Carambola de Honduras. Slinger Wayne, a U$.$S$.-$based private equity firm, is trying to determine what it should pay for a tool manufacturing firm in Honduras named Carambola. Slinger Wayne estimates that Carambola will generate a free cash flow of $14$ million Honduran lempiras $($Lp$)$ next year, and that this free cash flow will continue to grow at a constant rate of $9\mathrm{.}0\%$ per annum indefinitely.

A private equity firm like Slinger Wayne, however, is not interested in owning a company for long, and plans to sell Carambola at the end of three years for approximately $10$ times Carambola's free cash flow in that year. The current spot exchange rate is $Lp\frac{14\mathrm{.}7839}{\text{\$}},$ but the Honduran inflation rate is expected to remain at a relatively high rate of $17\mathrm{.}5\%$ per annum compared to the U$.$S$.$ doilar inflation rate of only $4\mathrm{.}0\%$ per annum. Slinger Wayne expects to earn at least a $24\%$ annual rate of return on international investments like Carambola.

a$.$ What is Carambola worth if the Honduran lempira were to remain fixed over the three$-$year investment period?

b$.$ What is Carambola worth if the Honduran lempira were to change in value over time according to purchasing power parity?