Question

One year ago Lerner and Luckmann Co. issued 15-year, noncallable, 5% annual coupon bonds at their par value of $1,000. Today, the market interest rate on these bonds is 5.5%. What is the current price of the bonds, given that they now have 14 years to maturity?

Select the correct answer.

a. $947.41

b. $952.05

c. $945.09

d. $954.37

e. $949.73

Answer 1

Current Price is the sum of the Present Values of

1. all future coupons on the bond ,till maturity

2. Face value to be received at maturity

both discounted at the market interest rate which is the yield on the bond

based on which the investor will fix the price(as above)

So,

Current price/PV=(Pmt.*(1-(1+r)^-n)/r)+(FV/(1+r)^n)

where ,

Pmt.=Annual coupon payment,ie. 1000*5%=50 ;

r=Market interest rate or Yield or Yield to maturity, ie. 5.5% or 0.055

n= No.of coupon -periods still pending to maturity, ie. 14

FV= Face Value,ie. 1000

Substituting the numerical values in the above formula,

Current price/PV=(50*(1-(1+0.055)^-14)/0.055)+(1000/(1+0.055)^14)=

952.05

So,

ANSWER: b. $ 952.05