QUESTION THREE

A$.$ Supplier DEF, based in Europe, sells goods to a buyer in South America and seeks factoring services to optimize cash flow. The total invoice value for the transaction is $70,000.$ The factoring company charges a fee of $2\mathrm{.}5\%$ of the invoice value for providing the factoring service. The factoring company also charges a one$-$time setup fee of $500$ for initiating the factoring arrangement and applies an additional discount rate of $1\mathrm{.}2\%$ per month on the total invoice value until the buyer settles the invoice. If the Supplier receives payment after $6$ months, calculate the total amount of fees and charges paid by Supplier DEF to the factoring company. $(5$ Marks$)$

B$.$ A one$-$step binomial tree is used to model the impact of an important announcement on the stock price of Company XYZ$.$ There is a $50\%$ chance that the announcement will be positive for the company. The Company does not pay dividends.

Current stock price $=K20$

Time period $=3$ years

Risk$-$free rate continuous compounding