Explain nouns $(30\%)$

$1\mathrm{.}1$ Asset substitutuion

$1\mathrm{.}2$ Golden parachute

$1\mathrm{.}3$ Modified IRR

$1\mathrm{.}4$ Taking poison pills

$1\mathrm{.}5$ Sensitivity analysis

$1\mathrm{.}6$ Risk avoidance

$1\mathrm{.}7$ White knight

$1\mathrm{.}8$ Sunk costs

$1\mathrm{.}9$ Risk premium during maturity $1\mathrm{.}10$ MCC

Please explain what is the equity agency problem? $(2\%)$ and please explain in detail the internal and external mechanisms that you have learned in class that can help alleviate this agency problem. $(6\%)$

Three $(1)$ Proposition $2$ of MM $(1958)$ states: Rs$=$Ra$+($Ra$-$Rd$)($D$/$E$)$ Please explain how the above formula is derived, and please explain this formula from the perspective of Business risk Financial risk financial implications. $(5\%)$

$(2)$ Proposition $1$ of MM $(1963)$ points out: the value of a company with debt $=$ the value of a company without debt $+$ tax$-$saving benefits, and points out that tax$-$saving benefits $=$ TcB$.(5\%)$

$(3)$ Please draw and explain in detail trade$-$off theory of capital structure $(8\%)$

$4.$ Assume that NUK Corp. currently has an investment plan that spends $60$ million at the beginning of the period and can create a cash flow of $10$ million at the end of each year for the next $9$ years. Please explain how to use the payback period method to evaluate whether the investment plan is worth investing. $(4\%)$ and please explain the advantages and disadvantages of the recovery period method $(6\%).$ In addition, assume that half of NUK Corp.$\text{'}$s funds come from common stocks and half from bank borrowings, and the borrowing interest rate is $4\%.$ The risk$-$free interest rate is $2\%,$ NUK Corp.$\text{'}$s account is $0\mathrm{.}8,$ the expected return on the market portfolio is $10\%,$ and the income tax rate is $20\%.$ What is NUK Corp.$\text{'}$s WACC? $(6\%).$ Please also use the net present value method to calculate the net present value of this project? $(4\%).$ Finally, please explain how to evaluate whether this investment plan has investment value using the IRR method. $(3\%)($Note: The IRR method only needs to list the calculation formula and explain it$,$ and does not need to calculate the precise IRR.$)$ Please also explain in detail the possible shortcomings of the IRR method compared to the NPV method. $(5\%)$

$5.$ Gaoda Company is considering whether to update its machinery and equipment. If the equipment is updated, it will require an investment of $70$ million. In the next $8$ years, it will need to spend $10$ million in maintenance fees at the end of each year. The residual value of the machine after $8$ years will be $12$ million. If the existing machine is The equipment can be sold for $35$ million yuan. If the existing machinery and equipment are used, the maintenance fee of $11$ million yuan will be paid after one year. After repair, it can be sold for $26$ million yuan. Should Gaoda Company replace the old ones with new ones now? Machinery and equipment? Assume capital cost is $10\%.(6\%)6.(1)$

Xiang En won the lottery ticket at the beginning of $2021.$ The bonus will be $1$ million yuan at the beginning of each year from $2021$ to $2040.$ Assuming that the market interest rate is $6\%,$ how much will the bonus be at the beginning of $2021?$ What is the value of $?(5$

$\%)(2)$

Assume that Peiying has just given birth to a child $($the current time point is $0),$ and Peiving plans to invest in stock funds for his children as study abroad funds at the end of each year in the next $18$ years. The expenditure required for studying abroad for four years is $19$ th $2$ million at the end of the year, $2\mathrm{.}5$ million at the end of the $20$th year, $3$ million at the end of the $211$ st year, and $3$ million at the end of the $22$ nd year. During these $18$ years, How much fund should Peiying save for her children every year, assuming the fund's investment return rate is $10\%.(5\%)$