Question

A bond has a face value of $1000 and the coupon rate is 6%. Coupons are paid semiannually. The bond matures in six years. The market interest rate is 7%. What is the present value of this bond? And Suppose the price of the bond equals to the present value of the bond. What is the current yield of this bond?

Answer 1

Answer : Calculation of Present Value of Bond

Present Value of Bond = (Coupon * PVAF @r% for n years) + (Face value * PVF @ r% for nth year)

Coupon (Semi - Annual) = Face Value * Coupon rate

= 1000 * (6%/2)

= 30

r = 7% / 2 = 3.5% (as coupons paid semiannually )

Note Market Interest rate is used as discounting rate for the purpose of calculation of Present value of Bond

n = 6 * 2 = 12

Present Value of Bond = (30 * PVAF @3.5% for 12 years ) + (1000 * PVF @ 3.5% for 12th year)

= (30 * 9.66333433426 ) + (1000 * 0.66178329825)

= 289.90 + 661.78

= $951.68

If the price of the bond equals to the present value of the bond then current yield is also equal to 7%

Verification:

Using Financial Calculator

=RATE(nper,pmt,pv,fv)

where nper is Number of years i.e 6*2=12

pmt is Interest payment i.e 1000 * 6% =60/2 = 30 (As semiannual coupon payment )

pv is Current Market Price

= - 951.68

Note : pv should be taken as negative.

fv is face value i.e 1000

=RATE(12,30,-951.68,1000)

therefore,Current Yield is 3.50% (Semiannual)

Current Yield of Debt is 7% (Annual)