Question

Martin Office Supplies paid a $5 dividend last year. The dividend is expected to grow at a constant rate of 9 percent over the next four years. The required rate of return is 12 percent (this will also serve as the discount rate in this problem). Use Appendix B for an approximate answer but calculate your final answer using the formula and financial calculator methods.

a. Compute the anticipated value of the dividends for the next four years. (Do not round intermediate calculations. Round your final answers to 2 decimal places.)

b. Calculate the present value of each of the anticipated dividends at a discount rate of 12 percent. (Do not round intermediate calculations. Round your final answers to 2 decimal places.)

c. Compute the price of the stock at the end of the fourth year (P₄). (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

d. Calculate the present value of the year 4 stock price at a discount rate of 12 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

e. Compute the current value of the stock. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

f. Use the formula given below to show that it will provide approximately the same answer as part e. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

P0	=	D1
		Ke − g

g. If current EPS were equal to $9.22 and the P/E ratio is 80% higher than the industry average of 11, what would the stock price be? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

h. By what dollar amount is the stock price in part g different from the stock price in part f? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

i. With regard to the stock price in part f, indicate which direction it would move if:

Answer 1

Solution
a. Anticipated value of dividend for next 4 years
Year	Dividend	growth	Dividend
1	5.00	9%	5.45
2	5.45	9%	5.94
3	5.94	9%	6.48
4	6.48	9%	7.06
b. Calculaiton of present value of each of the anticipated dividends at a discount rate of 12 percent
Year	Dividend	growth	Dividend	PV @12%	PV of Dividend
1	5.00	9%	5.45	0.8929	4.87
2	5.45	9%	5.94	0.7972	4.74
3	5.94	9%	6.48	0.7118	4.61
4	6.48	9%	7.06	0.6355	4.49
					18.70
c. Computation of the price of the stock at the end of the fourth year (P4) -Using dividend discount model
P0	= D1/Kc-g
Where,
P0 = Price	= ?
D1 = Next year dividend = 4.49
g= Growth = 9%
P0 =7.06/(0.12-0.09)
= $ 235.33
d. Calculation of the present value of the year 4 stock price at a discount rate of 12 percent.
= $ 235.33 * 0.6355
= $ 149.55
e. Computation of the current value of the stock.
=4.87+4.74+4.61+4.49+149.55
= $ 168.26
f. approximately the same answer as part e. Where,
P0	= D1/Kc-g
Where,
P0 = Price	= ?
D1 = Next year dividend = 5.45
g= Growth = 9%
P0 =5.45/(0.12-0.09)
= $ 181.67
g. If current EPS were equal to $9.22 and the P/E ratio is 80% higher than the industry average of 11, what would the stock price be?
P/E Retio
=11 +( 80%*11)
= 19.8
Stock price
=EPS* P/E
= 9.22*19.8
= $ 182.56
h. Difference in stock price in part g from the stock price in part f
= 181.67 -182.56
= - $ 0.89