a$.$ An all$-$equity company ABC has nine million outstanding shares, with a share price currently at$55.$ The company also has outstanding debt valued at $75$ million. Equity cost of capital is $6\mathrm{.}5\%.$ The company has made an announcement of issuing new debt valued at $210$ million. The proceeds of this issue will be used to repay outstanding debt and to pay out an immediate dividend. Assume capital markets are perfect.

Required:

i$.$ What is the share price just after the announcement, before the issue takes place?

ii$.$ Based on the market$-$value balance sheet, calculate the price of the share when the nnounced transaction is carried out.

iii. Assume that the existing outstanding debt bears no risk and has an expected return of $4\mathrm{.}75\%.$ Also assume that the new debt bears risk and has an expected return of $6\%.$ Calculate the equity cost of capital after the announced transaction is carried out.

b$.$ Company DEF is analyzing whether to issue debt or preference shares. The corporate tax rate is $45\%.$ Interest income is taxed at $30\%.$ The tax rate on dividends and gains from capital is $12\%.$ Dividends on preference shares are not allowed as a deduction from corporate tax.

Required:

i$.$ Calculate the cost of capital for preference shares if the debt interest rate is $5\%.$

ii$.$ Calculate the debt cost of capital after taxes and compare it with the cost of capital of preference shares calculated above. Should the company issue debt or preference shares?

iii. Show the relationship between the debt cost of capital after taxes, preference shares cost of capital, and tt$.$

c$)$ Discuss the two main agency costs of debt and how these costs can be mitigated.

d$)$ Discuss theories and arguments in favour of firms$$ policy of high dividend payments.