$($Please give clear step by step, and dont use excel$)$ KMS Corporation faces a choice between paying out $$200$ million cash through a share repurchase, and investing the $$200$ million in Treasury securities paying $7\%$ interest for one year. If shareholders are paid the cash through a share repurchase they are going to invest it in the same T$-$securities as KMS would. If KMS retains and invests cash it is going to pay the entire investment income out to shareholders in the form of dividends. Assume that capital gain taxes must be paid after the interest is received $($in $1$ year after the distribution$)$

Assume that corporate tax rate is $35\%$ and investors pay $15\%$ tax rate on dividends and capital gains and $30\%$ on interest income.

a$)$ What would shareholders want KMS to do with the cash? Explain, provide computations

b$)$ Now suppose that KMS plans an expansion project next year for which it will need $$200M.$ If the company retains the cash it would not need to raise new funds from the investors for the project. Raising new funds costs $F$ dollars, nominal issuance fees. The fees expense is tax deductible. If $F=$$$3M,$ what would be optimal for KMS to do $-$ retain cash or pay it out and raise cash in one year when it needs it for the project?