Question

Union local school district has a bond outstanding with a coupon rate of 3.7% paid semiannually and 16 years to maturity. The yield to the maturity on this bond is 3.9%, and the bond has a par value of $5000. What is the price of the bond?

Answer 1

Par value of bond = $5000

Semiannual interest = (($5000*3.7%)* 6 )/ 12

= $92.5

Yield to maturity is 3.9% per year and the same semiannually would be (3.9 * 6 )/ 12 that is 1.95%

Now the price of the bond would be present value of its future cashflows for 16 years

Price = Present Value (PV) of interest + PV of par value received on maturity

= (interest received semiannually * PVIFA @ 1.95% for 32 installments) + (Redemption amount * Present value interest factor @1.95% for the 32nd installment)

= ( $92.5 * 23.6398) + ( $ 5000 * 0.5390)

= $2186.6815 + $ 2695

= $4881.68

Therefore the price of the bond is $4881.68

Note:

1. PVIFA is the total that is cummulation of all the present value factors @1.95% for 32 installments.

2. Yield to maturity has also been taken semiannually because the interest on bond is received semiannually