Question

Mr. Joey bought a bond issued by City bank which has a $1,000 face value and pays semi- annual interest will mature in 9 years. The return on similar-risk investments is 12 percent and the bond pays $54 interest per year.

Calculate the current market value (price) of the bond & what will be the yield to maturity?

Answer 1

a.

Face value of bond = $1000

interest per year = $54

 

Semiannual interest = Annual interest /half yearly coupons in year

                                    = 54/2 = 27

 

Years to maturity =9

Semiannual years to maturity (n) = 9*2

                                                            = 18

 

Return on similar risky investment or required return = 12%

 

Semiannual required return (i) = 12%/2

                                                       = 6%

 

We will calculate current market price using bond price formula:

 

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

                                   = (27*(1-(1/(1+6%)^18))/6%) + (1000/(1+6%)^18)

                                   = $642.69

 

So current bond price is $642.69

 

b.

Yield to maturity is that rate at which Present value of coupons and present value of Face value is equal to current price of bond. It is also the required rate of return on this bond.

 

As required rate on this bond is 12%, Yield to maturity of this bond is 12%

So current bond price is $642.69

Yield to maturity of this bond is 12%