excel

Explanation / Answer

Current Dividend D0 $0.06 Dividend Growth rate g1 = 80% for 11 years Dividend Growth rate g2 = 15% for 12 years after 11 years Dividend Growth rate g3 = 4% constant after 23 years Yield on 10 year treasury bond rf = 2% (taken from Bloomberg website) Market return rm = 8.5% Stock Beta = 1.74 Using CAPM, required rate of return on Stock A is rA = rf + Beta (rm - rf) =2%+1.74*(8.5-2) = 13.31% or 0.1331 Expected Dividends Year Dividend in previous year Growth rate Dividend paid Discounting factor Present Value 1 0.06 80% 0.108 0.882534639 0.095313741 2 0.108 80% 0.1944 0.77886739 0.151411821 3 0.1944 80% 0.34992 0.687377451 0.240527118 4 0.34992 80% 0.629856 0.606634411 0.382092324 5 0.629856 80% 1.1337408 0.535375881 0.60697748 6 1.1337408 80% 2.04073344 0.47248776 0.964221573 7 2.04073344 80% 3.673320192 0.416986815 1.531726088 8 3.673320192 80% 6.611976346 0.368005309 2.433242396 9 6.611976346 80% 11.90155742 0.324777432 3.865357261 10 11.90155742 80% 21.42280336 0.286627334 6.140361018 11 21.42280336 80% 38.56104605 0.252958551 9.754346336 12 38.56104605 15% 44.34520295 0.223244684 9.899830806 13 44.34520295 15% 50.9969834 0.197021166 10.04748515 14 50.9969834 15% 58.64653091 0.173878004 10.19734174 15 58.64653091 15% 67.44351054 0.153453362 10.34943341 16 67.44351054 15% 77.56003713 0.135427907 10.50379351 17 77.56003713 15% 89.19404269 0.119519819 10.66045586 18 89.19404269 15% 102.5731491 0.105480381 10.81945481 19 102.5731491 15% 117.9591215 0.09309009 10.98082519 20 117.9591215 15% 135.6529897 0.082155229 11.14460239 21 135.6529897 15% 156.0009381 0.072504835 11.3108223 22 156.0009381 15% 179.4010789 0.063988029 11.47952136 23 179.4010789 15% 206.3112407 0.056471652 11.65073653 Total Present Value 155.2098802 Discounting Factor is 1/(1+r)^ where r is13.31% and n is equal to 1,2,--23 Present Value in year 24 when the dividends are expected to grow at a 4% constant rate can be calculated using the formula Present Value = D23/r - g Substituting the values Present value = 206.3112407/0.1331 - 0.04 Present Value = 206.3112407/0.0931 2216.01762 The is the present value in year 23. This needs to be brought to current date by multiplication with the discounting factor 0.056471652 Present Value now of the value 125.142175 Current Share Price = Total Present Value of Dividends growing at two different rates + present value of dividends at constant growth Current Share Price 280.3520556 or 280.35 (rounded off)

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