Question

2. Mega Co. has issued a perpetual preferred stock. The issue will pay a dividend of 5% (based on a par value of $100) in perpetuity, starting 10 years from now. If investors’ required rate of return is 8%, what is the current value of these stocks?

Answer 1

A perpetual preferred stock will pay fix dividend infinitely as long as company is in business.

Dividend at 10th year = 5% (at par value = 100)

required arte of return = 8%

Therefore,

par value at 10th year = 100 * (1 + 0.08)^10

= 100 * 2.1589

= 215.89 = 216.

Dividend at 10th year = 5% * 216 = 10.8

Now, dividend discount model is

Share price = D1 / ( r - g )

where

D1 = next year's dividenf

r = required cost of capital

g = dividend growth ( 0 in this case)

Now,

Share price in 9th year = Dividend in 10th year / ( 0.08 )

= 10.8 / 0.08

= 135.

therefore, current share price = share price in 9th year / ( 1 + 0.08 ) ^ 9

= 135 / 1.999

= 67.53

therefore, current share price is 67.53 or 68.