Most corporations pay quarterly dividends on their common stock rather than annu

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 3 percent per year indefinitely. If the required return on this stock is 13 percent, what is the current share price? (Do not round intermediate calculations and 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 $.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 answer to 2 decimal places, e.g., 32.16.)

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 3 percent per year indefinitely. If the required return on this stock is 13 percent, what is the current share price? (Do not round intermediate calculations and 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 $.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 answer to 2 decimal places, e.g., 32.16.)

Explanation / Answer

Answer

a) Current Dividend (Do) = $2.8, Growth rate of dividend (g) = 3% and Required rate of return (K) - 13%, Current share price (Po) = ?

This is a case of growing perpetuity where the value of dividend is increased every year by a constant growth rate, hence we will use constant growth formula or Gordon growth model formula to discount the future dividends & calculate the present value of stock.

Po= D1/(1+K) + D2/(1+K)2 + D3/(1+K)3 + .......... so on

where D1, D2, D3.... are the dividends starting from next year onwards.

Since D1=Do*(1+g), D2=Do*(1+g)2, D3=Do*(1+g)3.........

Po = (Do*(1+g)/(1+K)) + (Do*(1+g)2/(1+K)2) + (Do*(1+g)3/(1+K)3+ .........

= Do[((1+g)/(1+K)) + (1+g)2/(1+K)2 + (1+g)3/(1+K)3 + ......]

= Do*(1+g)/(1+K)[1 + (1+g)/(1+K) + (1+g)2/(1+K)2 + ...... ]

= Do*(1+g)/(1+K)[ (1/1-((1+g)/(1+K))]

= Do*(1+g)/(1+K)[ (1+K)/(K-g)]

= Do* (1+g)/(K-g)

where Do = $2.8, g = 3% and K = 13%

= $2.8 * (1+.03)/(.13-.03)

= $28.84

Hence, the current share price of the stock is $28.84

b) Now the company pays its annual dividend in equal quarterly installments of $0.70 each. In this case, the annual dividend will be more than previous part since we will assume that the quartery dividend is re invested again at 13%, hence the annual dividend in this case will be known as effective annual end of the year dividend.

Current quarter dividend (Qo) = $0.70

Hence Q1 = Qo * (1+g) ( Since the growth rate will same for quarter dividend as well)

Q1= $0.70 * (1+.03) = $0.721

Now this Q1 will reinvested at annual rate of 13% or effective quarterly rate of ((1+0.13)1/4 - 1)

So effective quarterly rate (i) = ((1+0.13)0.25 - 1) = 0.031

Hence effective annual dividend will be calculated using the future value of annuity formula as follows:

Effective annual dividend (D1) = Q1 * [((1 + i)4 - 1)/i]

= $0.721 * [(1+.031)4 - 1)/.031]

= $0.721 * [ 0.13/.031 ]

=$0.721 * 4.19

=$3.02

Hence D1 = $3.02

Now Po = Do * (1+g)/(K-g)

or Po = D1/(K-g)

= $3.02/(.13 -.03)

= $30.24

Hence, the current share price in this case would be $30.24

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