Question

share valuation: Most companies pay half-yearly dividends on their ordinary shares 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 installments to its shareholders.

a. suppose a company currently pays an annual dividend of $2.50 on its ordinary shares in a single annual installment and management plans on raising this dividend by 5% per year indefinitely. If the required return on this share is 13%, what is the current share price?

b. Now suppose the company in part a above actually pays its annual dividend in equal half yearly instalments; thus the company has just paid a $0.75 dividend per share as it has for the past half year. What is your value for the current share now? (Hint: find the equivalent end-of-year dividend for each year.) Comment on whether you think this model of share valuation is appropriate.

Answer 1

a.

Given annual dividend D= $2.50

Dividend growth g= 5%

Required return R = 13%

Price = [D*(1+g)]/ (R-g)

= [2.5* (1+ 0.05)/ (0.13-0.05)

= (2.5*1.05)/ 0.08 = 32.8125

Current share price = $32.81

b.

Now, given that the company makes half yearly dividend payments of $0.75

Half yearly payment = Dividend * (1+ 0.05) = 0.75 *1.05 = 0.7875

Effective half yearly dividend = (1+r)^1/n -1 = (1+ 0.13)^0.5 -1 = 1.13^0.5 -1 = 1.063 -1 = 0.063

Note: 0.5 considered as payments are half yearly (1/2)

Effective annual dividend = half yearly payment * [ {(1+r)^n -1}/ r]

Here r = effective half yearly dividend = 0.063

Effective annual dividend = 0.7875 * [ {1+0.063)^2 -1}/ 0.063]

= 0.7875 * 2.063 = 1.6246

Price of share = Effective annual dividend/ (r-g)

= 1.6246/ (0.13-0.05)

= 1.6246/ 0.08 = 20.3075

Price of share = $20.31