You are the owner of a hotel, planning to make a renovation of the hotel roof.

To finance the renovation, you are considering to ask a bank for a loan, backed

by the future two$-$year profits of the hotel. Specifically, you anticipate to receive

an after$-$tax profit of $$300,000$ in $6$ months, due to the summer vacation season;

another cash flow of $$200,000$ in one year time, due to the winter vacation

season; and to repeat the same the subsequent year. the following bonds are

available for trading: $(1)$ T$-$Notes with maturity $2$ years, a face of $$1,000$ and

a coupon rate of $10\%$ semi$-$annual, trade at par. $(2)$ T$-$Notes with maturity

$2$ years, a face of $$1,000$ and a coupon rate of $2\%$ semi$-$annual, trade at $$930.$

$(3)$ T$-$Bills with a maturity $1$ year, a face of $$1,000$ and a coupon rate of $0\%$

semi$-$annual, trade at $$950.(4)$ T$-$Bills with a maturity $0\mathrm{.}5$ year, a face of $$1,000$

and a coupon rate of $0\%$ semi$-$annual, trade at $$970.$

$1.$ What is the largest loan the bank would be willing to make you?

$2.$ Suppose now that there is expected to be inflation of $5\%$ every $6$ months.

What is the largest loan the bank would be willing to make you?

$3.$ Finally, suppose that T$-$Notes are different: T$-$Notes with maturity $2$ years,

a face of $$1,000$ and a coupon rate of $5\%$ semi$-$annual, trade at par. T$-$

Notes with maturity $2$ years, a face of $$1,000$ and a coupon rate of $2\%$

semi$-$annual, trade at $$930.$ What is the largest loan the bank would be

willing to make you? Comment on the difference with part $1.$