Question

	Chapter 8 - Master it!
	In practice, the use of the dividend discount model is refined from the method we presented in the textbook. Many analysts will estimate the dividend for the next 5 years and then estimate a perpetual growth rate at some point in the future, typically 10 years. Rather than have the dividend growth fall dramatically from the fast growth period to the perpetual growth period, linear interpolation is applied. That is, the dividend growth is projected to fall by an equal amount each year. For example, if the high growth period is 15 percent for the next 5 years and the dividends are expected to fall to a 5 percent perpetual growth rate 5 years later, the dividend growth rate would decline by 2 percent each year.
	The Value Line Investment Survey provides information for investors. Below, you will find information for IBM found in the 2014 edition of Value Line:
	2014 dividend:		$               3.95
	5-year dividend growth rate:		9.5%
	Although Value Line does not provide a perpetual growth rate or required return, we will assume they are:
	Perpetual growth rate:		4.0%
	Required return:		11.0%
a.	Assume that the perpetual growth rate begins 10 years from now and use linear interpolation between the high growth rate and perpetual growth rate. Construct a table that shows the dividend growth rate and dividend each year. What is the stock price at Year 10? What is the stock price today?
b.	How sensitive is the current stock price to changes in the perpetual growth rate? Graph the current stock price against the perpetual growth rate in 10 years to find out.
	Instead of applying the constant dividend growth model to find the stock price in the future, analysts will often combine the dividend discount method with price ratio valuation, often with the PE ratio. Remember that the forward PE ratio is the current price per share divided by the earnings per share next year. So, if we know what the PE ratio is, we can solve for the stock price. Suppose we also have the following information about IBM:
	Payout ratio:		25%
	Forward PE ratio at constant growth rate:		15
c.	Use the forward PE ratio to calculate the stock price when IBM reaches a perpetual growth rate in dividends. Now find the value of the stock today finding the present value of the dividends during the supernormal growth rate and the price you calculated using the PE ratio.
d.	How sensitive is the current stock price to changes in PE ratio when the stock reaches the perpetual growth rate? Graph the current stock price against the forward PE ratio in 10 years to find out. Master it! Solution a. The dividend growth rates, dividends, and stock price are: Year 1 2 3 4 5 6 7 8 9 10 11 Dividend growth: Dividend: Present Value of Dividend Present Value of Terminal Value (stock price in year 10) Sum of PV Dividends PV of TV Stock Price Today b. To graph the stock price for different growth rates, we need to calculate the price for various growth rates. Using a one-way data table, we get the following: Growth rate Stock price 0% Zero Growth Model 1% 2% 3% 4% Constant Growth Model 5% 6% 7% 8% 9% 10% c. The earnings and price in year 10 will be: Year 10 PE ratio: Year 11 earnings: Year 10 price: So, the stock price today with this valuation method is: Price today: d. Using a one-way data table, the stock price today at different PE ratios is: PE ratio Stock price 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00

Answer 1

		Decrease of growth per year=(9.5-4)/5=				1.1	%
		Year	Dividend growth	Dividend amount
	2014	0		$3.95
	2015	1	9.50%	$4.33	(3.95*	(1+0.095))
	2016	2	9.50%	$4.74	(4.33	(1+0.095))
	2017	3	9.50%	$5.19	(4.74*	(1+0.095))
	2018	4	9.50%	$5.68	(5.198	(1+0.095))
	2019	5	9.50%	$6.22	(5.68*	(1+0.095))
	2020	6	8.40%	$6.74	(6.22*	(1+0.084)
	2021	7	7.30%	$7.23	(6.74*	(1+0.073)
	2022	8	6.20%	$7.68	(7.23*	(1+0.062)
	2023	9	5.10%	$8.07	(7.68*	(1+0.051)
	2024	10	4.00%	$8.40	(8.07*	(1+0.040)
	2025	11	4.00%	$8.73	(8.40*	(1+0.040)
	Price in year 10 P10= 8.73/(0.11-0.04)=					$124.74
	CALCULTION OF STOCK PRICE TODAY =P0
	P0=Sum of present value(PV) of dividends in perpetuity=
	P0=Sum of pV of dividends till year 10+PV of Price in year 10
	PV of Price/Dividend in future=(Dividend or Price)/((1+i)^N)
	i=Required rate of return=0.11
	N= year of dividend or Price
		N		A	B=A/(1.11^N)
		Year	Growth rate	Dividend/Price	PV of dividend/price
	2015	1	9.50%	$4.33	3.89662
	2016	2	9.50%	$4.74	3.84396
	2017	3	9.50%	$5.19	3.79202
	2018	4	9.50%	$5.68	3.74078
	2019	5	9.50%	$6.22	3.69022
	2020	6	8.40%	$6.74	3.60379
	2021	7	7.30%	$7.23	3.48366
	2022	8	6.20%	$7.68	3.33302
	2023	9	5.10%	$8.07	3.15586
	2024	10	4.00%	$8.40	2.95684
P10	2024	10		$124.74	43.9302
				Total	79.4269
		P0=Price of stock today			$          79.43
	SENSITIVITY ANALYSIS
		2% PERPETUAL GROWTH
		N		A	B=A/(1.11^N)
		Year	Growth rate	Dividend/Price	PV of dividend/price
	2015	1	9.50%	$4.33	3.89662
	2016	2	9.50%	$4.74	3.84396
	2017	3	9.50%	$5.19	3.79202
	2018	4	9.50%	$5.68	3.74078
	2019	5	9.50%	$6.22	3.69022
	2020	6	8.00%	$6.72	3.59049
	2021	7	6.50%	$7.15	3.44493
	2022	8	5.00%	$7.51	3.25872
	2023	9	3.50%	$7.77	3.03853
	2024	10	2.00%	$7.93	2.79217
P10	2024	10		$    89.87	31.652
				Total	66.7404
		P10=Stock price in year 10=(7.93*1.02)/(0.11-0.02)=					$    89.87
		Price of Stock today=			$          66.74
	SENSITIVITY ANALYSIS
		3% PERPETUAL GROWTH
		N		A	B=A/(1.11^N)
		Year	Growth rate	Dividend/Price	PV of dividend/price
	2015	1	9.50%	$4.33	3.89662
	2016	2	9.50%	$4.74	3.84396
	2017	3	9.50%	$5.19	3.79202
	2018	4	9.50%	$5.68	3.74078
	2019	5	9.50%	$6.22	3.69022
	2020	6	8.20%	$6.73	3.59714
	2021	7	6.90%	$7.19	3.46427
	2022	8	5.60%	$7.60	3.29574
	2023	9	4.30%	$7.92	3.09681
	2024	10	3.00%	$8.16	2.87361
P10	2024	10		$105.06	37.0005
				Total	72.2917
		P10=Stock price in year 10=(8.16*1.03)/(0.11-0.03)=					$105.06
		Price of Stock today=			$          72.29
	SENSITIVITY ANALYSIS
		5% PERPETUAL GROWTH
		N		A	B=A/(1.11^N)
		Year	Growth rate	Dividend/Price	PV of dividend/price
	2015	1	9.50%	$4.33	3.89662
	2016	2	9.50%	$4.74	3.84396
	2017	3	9.50%	$5.19	3.79202
	2018	4	9.50%	$5.68	3.74078
	2019	5	9.50%	$6.22	3.69022
	2020	6	8.60%	$6.75	3.61044
	2021	7	7.70%	$7.27	3.5031
	2022	8	6.80%	$7.77	3.37055
	2023	9	5.90%	$8.23	3.21569
	2024	10	5.00%	$8.64	3.04187
P10	2024	10		$151.20	53.2503
				Total	88.9555
		P10=Stock price in year 10=(8.64*1.05)/(0.11-0.05)=					$151.20
		Price of Stock today=			$          88.96
	SENSITIVITY ANALYSIS
		6% PERPETUAL GROWTH
		N		A	B=A/(1.11^N)
		Year	Growth rate	Dividend/Price	PV of dividend/price
	2015	1	9.50%	$4.33	3.89662
	2016	2	9.50%	$4.74	3.84396
	2017	3	9.50%	$5.19	3.79202
	2018	4	9.50%	$5.68	3.74078
	2019	5	9.50%	$6.22	3.69022
	2020	6	8.80%	$6.77	3.61709
	2021	7	8.10%	$7.31	3.52258
	2022	8	7.40%	$7.85	3.40834
	2023	9	6.70%	$8.38	3.2763
	2024	10	6.00%	$8.88	3.12872
	2024	10		$188.26	66.3008
				Total	102.217
		P10=Stock price in year 10=(8.88*1.06)/(0.11-0.06)=					$188.26
		Price of Stock today=			$       102.22
		Perpetual growth rate	P0=Stock Price today	P10=Stock price in year10
		2%	$    66.74	$    89.87
		3%	$    72.29	$105.06
		4%	$    79.43	$124.74
		5%	$    88.96	$151.20
		6%	$102.22	$188.26