1. Five year ago, you invested in a 5% semi-annual coupon bond with a face value
ID: 2644845 • Letter: 1
Question
1. Five year ago, you invested in a 5% semi-annual coupon bond with a face value $1,000 for $910. Today, at the date of maturity, the bond issuer announces that default occurs with a renegotiation price $950. If you accept the renegotiation price at the date of maturity, what is your realized annual rate of return?
2. On the issue date, you bought a 30-year maturity, 8% semi-annual coupon bond. The bond then sold at YTM of 7%. Now, 5 years later, the similar bond sells at YTM of 9%. If you hold the bond now, what is your realized rate of return for the 5 year holding period?
Explanation / Answer
Solution :
1) Price at end of 5 years = $ 950
Annual coupon payment = 5% of face value
Annual coupon payment = 0.05 X $ 1000
Annual coupon payment = $ 50
Annual coupon payment must be divided by 2 because it is semi-annual coupon payment
Semi-annual coupon payment = $ 25
Coupon payment received at end of 5 years = $250
Realized annual rate of return =( ending price + semi-annual coupon payments - beginning price )beginning price
Realized annual rate of return = ($ 950 + $ 250 - $ 910) / $ 910
Realized annual rate of return = 31.87%
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2) Let the face value of the bond be $ 1000
The bond pays -annual coupons = 0.08X $ 1000
annual coupon = $ 80
semi-annual payment = $ 40
Price of the bond at the time of issue = 40 [ 1+0.07/2)2X1 - 1] / 0.07/2 ( 1+0.07/2)2X1 + 1000/(1+0.07/2)2X1
Price of the bond at the time of issue = 75.98 + $ 933.51
Price of the bond at the time of issue = $ 1009.49.
Price of the bond at the end of 5 years = 40 [ ( 1+0.09/2)2X5 -1] /0.09/2 X ( 1+0.09/2)2X5 + 1000/(1+0.09/2)2X5
Price of the bond at the end of 5 years = $ 316.38 + $ 643.92
Price of the bond at the end of 5 years = $ 960.30
Realized rate of return for the 5 year holding period = (ending price + semi-annual coupon payments - beginning price) / beginning price
Realized rate of return for the 5 year holding period = ($ 960.30 + $ 400 - $ 1009.49) / $ 1009.49
Realized rate of return for the 5 year holding period = 34.75 %
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