In: Finance
7 years ago, Delicious Mills, Inc. issued 30-year to maturity bonds that had a 8.10 percent annual coupon rate, paid semiannually. The bonds had a $1,000 face value. Since then, interest rates in general have changed and the yield to maturity on the Delicious Mills bonds is now 10.92 percent. Given this information, what is the price today for a Delicious Mills bond?
Par/Face value | 1000 | ||||||||||||||||||||||
Annual Coupon rate | 0.081 | ||||||||||||||||||||||
Annual coupon | 81 | ||||||||||||||||||||||
semi-annual coupon | 40.5 | ||||||||||||||||||||||
Present Value = Future value/[(1+(r/m))^mt] | |||||||||||||||||||||||
r is the interest rate that is 10.92%. | |||||||||||||||||||||||
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 | 0.0546 | r | 0.1092 | ||||||||||||||||||||
mt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 |
future cash flow | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 40.5 | 1040.5 |
present value | 38.40319 | 36.41493 | 34.52961 | 32.74191 | 31.04675 | 29.43936 | 27.91519 | 26.46994 | 25.0995 | 23.80002 | 22.56782 | 21.39941 | 20.2915 | 19.24094 | 18.24478 | 17.30019 | 16.4045 | 15.55519 | 14.74984 | 13.9862 | 13.26209 | 12.57547 | 306.3539 |
sum of present values | 817.79 | ||||||||||||||||||||||
The price today for a Delicious Mills bond is $817.79. |