Question

Most corporations pay quarterly dividends on their common stock rather than annual dividends. Barring any unusual circumstances during the year, the board raises, lowers, or maintains the current dividend once a year and then pays this dividend out in equal quarterly installments to its shareholders.

a.) Suppose a company currently pays an annual dividend of $3.40 on its common stock in a single annual installment, and management plans on raising this dividend by 3.8 percent per year indefinitely. If the required return on this stock is 10.5 percent, what is the current share price?

b.) Now suppose the company in (a) actually pays its annual dividend in equal quarterly installments; thus, the company has just paid a dividend of $.85 per share, as it has for the previous three quarters. What is your value for the current share price now? (Hint: Find the equivalent annual end-of-year dividend for each year.)

Answer 1

(a) Annual Dividend paid (D0) = $ 3.4

Required Rate of Return (Ke) = 10.5%

Growth Rate (g) = 3.8%

Price per Share =

Po = Do (1+g) / Ke - g

Po = $ 3.4 (1+0.038) / 0.105 - 0.038

Po = ($ 3.4 * 1.038) / 0.067

Po = $ 52.67

(b)

Equivalent annual end-of-year dividend = $ 0.85 FVAF((10.5%/4),4 Qaurters)

Equivalent annual end-of-year dividend = $ 0.85 * 4.16

Equivalent annual end-of-year dividend = $ 3.536

Computation of FVAF:
r	1+r	(1+r)^n	[(1+r)^n] - 1	[(1+r)^n] - 1 / r
2.63%	1.0263	1.1092	0.1092	4.1600

Price per Share =

Po = Do (1+g) / Ke - g

Po = $ 3.536 (1+0.038) / 0.105 - 0.038

Po = ($ 3.536 * 1.038) / 0.067

Po = $ 54.78