helpQUESTION $5$

a$)$ SuperPower Company wants to raise $$20$ million. The subscription price is $$40,$ and

the current stock price is $$50.$ The firm currently has $5,000,000$ shares outstanding.

i$.$ Determine the number of shares that must be issued.

ii$.$ Calculate the number of rights.

iii. Compute the value of a rights.

b$)$ Your parents have a retirement fund of RM$450,000.$ They wish to retire in $15$ years.

Their annual incomes currently total RM$145,000,$ which is expected to increase at a

conservative rate of $6\%$ next year. Your parents think that they can consistently

deposit $20\%$ of the next year's incomes to the retirement fund in the next $15$ years.

The first deposit will occur at the end of Year $1,$ and subsequent deposits will be

made at the end of each year. The last deposit will be made at the end of Year $15.$

They expect to withdraw RM$180,000$ per year from the accumulated fund starting

from a year after retirement. Assume the fund earns a compound annual return of

$7\mathrm{.}5\%$ throughout the pre$-$ and post$-$retirement life.

i$,$ Calculate the remaining amount after the third withdrawal of RM$180,000.$

ii$.$ Determine the duration for which the fund can sustain after retirement if the

annual withdrawal of RM$180,000$ continues in the subsequent years.