Question

In: Finance

A 6% coupon, 24-year annual bond has a yield to maturity of 4.4%. Assuming the par...

A 6% coupon, 24-year annual bond has a yield to maturity of 4.4%. Assuming the par value is $1,000 and the YTM does not change over the next year, what will the price of the bond be today? What will the bond price be in one year? What is the capital gains yield for this bond?

Solutions

Expert Solution

what will the price of the bond be today?

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 Premium as YTM<coupon rate

Year Cash flow PVAF/[email protected]% Present Value (Cashflow*PVAF/PVF)
1-24 60 14.6412* 878.47
24 1000 0.3558** 355.79

Current Market Price of Bonds P0 = Cashflow*PVAF/PVF

= 878.47+355.79

= $1234.26

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

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

What will the bond price be in one year?

Year Cash flow PVAF/[email protected]% Present Value (Cashflow*PVAF/PVF)
1-23 60 14.2855 857.13
23 1000 0.3714 371.44

Current Market Price of Bonds P1 = Cashflow*PVAF/PVF

= 857.13+371.44

= $1228.57

What is the capital gains yield for this bond?

Capital Gain / -loss Yield = (P1-P0)/P0

= (1228.57-1234.26)/1234.26

= -5.69/1234.26

= -0.46%


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