2 times a year, a corporate bond you own pays a coupon of $78. You bought 6 certificates of this bond when it was first issued at par value. Each of these certificates had cost you exactly $1,000 at that time. The issuer has just paid the latest coupon and the bond still has another 18 years before it matures. Your bond dealer tells you this bond is currently priced to yield 17.93%. What is the total value of your bond certificates?
Par/Face value | 1000 | |||||||||||||||||||||||||||||||||||
Annual coupon | 156 | |||||||||||||||||||||||||||||||||||
semi-annual coupon | 78 | |||||||||||||||||||||||||||||||||||
Present Value = Future value/[(1+(r/m))^mt] | ||||||||||||||||||||||||||||||||||||
r is the interest rate that is .1793. | ||||||||||||||||||||||||||||||||||||
m is the compounding period that is 2 | ||||||||||||||||||||||||||||||||||||
mt is the time period. | ||||||||||||||||||||||||||||||||||||
price of the bond = sum of present values of future cash flows | ||||||||||||||||||||||||||||||||||||
r/2 | 0.08965 | |||||||||||||||||||||||||||||||||||
mt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 |
future cash flow | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 1078 |
present value | 71.58262 | 65.69322 | 60.28837 | 55.3282 | 50.77612 | 46.59856 | 42.7647 | 39.24627 | 36.01732 | 33.05403 | 30.33454 | 27.83879 | 25.54838 | 23.44641 | 21.51737 | 19.74705 | 18.12238 | 16.63138 | 15.26304 | 14.00729 | 12.85485 | 11.79723 | 10.82662 | 9.935873 | 9.118408 | 8.368199 | 7.679713 | 7.047871 | 6.468014 | 5.935864 | 5.447496 | 4.999308 | 4.587994 | 4.210521 | 3.864104 | 49.01014 |
sum of present values | 875.96 | |||||||||||||||||||||||||||||||||||
The value of 1 bond certificate is $875.96. | ||||||||||||||||||||||||||||||||||||
Total value of 6 bond certificates = 6*875.96 | ||||||||||||||||||||||||||||||||||||
Total value of 6 bond certificates = 5255.75. | ||||||||||||||||||||||||||||||||||||
The total value of your bond certificates is $5255.75. |
2 times a year, a corporate bond you own pays a coupon of $78. You bought...
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