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 $2.80 on its common stock in a single annual installment, and management plans on raising this dividend by 2 percent per year indefinitely. If the required return on this stock is 12percent, what is the current share price? (Round your answer to 2 decimal places. (e.g., 32.16)) 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 $0.70 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.) (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Answer 1

(a).

Current stock price = $28.56

Explanation;

Current stock price = D0 (1 + g) / (R – g)

Current stock price = $2.80 (1 + .02) / (.12 – .02)

Current stock price = $2.80 * 1.02 / (0.10)

Current stock price = $2.856 / (0.10)

Current stock price = $28.56

(b).

Current stock price = $29.80

Explanation;

First of all let’s calculate quarterly dividend;

Quarterly dividend (0.70 * 1.02) = $0.714

Now, let’s calculate effective quarterly rate;

1.12^0.25 – 1

= .0287 or 2.87%

Now, let’s calculate effective D1;

Effective D1 = $0.714 (FVIFA 2.87%,4) = $2.98

Now, we will calculate current price of the stock;

Current stock price = $2.98 / (.12 – .02)

Current stock price = $2.98 / (0.10)

Current stock price = $29.80