$2.(20$ pts$)$ Consider the following spot exchange rates: $1\mathrm{.}07$ EUR$/$USD $1\mathrm{.}24$ GBP$/$USD $17\mathrm{.}00$ USD$/$MXN $19\mathrm{.}18$ EUR$/$MXN a$.$ What is the EUR$/$GBP crossrate? b$.$ If you have $10,000$ USD, how much profit is possible in triangular arbitrage between USD, EUR, and MEX $($ignore transaction costs$)?$ In what order must you exchange your currency to profit? Consider the previous spot exchange rates and the following interest rates: a$.$ Mexico $5-$year treasury rate $10\mathrm{.}329\%$ b$.$ US $5-$year treasury rate $4\mathrm{.}62\%$ c$.$ UK $5-$year treasury rate $4\mathrm{.}12\%$ c$.$ What should the $5-$year USD$/$GBP forward rate be$?$ d$.$ What should the $5-$year MEX$/$USD forward rate be$?3.(15$ pts$)$ Suppose you own a small business and are considering your capital structure. Discuss the various theories on capital structure, the empirical evidence pertaining to these theories, and its implications for how you should handle your business$$s leverage. What are the dangers of being over$-$levered? Under$-$levered? $4.(25$ pts$)$ Suppose you own a clothing boutique to pass the time in your retirement. This business currently has no debt, no short$-$term investments, $100,000$ shares outstanding, a beta of $1\mathrm{.}2,$ current$-$year free cash flows of $$100,000,$ and expected growth of $4\%$ per year. a$.$ If the current business tax rate is $40\%,$ the risk$-$free rate is $4\%,$ and the market risk premium is $8\%,$ find the weighted average cost of capital $($WACC$),$ value of equity, and price per share for your firm. You know from your MBA finance course that leverage can add value to your firm, so you consider changing your capital structure. The banker gives you interest rate quotes for the following capital structures: wd $12\mathrm{.}5\%25\%37\mathrm{.}5\%50\%$ rd $5\mathrm{.}00\%7\mathrm{.}00\%10\mathrm{.}00\%12\mathrm{.}00\%$ b$.$ Assuming you repurchase shares of stock with the money raised from the debt issuance, for each capital structure, calculate the new cost of equity, WACC, value of operations, and the amount of debt issued. What is the optimal capital structure for your boutique, and why? c$.$ For the optimal capital structure, calculate the number of shares to be repurchased, the new value of equity, and the new price per share. d$.$ Suppose the tax rate on business income is lowered from $40\%$ to $21\%.$ What is your new optimal capital structure? Why does a lower tax rate have this effect on the use of debt?