Question

Problem 6-34 Stock Valuation

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 5 percent per year indefinitely. If the required return on this stock is 12 percent, what is the current share price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Current share price           $

b. Now suppose the company in (a) actually pays its annual dividend in equal quarterly installments; thus, this company has just paid a dividend per share of $.70, 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 answer to 2 decimal places, e.g., 32.16.)

Current share price           $

Answer 1

a). P0 = [D0 * (1 + g)] / [r - g]

= [$2.80 * (1 + 0.05)] / [0.12 - 0.05]

= $2.94 / 0.07 = $42

b). Next Quarterly Dividend = [D0 * (1 + g)] / 4 = [$2.80 * (1 + 0.05)] / 4 = $0.735

Effective Quarterly Rate = [1 + r]^1/4 - 1

= [1 + 0.12]^0.25 - 1 = 1.0287 - 1 = 0.0287, or 2.87%

Effective D1 = Next Quarterly Dividend * [FVIFA(r%,n)

= $0.735 * [FVIFA(2.87%,4)]

= $0.735 * 4.1758 = $3.0692

P0 = D1 / [r - g]

= $3.0692 / [0.12 - 0.05]

= $3.0692 / 0.07 = $43.85

Note that we cannot simply find the quarterly effective required return and growth rate to find the value of the stock. This would assume the dividends increased each quarter, not each year.