Question

(perpetuity)

- first dividend of $10 per share is planned 3 years from today.

- after that dividends will decline at 5% p.a. for next two years, and then grow at rate of 3% p.a.

- dividends paid annualy

- required rate of return is 0.5/fornight

ask: how many shares need to sell to raise $500000

Answer 1

First dividend is payable in three years from today which means dividend on 3rd year would $10 and the apply growth (-5%) for fourth and fifth year thereafter 3% growth.

Ke is given to compound fortnightly, have been converted on annual basis by multiplying

0.5 % * 2 (fortnight in a month) * 12 ( months in an year)

= 12% PA

Yearly PV Factor is computed by dividing 1 / (1+interest rate) and thereafter all resultant numbers to be divided by (1+int. rate).

Formula to compute share price is mentioned in the table below.

P0 is price of the share, D1 is next period dividend (dividend paid * growth rate) and Ke is cost of equity.

Dividend for 6th year is 9.3 and discount rate is 0.51 therefore price of the share would be 9.3 divided by 12% - 3% (Ke - g)

The final figure is 103.29 on 6th year which is converted back to PV at 6th year discount rate by dividing 103.29 / 0.51 = 203.87

Number of share to be issued today would be $500,000 / 203.87 (current share price ) = 4841 shares.