Question

Rework Table 7.4 for horizon years 1, 2, 3, and 10, assuming that investors expect the dividend and the stock price to increase at only 6% a year and that each investor requires the same 12% expected return. Current dividends are $720. What value would Dritter place on the stock and what about Zehnte who has a 10-year horizon? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Horizon PV PV (Terminal Price) Value per Share s) (Dividends) ears 10 TABLE 7.4 Value of Blue Skies Horlzon (years PV (dlvidends) +PV (terminal price) Value per Share $2.68 $72.32 $75 75 2 5.26 69.74 7.75 67.25 75 52.13 10 22.87 75 38.76 20 36.24 75 49.81 25.19 75 30 50 62.83 12.17 75 100 73.02 1.98 75

Answer 1

First let us calculate the dividend for each year at 6% growth rate and the discount factor at 12%:

Year	Calculation	Dividend	Discount factor
0	Given	7.2	1/1.12^0	=	1
1	7.2x(1.06)=	7.632	1/1.12^1	=	0.892857143
2	7.632x(1.06)=	8.08992	1/1.12^2	=	0.797193878
3	8.08992x(1.06)=	8.5753152	1/1.12^3	=	0.711780248
4	8.5753152x(1.06)=	9.089834112	1/1.12^4	=	0.635518078
5	9.089834112x(1.06)=	9.635224159	1/1.12^5	=	0.567426856
6	9.63522415872x(1.06)=	10.21333761	1/1.12^6	=	0.506631121
7	10.2133376082432x(1.06)=	10.82613786	1/1.12^7	=	0.452349215
8	10.8261378647378x(1.06)=	11.47570614	1/1.12^8	=	0.403883228
9	11.4757061366221x(1.06)=	12.1642485	1/1.12^9	=	0.360610025
10	12.1642485048194x(1.06)=	12.89410342	1/1.12^10	=	0.321973237

Next Let us calculate the PV of dividends for 1, 2, 3 and 10 years time horizon:

Horizon	1	2	3	4	5	6	7	8	9	10	Dividend PV
1year	7.632
Discount Factor	0.892857143
Discounted CF	7.632 x 0.892857143 = 6.814285714										6.814285714
2Year	7.632	8.08992
Discount Factor	0.892857143	0.797193878
Discounted CF	7.632 x 0.892857143 = 6.814285714	8.08992 x 0.797193878 = 6.449234694									13.26352041
3Year	7.632	8.08992	8.5753152
Discount Factor	0.892857143	0.797193878	0.711780248
Discounted CF	7.632 x 0.892857143 = 6.814285714	8.08992 x 0.797193878​​​​​​​ = 6.449234694	8.5753152 x 0.711780248 = 6.103739978								19.36726039
10Year	7.632	8.08992	8.5753152	9.089834112	9.635224159	10.21333761	10.82613786	11.47570614	12.1642485	12.89410342
Discount Factor	0.892857143	0.797193878	0.711780248	0.635518078	0.567426856	0.506631121	0.452349215	0.403883228	0.360610025	0.321973237
Discounted CF = Dividend x Discount factor	7.632 x 0.892857143​​​​​​​ = 6.814285714	8.08992 x 0.797193878​​​​​​​ = 6.449234694	8.5753152 x 0.711780248​​​​​​​ = 6.103739978	5.776753908	5.467284949	5.174394683	4.897194968	4.634845238	4.386549957	4.151556209	53.8558403

Now lets calculate the terminal value and their PV:

Formula for TV : Here n= horizon year

TV-Dnx(1+1)

Once TV is calculated it is discounted using the discount factor of the horizon year

Horizon	Terminal value PV
1year	7.632 x 1.06/(0.12-0.06)=134.832
Discount Factor	0.892857143
Discounted CF	120.3857143
2Year	8.08992 x 1.06/(0.12-0.06)=142.92192
Discount Factor	0.797193878
Discounted CF	113.9364796
3Year	8.5753152 x 1.06/(0.12-0.06)=151.4972352
Discount Factor	0.635518078
Discounted CF	96.2792318
10Year	12.89410342 x 1.06/(0.12-0.06)=227.795827
Discount Factor	0.321973237
Discounted CF	73.3441597

So the value per share is as follows:

Horizon	Dividend PV	Terminal value PV	Value per share
1year	6.81	120.39	6.81+120.39=127.20
2Year	13.26	113.94	113.26+113.94=27.20
3Year	19.37	96.28	19.37+96.28=115.65
10Year	53.86	73.34	53.86+73.34=127.20