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A government bond with a face value of $1,000 was issued eight years ago there are...

A government bond with a face value of $1,000 was issued eight years ago there are seven years remaining unit maturity. The bond pays semi-annual coupon payments of $45, the coupon rate is 9% p.a. paid twice yearly and rate in the marketplace are 9.6% p.a. compounded semi annually. What is the value of the bond today?

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Answer #1

Bond Valuation: The value of bond is the present value of the expected cashflows from the bond,discounted at Yield to Maturity(YTM).

Prima facie, the bond will trade at Discount as YTM>coupon rate

Year Cash flow PVAF/PVF@4.8% Present Value (Cashflow*PVAF/PVF)
1-14                  45 10.0264                                 451.19
14            1,000 0.5187                                 518.73

Current Market Price of Bonds = \sumCashflow*PVAF/PVF

= 451.19+518.73

= $969.92

Note : Since the bond makes semiannual interest payments, total no. of period is 14 (7*2), and cashflows are discounted at 4.8% (9.6/2)

*PVAF = (1-(1+r)^-n)/r

**PVF = 1 / (1+r)^n

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