Question

1.

Kiss the Sky Enterprises has bonds on the market making annual payments, with 20 years to maturity, and selling for $880. At this price, the bonds yield 7.1 percent. What must the coupon rate be on the bonds?

2.

Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 15 years to maturity, and a coupon rate of 6.5 percent paid annually.

If the yield to maturity is 7.6 percent, what is the current price of the bond?

Answer 1

1. Coupon rate on the bond:

Maturity = 20 years

Price now = $880

Yield = 7.1%

Price of the bond = Present value of monthly coupon payments at yield % for 20 years+ present value of par value on 20th year

Let monthly coupon payment be X

$880 = (X * ((1-(1+7.1%)^-20))/7.1%)+($1,000*(1/(1+7.1%)^20) =

$880 = 10.51217X+253.64

10.51217X = $880-$253.64 = $626.36

X = 626.36/10.51217 = $59.58

Thus, monthly coupon payment = $59.58

Coupon rate = Monthly coupon payment / Par value = $59.58/$1,000 = 5.96%

This can also be found using excel PMT function as follows:

monthly payment =PMT(rate,nper,pv,fv) where rate = 7.1%; nper = 20; pv = -$880, fv=$1,000

=PMT(7.1%,20,-880,1000) = $59.58

2.

Par Value = 1,000

Maturity = 15 years

Coupon rate = 6.5% or 65 (1,000*6.5%)

Yield = 7.6%

Price of the bond = Present value of monthly coupon payments at yield % for 15 years+ present value of par value on 15th year

= (65 * ((1-(1+7.6%)^-15))/7.6%)+($1,000*(1/(1+7.6%)^15) = 570.22+333.29 = €903.50

Price of the bond = €903.50

This can also be found with the excel function PV as follows:

=PV(rate,nper,pmt,fv) where rate = 7.6%, nper = 15 years, pmt = 65, fv = 1,000

=PV(7.6%,15,-65,-1000) = €903.50