Please help stuck with this question

TCOM – The company has 5 million $0.25 ordinary shares and $20m loan capital. The BOD of TCOM has decided to reduce the burden of debt by raising $10m through a rights issue and then using the amount raised to redeem some of the loan capital.

Profits after tax were $6m and the board expects to achieve 20% increase in this figure in the forthcoming yearm assuming the rights issue is successful and operational targets are met. The Board has committed the company to a dividend pay out ratio 25% for future years and belives the dividend growth will be 4% per annum for the indefinate future.

The board believes that the rights shares should be issued at a 40% discount to the current market value.

Shareholders have a required rate of retun of 10%

Calculate the total Market value of shares, using the dividend forecast, assuming successful rights issu is made

(I did the following $6m*0.20 = $7.2m*0.25 = $1,800,000 = dividend pay out.
Then for the total market value
$1,800,000*1.04 = £1,872,000/(0.10-0.04) = $31,200,000 = Total market value)

Calculate the price at which a rights share in TCOM should be issued
(I did the following $31,200,000 – $10,000,000 = $21,200,000/5m shares = $4.24 per MV Share to be issued)

Calculate the number of rights shares that should be issued to raise finance required
(I did the following $4.24*0.40 = $1.696
$10,000,000/$1.696 = 5,896,226 right shares to be issued)

Please could someone advise if I am on the right path as I feel I have done this totally wrong.
Any help is really appreciated

Thanks,
Shelley