A mutual fund portfolio currently is worth $$100$ million. Last year, the fund sold $50,000$ shares of Microsoft for $$60$ per share, $20,000$ shares of Ford for $$40$ per share, and $30,000$ shares of Boeing for $$50$ per share. The proceeds are used to buy $100,000$ shares of IBM at $$53.$

a$)$ What was the portfolio turnover rate?

b$)$ Assume there are no liabilities and $2,500,000$ shares outstanding. What is the net asset value of the fund?

c$)$ Assume you own $1,000$ shares of the mutual fund. What is your portfolio worth?

d$)$ If the shares in Microsoft originally were purchased for $$40$ each, shares on Ford for $$30,$ shares in Boeing for $$35,$ and if your tax rate on capital gains income is $20\%,$ how much extra will you owe this year in taxes as a result of these transactions?

e$)$ If in December, the NAV of the fund depreciated to $$25.$ What is your end$-$of$-$year portfolio worth? How much extra taxes will you owe now?