Question 25 2 points Ten years ago Salmon Acqua Farming Inc

Question 25 (2 points) Ten years ago Salmon Acqua Farming Inc. issued twenty-five-year 8% annual coupon bonds with a $1,000 face value each. Since then, interest rates in general have fallen and the yield to maturity on the Bacon bonds is now 7%. Given this information, what is the price today for such a bond? $1,000 $1,116.54 $1,091.08 $914.41

Solution

C.$1,091.08.

the following is the calculation of price of bond:

[coupon payments] *[present value of annuity factor] + [present value factor ]* [face value]

here,

coupon payments = $1000*8%.=>$80.

present value of annuity factor = [1 - (1+r)^(-n) / r]

here,

r = 7% =>0.07.

n = 15 years remaining

=> present valur of annuity factor = [1-(1.07)^(-15)]/0.07

=>9.1079143.

facevalue = $1000

present value factor = 1 /(1+r)^n

=>1 /(1.07)^15

=>0.36244602.

price of bond = 9.1079143 * [$80] + 0.36244602*[$1,000]

=>728.633144+362.44602

=>$1,091.08.