Question

2. Ultimate Electric, Inc. has just developed a solar panel capable of generating 200 percent more electricity than any solar panel currently on the market. As a result, Ultimate is expected to experience a 15 percent annual growth rate for the next five years. When the five-year period ends, other firms will have developed comparable technology, and Ultimate’s growth rate will slow to 5 percent per year indefinitely. Stockholders require a return of 12 percent on Ultimate’s stock. The firm’s most recent annual dividend (D0), which was paid yesterday, was $1.75 per share.

a. Calculate the value of the stock today.

b. Calculate the dividend yield, Dˆ 1 /P0, the expected capital gains yield, and the expected total return (dividend yield plus capital gains yield) for this year. Calculate these same three yields for Year 5.

c. Suppose your boss believes that Ultimate’s annual growth rate will be only 12 percent during the next five years and that the firm’s normal growth rate will be only 4 percent. Under these conditions, what is the price of Ultimate’s stock?

d. Suppose your boss regards Ultimate as being quite risky and believes that the required rate of return should be higher than the 12 percent originally specified. Rework the problem under the conditions originally given, except change the required rate of return to (1) 13 percent, (2) 15 percent, and (3) 20 percent to determine the effects of the higher required rates of return on Ultimate’s stock price.

Answer 1

a)

Ultimate Electric Inc					Cost of Equity	12%	Return Required
	0	1	2	3	4	5	6
Dividend	1.75	2.0125	2.314375	2.66153125	3.060760938	3.519875078	3.695868832
		=B4*(1+C6)	=C4*(1+D6)	=D4*(1+E6)	=E4*(1+F6)	=F4*(1+G6)	=G4*(1+H6)
Growth Rate		15%	15%	15%	15%	15%	5%
Terminal Value							52.79812617	=H4/(G1-H6)
Discount Factor		1.12	1.2544	1.404928	1.57351936	1.762341683
		=(1+$G$1)^C3	=(1+$G$1)^D3	=(1+$G$1)^E3	=(1+$G$1)^F3	=(1+$G$1)^G3
PV		1.796875	1.84500558	1.894425373	1.945168909	1.997271648
PV of Terminal Value						29.95907472	=H7/G8
Value of Stock	39.43782	=C10+D10+E10+F10+G10+G11
			In this question, we have applied multistage dividend discount model (gorden growth model). Where P = D0 * (1+g)/ (Cost of Equity - g)

b)

Year1				Year 5
Dividend Yield	2.0125/39.43782	5.10%		Dividend Yield	3.52/29.95	11.75%

c)

Ultimate Electric Inc					Cost of Equity	12%	Return Required
	0	1	2	3	4	5	6
Dividend	1.75	1.96	2.1952	2.458624	2.75365888	3.084097946	3.207461863
		=B4*(1+C6)	=C4*(1+D6)	=D4*(1+E6)	=E4*(1+F6)	=F4*(1+G6)	=G4*(1+H6)
Growth Rate		12%	12%	12%	12%	12%	4%
Terminal Value							40.09327329	=H4/(G1-H6)
Discount Factor		1.12	1.2544	1.404928	1.57351936	1.762341683
		=(1+$G$1)^C3	=(1+$G$1)^D3	=(1+$G$1)^E3	=(1+$G$1)^F3	=(1+$G$1)^G3
PV		1.75	1.75	1.75	1.75	1.75
PV of Terminal Value						22.75	=H7/G8
Value of Stock	31.5	=C10+D10+E10+F10+G10+G11
			In this question, we have applied multistage dividend discount model (gorden growth model). Where P = D0 * (1+g)/ (Cost of Equity - g)

d)

Ultimate Electric Inc					Cost of Equity	13%	Return Required
	0	1	2	3	4	5	6
Dividend	1.75	2.0125	2.314375	2.66153125	3.060760938	3.519875078	3.695868832
		=B4*(1+C6)	=C4*(1+D6)	=D4*(1+E6)	=E4*(1+F6)	=F4*(1+G6)	=G4*(1+H6)
Growth Rate		15%	15%	15%	15%	15%	5%
Terminal Value							46.1983604	=H4/(G1-H6)
Discount Factor		1.13	1.2769	1.442897	1.63047361	1.842435179
		=(1+$G$1)^C3	=(1+$G$1)^D3	=(1+$G$1)^E3	=(1+$G$1)^F3	=(1+$G$1)^G3
PV		1.780973451	1.812495105	1.844574665	1.877222004	1.910447172
PV of Terminal Value						25.07461913	=H7/G8
Value of Stock	34.30033	=C10+D10+E10+F10+G10+G11
			In this question, we have applied multistage dividend discount model (gorden growth model). Where P = D0 * (1+g)/ (Cost of Equity - g)

Ultimate Electric Inc					Cost of Equity	15%	Return Required
	0	1	2	3	4	5	6
Dividend	1.75	2.0125	2.314375	2.66153125	3.060760938	3.519875078	3.695868832
		=B4*(1+C6)	=C4*(1+D6)	=D4*(1+E6)	=E4*(1+F6)	=F4*(1+G6)	=G4*(1+H6)
Growth Rate		15%	15%	15%	15%	15%	5%
Terminal Value							36.95868832	=H4/(G1-H6)
Discount Factor		1.15	1.3225	1.520875	1.74900625	2.011357188
		=(1+$G$1)^C3	=(1+$G$1)^D3	=(1+$G$1)^E3	=(1+$G$1)^F3	=(1+$G$1)^G3
PV		1.75	1.75	1.75	1.75	1.75
PV of Terminal Value						18.375	=H7/G8
Value of Stock	27.125	=C10+D10+E10+F10+G10+G11
			In this question, we have applied multistage dividend discount model (gorden growth model). Where P = D0 * (1+g)/ (Cost of Equity - g)

Ultimate Electric Inc					Cost of Equity	20%	Return Required
	0	1	2	3	4	5	6
Dividend	1.75	2.0125	2.314375	2.66153125	3.060760938	3.519875078	3.695868832
		=B4*(1+C6)	=C4*(1+D6)	=D4*(1+E6)	=E4*(1+F6)	=F4*(1+G6)	=G4*(1+H6)
Growth Rate		15%	15%	15%	15%	15%	5%
Terminal Value							24.63912555	=H4/(G1-H6)
Discount Factor		1.2	1.44	1.728	2.0736	2.48832
		=(1+$G$1)^C3	=(1+$G$1)^D3	=(1+$G$1)^E3	=(1+$G$1)^F3	=(1+$G$1)^G3
PV		1.677083333	1.607204861	1.540237992	1.476061409	1.41455885
PV of Terminal Value						9.901911951	=H7/G8
Value of Stock	17.61706	=C10+D10+E10+F10+G10+G11
			In this question, we have applied multistage dividend discount model (gorden growth model). Where P = D0 * (1+g)/ (Cost of Equity - g)