Cheat Sheet for Fnce 611

Example: Suppose you are looking to buy a house in West Philadelphia and consider taking out a $300,000 mortgage with a fixed interest rate for 15 years. You have two financing options: Your first offer is from a local bank stating an APR with monthly compounding of 2.80% p.a. Your second offer is from a nationwide bank stating an effective annual rate of 2.80% p.a. Which financing option appears more attractive to you, and why? – 5 points

*when you see EAR for annuity problem convert to APR*

 [1] , because green option has lower APR (note we can also compare both on EAR basis) it is the preferred option.[pic 1]

Then apply annuity formula and solve for C, monthly payment. We always use APR for annuity

Sometimes mortgage lenders make ‘special’ offers for borrowers that can’t yet afford their monthly payment. For example, the mortgage remains a 15-year loan, but the borrower does not have to make any payment for one year. Please assume the first payment on this ‘special’ mortgage occurs 13 months from today, using the same rate you used in part b; the loan amount of $300,000 becomes available today. What is the monthly payment?

To solve grow the PV/loan amount by the interest for the time we are not paying it down, i.e.

300k*(1.028) = 308,400, then apply the annuity formula with the updated time horizon, 14 years

[pic 4]

Notes

[1] Longer term mortgages have higher interest rates because due to more default risk, upward sloping term structure of risk-free rates, inflation

------------

Facts about Treasury Securities

[1] T-bills – less than 1 year to maturity sold at discount

[2] T-notes – 1-10 year maturities, pay interest on semi-annual basis at fixed rate

[3] T-bond - 10-30 year maturities, pay interest on semi-annual basis at fixed rate

[4] Treasury inflation protected securities – 5-20 years maturity, principal increases with inflation, pay interest on semi-annual basis at fixed rate

[5] Treasury Floating Rate Notes – pay interest on a quarterly basis at a variable rate

------------

Given a corporate bond with yield y, years to maturity T, face value FV, compounding periods, m, and coupon, C, then we can calculate the price or PV using.

[pic 5]

Example: Apple is a highly-rated company and has easy access to capital markets these days. Suppose they can borrow at a yield to maturity of 1.5% p.a.(annual compounding) when issuing 3-year bonds, and at a yield to maturity of 2.0% p.a. (annual compounding) when issuing 5-year bonds. Investors, however, expect the same coupon rate of 3% p.a., paid annually. Which bond do investors prefer with annual compounding?