Question

2 Suppose that you are considering investing in a four-year bond that has a par value of $1,000 and a coupon rate of 6%. (a) Draw a timeline for this bond (b) What is the price of the bond if the market interest rate on similar bonds is 6%? what is the (c) Suppose that you purchase the bond, and the next day the market interest rate on similar (d) Now suppose that one year has gone by since your bought the bond, and you have received bond's current yield? bonds falls to 5%. What will be price of your bond be now? what will its current yield be? the first coupon payment. How much would another investor now be willing to pay for the bond? What was your total return on the bond? (Market interest rate remains at 5%.) (e) Now suppose that two years have gone by since you bought the bond and that you have received the first two coupon payments. At this point, the market interest rate on similar bonds unexpectedly rises to 10%. How much would another investor be willing to pay for your bondi?

Answer 1

Annual coupon payment = $1,000 x 6% = $60

In year 4, total amount received = Par value + Annual coupon = $1,000 + $60 = $1,060

(a) Cash flow diagram as follows.

5 1000 460 460 ч60 1060 0 3

(b) When market interest rate is 6% (= bond coupon rate), the bond will sale at par value and bond price is equal to par value of $1,000. When a bond sells at par, its current yield equals coupon rate of 6%.

(c) When market rate = 5%,

Bond price ($) = PV of future coupon payments + PV of par value

= 60 x P/A(5%, 4) + 1,000 x P/F(5%, 4)

= 60 x 3.546** + 1,000 x 0.8227**

= 207.36 + 822.7

= 1,030.06

Current yield = Annual coupon / Bond price = $60 / $1,030.06 = 0.0582 = 5.82%

(d) After 1 year, Years to maturity = 4 - 1 = 3 years

Bond price ($) = PV of future coupon payments + PV of par value

= 60 x P/A(5%, 3) + 1,000 x P/F(5%, 3)

= 60 x 2.7232** + 1,000 x 0.8638**

= 163.39 + 863.8

= 1,027.19

Total return = [(Bond price after 1 year + Coupon payment for 1 year) / Purchase price] - 1 = [$(1,027.19 + 60) / $1,030.6] - 1

= ($1,087.19 / $1,030.6) - 1 = 1.0549 - 1 = 0.0549 = 5.49%

**From P/A and P/F Factor tables

NOTE: As per Answering Policy, 1st 4 parts are answered.