Suppose you enter into a loan agreement to borrow $$100,000$ to help finance the

purchase of a new home. The loan contract specifies a term of $30$ years with fixed

monthly payments determined at a fixed rate of $6\%$ per year $($APR compounding

monthly$).$

$2$

a$.$ What is the amount of your monthly payments?

b$.$ Now suppose exactly five years have passed $($you made the $60$th payment

yesterday$).$ A rival lender offers to refinance your loan at a fixed rate of $5\%$ per

year $($APR compounding monthly$).$ Costs associated with this refinancing amount

to $$2,000.$ Should you refinance? You can assume the new loan has a term of

either $25$ or $30$ years.

The next $4$ questions cover bond valuation. They are meant to provide additional

practice while also asking you to think about potential risks in bond markets.

Question $5$: U$.$S$.$ Treasury Securities

Yields implicit in U$.$S$.$ Treasury securities are benchmark rates throughout the U$.$S$.$

economy, as well as in international capital markets. The $7-$year yield to maturity

was $3\mathrm{.}73\%($APR compounding semiannually$)$ on the day our course started. What

was the price of a $7-$year Treasury note with a coupon rate of $4\%$ per year, paid

semiannually? Feel free to assume a face value of $$100.$

Question $6$: Corporate Bonds

The pandemic years were a very active time for Corporate Bonds, as many

companies attempted to raise cash at record$-$low rates. For example, AT&T raised

cash by selling a corporate bond in May $2020,$ with a time to maturity of $7$ years.

They raised $2\mathrm{.}495$ billion USD, promising a face value of $2\mathrm{.}500$ billion USD, and a

coupon rate of $2\mathrm{.}3\%$ per year, paid semiannually.

a$.$ What was the yield to maturity that investors required in May $2020?$

b$.$ Suppose a comparable U$.$S$.$ Treasury security showed a yield to maturity of

$0\mathrm{.}53\%$ in May $2020.$ What was AT&T$$s credit spread?

Aside: This corporate bond was part of a larger transaction. In total, AT&T raised

$12\mathrm{.}5$ billion USD using bonds with $5$ different maturities. AT&T used the cash to

refinance existing debt.

Question $7$: Duration

Duration is a popular measure of risk in bond markets. It allows us to answer, how

sensitive is the price of a bond to changes in its yield?

a$.$ Please calculate the modified duration of the two bonds, i$.$e$.$ the U$.$S$.$ Treasury

bond in Question $5,$ and AT&T corporate bond in Question $6.$

b$.$ According to modified duration, which of the two bonds carries more risk?