Question

IBM has generated annual dividend growth of 15.1% over the past 3 years. IBM's most recent annual dividend is $2.90. Assume IBM will continue to increase dividends at 15.1% for the next 5 years before reducing its dividend growth to 6% for the long term. Also assume that the required return for IBM stock is 9.5%. It is currently trading for $179.90.

Use the two-stage dividend discount model to determine the current intrinsic value for IBM given these assumptions.

Is the stock overvalued or undervalued? Briefly explain the possible reasons for your response.

What long term dividend growth rate will provide an intrinsic value similar to the current market price?

(Leave all other assumptions in place.)

Reset the long term dividend growth rate to 6%.

What required rate of return would provide an intrinsic value similar to the current market price?

(Leave all other assumptions in place.)

Answer 1

1)	Two-stage dividend discount model to determine the current intrinsic value.
	Intrinsic value of the stock is the PV of the expected dividends discounted at the
	required return of 9.5%.
	The calculations are done below:
	Year	Expected Dividend	PVIF at 9.5%	PV at 9.5%
	0	2.90	1
	1	3.34	0.91324	$                 3.05
	2	3.84	0.83401	$                 3.20
	3	4.42	0.76165	$                 3.37
	4	5.09	0.69557	$                 3.54
	5	5.86	0.63523	$                 3.72
	Sum of PVs of dividends of Years t1 to t5 =			$               16.88
	Continuing value of dividends = 5.86*1.06/(0.095-0.06) =				$      177.47
	PV of continuing value = 177.47*0.63523 =			$             112.74
	Current intrinsic value of the stock			$             129.62
2)	Is the stock overvalued or undervalued?
	The stock is over valued by the market. The market price should be
	based on a lower required return.
3)	What long term dividend growth rate will provide an intrinsic value similar to the current market price?
	Refer to calculations for (1) above.
	To get $179.90, the PV of the continuing value should be 179.90-16.88=					$     163.02
	The continuing value for a PV of 163.02 should be 163.02/0.63523 =					$     256.63
	Next, with the same stream of dividends,
	256.83 = 5.86*1.05/(0.095-g)
	(5.86*1.05)/256.83-0.095 =
	0.095-g =	0.024
	g = 0.095-0.0240 =		7.10%	= Long term dividend growth rate.
	CHECK:
	Continuing value of dividends = 5.86*1.06/(0.095-0.071) =				258.82
	PV of continuing value = 258.82*0.63523 =				164.41
	Intrinsic value of the stock = 16.88+164.41 =				181.29
	Differene due to approximation
4)	The required return has to be found out by trial and error by discounting the
	expected dividends at different rates.
	Discounting at 9%
	Year	Expected Dividend	PVIF at 9%	PV at 9%
	0	2.90	1
	1	3.34	0.91743	$                 3.06
	2	3.84	0.84168	$                 3.23
	3	4.42	0.77218	$                 3.41
	4	5.09	0.70843	$                 3.61
	5	5.86	0.64993	$                 3.81
	Sum of PVs of dividends of Years t1 to t5 =			$               17.12
	Continuing value of dividends = 5.86*1.06/(0.09-0.06) =				$      207.05
	PV of continuing value = 207.05*0.64993 =			$             134.57
	Current intrinsic value of the stock			$             151.69
	Discounting at 8%
	Year	Expected Dividend	PVIF at 8%	PV at 8%
	0	2.90	1
	1	3.34	0.92593	$                 3.09
	2	3.84	0.85734	$                 3.29
	3	4.42	0.79383	$                 3.51
	4	5.09	0.73503	$                 3.74
	5	5.86	0.68058	$                 3.99
	Sum of PVs of dividends of Years t1 to t5 =			$               17.62
	Continuing value of dividends = 5.86*1.06/(0.08-0.06) =				$      310.58
	PV of continuing value = 310.58*0.68058 =			$             211.38
	Current intrinsic value of the stock			$             229.00
	The required rate for an intrinsic value of 179.90 lies between 9% and 8%
	= 8+(229-179.9)/(229-151.69) =			8.64%