a. A $1,000 bond has a 7.5 percent coupon and matures after 10years. If current

Question

a. A $1,000 bond has a 7.5 percent coupon and matures after 10years. If current
interest rates are 10 percent, what should be the price of thebond?

b. If after six years interest rates are still 10 percent, whatshould be the price of the bond?

c. Even though interest rates did not change in a and b, why didthe price of the bond
change?

d. Change the interest rate in a and b to 6 percent and rework youranswers. Even though
the interest rate is 6 percent in both calculations, why are thebond prices different?

Explanation / Answer

Annual Coupon Amount[$1,000 * 7.5%] $75 Yield to Maturity ( r) 10.00% Par Value (or) Face Value of thebond (F) $1,000 Number of Years to Maturity(t) 10 years Calculating Bond ValueUsing Present Value Tabels: Bond Value = Annual Coupon Payment[PVOA(10%, 10)] + $1,000 [PVF(10%,10)] Bond Value = $75 * 6.1446 + $1,000 *0.3855 Bond Value = $460.85 +$385.50 Bond Value =$846.35 Calculating Bond ValueUsing Formula: Bond Value = C *[1-1/(1+r)t] / r + F/(1+r)t Bond Value = $75* [1-1/(1+0.10)10 ] / 0.10 +   $1,000 /(1+0.10)10 Bond Value = $75* [1-1/(1.10)10 ] / 0.10 + $1,000 /(1.10)10 Bond Value = $75 * [1-(1/2.59374246)] / 0.10 + $385.50 Bond Value = $75* 6.145 + $385.50 BondValue = $846.35 (b) Calculating bondprice after six years: Calculating Bond Value Using PresentValue Tabels: Bond Value = Annual Coupon Payment[PVOA(10%, 6)] + $1,000 [PVF(10%,6)] Bond Value = $75 * 4.3553 + $1,000 *0.5645 Bond Value = $326.65 +$564.50 Bond Value = $891.15 ( c) Compared to(a) part with (b), the bond price is more in (b), because here wecalculated the bond price for 6 years only and there is nochange in interest rate.        (d) Calculating BondPrices: Calculating Bond Value UsingPresent Value Tabels: Bond Value = Annual Coupon Payment[PVOA(6%, 10)] + $1,000 [PVF(6%,10)] Bond Value = $75 * 7.3601+ $1,000 *0.5584 Bond Value = $552 +$558.40 Bond Value =$1,110.40 Calculating Bond Value UsingFormula: Bond Value = C *[1-1/(1+r)t] / r + F/(1+r)t Bond Value = $75* [1-1/(1+0.06)10 ] / 0.06+   $1,000 /(1+0.06)10 Bond Value = $75* [1-1/(1.06)10 ] / 0.06 + $1,000 /(1.06)10 Bond Value = $75 * [1-(1/1.790847697)] / 0.06 + $558.40 Bond Value = $75* 7.3601 + $558.40 BondValue = $1,110.40 Calculating bondprice after six years: Calculating Bond Value Using PresentValue Tabels: Bond Value = Annual Coupon Payment[PVOA(6%, 6)] + $1,000 [PVF(6%,6)] Bond Value = $75 * 4.9173 + $1,000 *0.7050 Bond Value = $368.80 +$705 Bond Value =$1,073.80 Annual Coupon Amount[$1,000 * 7.5%] $75 Yield to Maturity ( r) 10.00% Par Value (or) Face Value of thebond (F) $1,000 Number of Years to Maturity(t) 10 years Calculating Bond ValueUsing Present Value Tabels: Bond Value = Annual Coupon Payment[PVOA(10%, 10)] + $1,000 [PVF(10%,10)] Bond Value = $75 * 6.1446 + $1,000 *0.3855 Bond Value = $460.85 +$385.50 Bond Value =$846.35 Calculating Bond ValueUsing Formula: Bond Value = C *[1-1/(1+r)t] / r + F/(1+r)t Bond Value = $75* [1-1/(1+0.10)10 ] / 0.10 +   $1,000 /(1+0.10)10 Bond Value = $75* [1-1/(1.10)10 ] / 0.10 + $1,000 /(1.10)10 Bond Value = $75 * [1-(1/2.59374246)] / 0.10 + $385.50 Bond Value = $75* 6.145 + $385.50 BondValue = $846.35 (b) Calculating bondprice after six years: Calculating Bond Value Using PresentValue Tabels: Bond Value = Annual Coupon Payment[PVOA(10%, 6)] + $1,000 [PVF(10%,6)] Bond Value = $75 * 4.3553 + $1,000 *0.5645 Bond Value = $326.65 +$564.50 Bond Value = $891.15 ( c) Compared to(a) part with (b), the bond price is more in (b), because here wecalculated the bond price for 6 years only and there is nochange in interest rate.        (d) Calculating BondPrices: Calculating Bond Value UsingPresent Value Tabels: Bond Value = Annual Coupon Payment[PVOA(6%, 10)] + $1,000 [PVF(6%,10)] Bond Value = $75 * 7.3601+ $1,000 *0.5584 Bond Value = $552 +$558.40 Bond Value =$1,110.40 Calculating Bond Value UsingFormula: Bond Value = C *[1-1/(1+r)t] / r + F/(1+r)t Bond Value = $75* [1-1/(1+0.06)10 ] / 0.06+   $1,000 /(1+0.06)10 Bond Value = $75* [1-1/(1.06)10 ] / 0.06 + $1,000 /(1.06)10 Bond Value = $75 * [1-(1/1.790847697)] / 0.06 + $558.40 Bond Value = $75* 7.3601 + $558.40 BondValue = $1,110.40 Calculating bondprice after six years: Calculating Bond Value Using PresentValue Tabels: Bond Value = Annual Coupon Payment[PVOA(6%, 6)] + $1,000 [PVF(6%,6)] Bond Value = $75 * 4.9173 + $1,000 *0.7050 Bond Value = $368.80 +$705 Bond Value =$1,073.80

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