Question

An-investor initially purchases a 5-year, 6% annual coupon payment bond at par value of $100. Assume the interest rates go up by 1% right after the first coupon is received and then go down by 2% right after the fourth coupon is received. Assume the term structure is flat and coupon payments are reinvested in zero-coupon bonds that mature at the end of investment horizon.

a) What is investor's realized rate of return if he holds the bond until maturity?

b) What is investor's realized rate of return if he sells the bond after four years?

Answer 1

A) Realized Rate of Return if bond is held until maturity:-

Investor initially purchases a 5-year, 6% annual coupon payment bond at par value of $100.

Since, purchase price of the bond = Par Value, the prevailing market interest rate must be equal to the coupon rate of 6%

Interest rates after first coupon = 6% + 1% = 7%

Interest rates after fourth coupon = 7% - 2% = 5%

The coupon payments are reinvested in Zero-coupon bonds (ZCBs) whenever they are received. The ZCBs mature at the end of investment horizon. Hence, re-investment yield earned on ZCBs will be equal to the prevailing market interest rates.

Attaching the Excel Sheet showing calculations and formulas used :-

A. C F 1 Par Value of the Bond 2 100 Coupon rate 6% 3 4 Cash Flows Re-investment rate Remaining Years to maturity Total Amount 5 Year 7% 6 1 6 4 7.8648 7% 7 2. 6 7.3503 7% 6 2 6.8694 5% 4 6 1 6.3000 5% 10 5 6 0 6.0000 5% 11 5 100 0 100.0000 12 Sum 134.3844 13 Total Return earned 14 6.089% LO st

A. C E F 1 Par Value of the Bond 2 100 3 Coupon rate 0.06 4 Cash Flows Re-investment rate Remaining Years to maturity Total Amount 5 Year C$3*C$2 -$B$10-B6 C6*(1+D6)^E6 =C7*(1+D7)^E7 6 1 0.07 C$3*C$2 SB$10-B7 7 2 0.07 C$3*C$2 $B$10-B8 C8*(1+D8)^E8 |C9*(1+D9)^E9 0.07 | C$3*C$2 C$3*C$2 -$B$10-B9 4 0.05 -$B$10-B10 C10*(1+D10)^E10 10 5 0.05 =$B$10-B11 C11*(1+D11)^E11 11 5 100 0.05 -SUM(F6:F11) 12 Sum 13 F12/C2)^(1/5)-1 Total Return earned 14 nst st LO LD

Realized Rate of Return = 6.089%

B)

Market Rate of Interest after 4 years = 5%

Let us find out the selling price of bond at the end of 4 years, by discounting the cash flows:-

Total cash flows to be received in year 5 = (6+100) = 106

Hence, market Price = 106 / 1.05 = 100.95

Let us calculated the total return by discounting all the cash flows.

Attaching the calculations with values and formulas used:-

15 Par Value of the Bond 16 100 6% 17 Coupon rate 18 Cash Flows Re-investment rate Remaining Years to maturity Total Amount 19 Year 7% 20 1 6 7.3503 7% 21. 2 6 2 6.8694 7% 22 3 6 1 6.4200 5% 6.0000 23 6 0 5% 24 100.95 0 100.9500 25 Sum 127,5897 26 6.2806% Total Return earned 27 st

15 Par Value of the Bond 16 100 17 Coupon rate 0.06 18 Cash Flows Re-investment rate Remaining Years to maturity Total Amount C20*(1+D20)^E20 19 Year C$3*C$2 -$B$24-B20 $B$24-B21 0.07 20 1 C$3*C$2 C21*(1+D21)^E21 C22*(1+D22)^E22 C23*(1+D23)AE23 21 2 0.07 C$3*C$2 $B$24-B22 22 3 0.07 c$3*C$2 -$B$24-B23 0.05 23 =$B$24-B24 100.95 C24*(1+D24)^E24 24 0.05 -SUM(F20:F24) 25 Sum 26 =(F25/C16)^(1/4)-1 Total Return earned 27 st st

Hence, Return earned = 6.28%