Sfm problem-doubt

hI fRIENDS

NOT ABLE TO UNDERSTAND THIS ONE

A share having face value of Rs.100 is currently quoted in the market at a
price of Rs.480. Annual expected dividend is 30%. During the 5th year, the
shareholder is expecting a bonus in the ratio of 1:5. Dividend rate is expected to be
maintained on the expanded capital base. The shareholder intends to retain the share
till the end of the 8th year. At that time the value of the share is expected to be
Rs.1,000. Incidental expenses at the time of purchase and sale are estimated at 5%
on the market price. Ignore tax. Ke = 15%. Should she buy the share? What is the
maximum price she can pay for the share?
Answer
Let the equilibrium market price per share = x
1.05x = 30/ (1.15)1 +30/ (1.15)2 +30/ (1.15)3 +30/ (1.15)4 +36/ (1.15)5 +36/ (1.15)6
+ 36/ (1.15)7 +1176/ (1.15)8
x = Rs.492.55.
The investor will earn the required rate of return if he pays “Rs.492.55 per share +
incidental expenses regarding purchase.”
The market price per share Rs.480 is less than this amount. Hence, buy the share.

The fair value of a share today is the PV of its future cash flows, which is for 8 years in this case. As the purchase expenses are 5% of cost, the cost 'x' of 1 share has been compounded with the factor 1.05. The dividend (cash flow) is Rs.30 per share for first 4 years. Bonus is 1/5 and therefore dividend will increase by 1/5th of the amount from 5th year. Therefore, dividend is Rs.36 from the 5th year onwards.

For every 1 share held there will be 0.2 share bonus share received. In the last year each share will have value of Rs.1,000 & hence 1.2 shares are value at Rs.1,200. After deducting 5% selling expenses we have Rs.1,140. Add Rs.36 dividend and we get the 8th year's cash flow Rs.1,176.