1. One benefit of being a UB professor is that the school will pay 75% of your...

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1. One benefit of being a UB professor is that the school will pay 75% of your childrens' tuition. I have three children who will be college-age starting in 11, 13, and 15 years. UB's current tuition for the coming academic year is $57,100. Assume that it is expected to grow at 3% each year for the foreseeable future.

(a) What is the present value of UB's tuition benefit to me assuming that all three of my children attend UB for four years with the tuition being payable in full annual installments at the start of each year? Assume a discount rate of 7% (for example, I will make tuition payments for my eldest child exactly 11, 12, 13, and 14 years from now).

(b) Assuming the benefit is spread equally over the next 18 years (i.e., from the end of this year until my youngest graduates in 18 years), how much of an annual increase in salary would I have to earn to compensate for the tuition benefit?

2. On June 18, 2021, the U.S. Treasury rates were as follows:

Table 1: U.S. Treasury Rates: (Duration-Interest Rate) (1 year-0.09%) (2 year-0.26%) (3 year-0.47%) (5 year-0.89%) (7 year-1.22%) (10 year-1.45%) (20 year-1.97%) (30 year-2.01%)

(a) Based on the above yield curve data, what would you expect the risk-free rate of return for a one-year investment starting on June 18, 2022 (i.e., one year out from the published rates) to be?

(b) How much would you expect to pay per $1,000 of face value for a 2.5% coupon risk-free bond that matures in three years? Assume the coupons are paid annually with the first payment due one year from today.

(c) Suppose you purchased $1,000,000 in the face value of the above bonds on June 18 (at the price you just calculated). Immediately after you bought the bonds, the Federal Reserve announces that they are increasing the Federal Funds rate by 0.5% and as a consequence, all the above rates immediately increase by 0.5%. What is the new price of the bond?

3. Suppose you have a student loan balance of $30,000. Your interest rate is 5.25% APR, with interest compounded monthly.

(a) What is your effective annual interest rate (EAR)?

(b) How much would you have to pay on a monthly basis to pay off your account in exactly 10 years? Assume you make your first of 120 equal monthly payments one month from today.

(d) How much of your first monthly payment would go to the principal?

(e) How much total interest would you pay in the first 5 years?

4. Suppose that you have an outstanding credit card balance of $12,000 with an APR of 12.99% with monthly compounding.

(a) What is your effective annual interest rate (EAR)?

(b) If you want to pay off your card in exactly three years, how much would your annual payment be if you made 36 equal monthly installments starting one month from today?

(c) You also have an offer for a new credit card that will charge 0% APR for the first twelve months and then increase to 16.99% APR (with monthly compounding) thereafter. The new card also charges a 2% balance transfer fee (meaning that 2% of the outstanding balance will be added to the principal). How much would you have to pay per month to pay off this credit card in full with 36 equal monthly installments starting one month from today?

(d) Which option should you choose?

5. Consider a company that just issued $10 million in 10-year bonds where the coupons are paid semiannually.

(a) If the bond has an initial yield to maturity of 6% (stated as an APR with semiannual compounding) and is trading at $980 per $1,000 of face value, what is the bond's coupon rate?

(b) If one year later, the yield to maturity on the bond increases to 7%, what is the new price immediately before the company makes the second coupon payment?

(c) If after two years (from the initial borrowing), the yield to maturity on the bond has now decreased to 4%, what is the new price immediately after the company makes the fourth coupon payment?