Question

mike wants to buy a U.S. government Treasury bond that has 12 years remaining until maturity. The coupon rate is 6% per year and is paid out semiannually. The face or par value of the bond is $100,000. The current yield-to-maturity (YTM) of this bond is 5%. Calculate (1) the current market price of this bond, and (2) the new price if the required YTM rises from 5% to 6% due to a market change in bond interest rates.

Answer 1

Par value of the bond (FV) = 100,000

Annual coupon = 6% * 100,000 = 6000

Semi- annual coupon (PMT) = 3000

YTM of the bond (rate) = 5% pa = 2.5% per half year

Years to maturity = 12

Periods to maturity (nper) = 12*2 = 24 periods

1)

Market Price of the bond (PV) =
=pv(2.5%,24,3000,100000 PV(rate, nper, pmt, [fv], [type])
= $ 108,942.29

2)

New YTM (rate) = 6% = 3% semi annual (ie YTM = coupon rate)

Market Price of the bond = $ 100,000 (as the bond is now trading at par)