Question

If you can go over each step I would greatly appreciate it!

You just received a lump sum of $100,000. You do not need the money until you retire at age 62. You are risk averse and are considering two bonds. Bond A sells at par and matures when you retire. Bond B has a duration equal to the number of years until your retirement. Both bonds have a yield to maturity of 4.5% and pay coupons annually.

Q1. How many years until you turn age 62? 19 years

Q2. What are the fab 5 (n, i, PV, PMT, FV) values for bond A? (Hint: FV=100,000)

Q3. What are the fab 5 values for Bond B such that the yield to maturity (I) remains 4.5% yet, the duration ( D m a c ) is the number of years until you retire, and PV=-100,000? Hint: The value of FV and PMT are flexible and you can use Excel Solver in a manner similar to the quiz example available on my Dropbox: XLSX (Links to an external site.). Or, for an additional reference example, try this one: XLSX.

Q4. If rates drop from 4.5% to 3.5% immediately after you purchase the bond, what will your total ending wealth be at retirement for Bond A?

Q5. If rates drop from 4.5% to 3.5% immediately after you purchase the bond, what will your total ending wealth be at retirement for Bond B?

Q6. If rates rise from 4.5% to 5.5% immediately after you purchase the bond, what will your total ending wealth be at retirement for Bond A?

Q7. If rates rise from 4.5% to 5.5% immediately after you purchase the bond, what will your total ending wealth be at retirement for Bond B?

Answer 1

2) Bond A sells at par which means coupon rate is equal to yield to maturity

n = 19, PMT = 4.5% x 100,000 = 4,500, i = 4.5%, FV = 100,000, PV = -100,000

3) If duration equal to no. of years to retirement, then it is zero coupon bond.

n = 19, PMT = 0, i = 4.5%, PV = -100,000, FV = 100,000 x (1 + 4.5%)^19 = 230,786

4) Bond A will give you 100,000 at retirement and future value of all coupons reinvested at 3.5% can be calculated using FV function

n = 19, PMT = 4,500, PV = 0, i = 3.5% => Compute FV = 118,607

Total Value = 218,607

5&7) Here, you will get 230,786

6) if i = 5.5% in 4, then FV = 144,462

=> Total Value = 244,462