Question

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 has a bond outstanding with a par value of €1,000, 10 years to maturity, and a coupon rate of 7.6 percent paid annually. If the yield to maturity is 8.7 percent, what is the current price of the bond? g

Answer 1

€928.46

Step-by-step explanation:

Since it was hinted that bonds issued outside of the United States pay coupons annually, it is expected that the bonds issued in Germany pay annual coupons, and its price is computed below using the bond price formula, excel PV function, and financial calculator:

Bond price=face value/(1+r)^n+annual coupon*(1-(1+r)^-n/r

face value=€1,000

r=yield to maturity=8.7%

n=number of annual coupons in 10 years=10

annual coupon=face value*coupon rate=€1,000*7.6%=€76

bond price=1000/(1+8.7%)^10+76*(1-(1+8.7%)^-10/8.7%

bond price=1000/(1.087)^10+76*(1-(1.087)^-10/0.087

bond price=1000/2.30300797+76*(1-0.43421474)/0.087

bond price=1000/2.30300797+76*0.56578526/0.087

bond price= 434.21+494.25= €928.46

Excel PV function:

=-pv(rate,nper,pmt,fv)

=-pv(8.7%,10,76,1000)

pv=€928.46

Financial calculator:

N=10

PMT=76

I/Y=8.7

FV=1000

CPT PV=€928.46