Question

A 6% semiannual coupon bond has 8 years until maturity. Its quoted price is 107.50. if its YTM stays constant, what should be its quoted price 1 year from now?

Answer 1

YTM = [ Coupen Amount + { ( Face value - Market price ) / Number of years } ] / [ ( Face value + Market price ) / 2 ]

       = [ ( 6 % * 100 ) + { ( 100 - 107.50 ) / 8 } ] / [ ( 100 + 107.50 ) / 2 ]
       = [ 6 - 0.9375 ] / 103.75

       = 5.0625 / 103.75

       = 0.0488 or 4.88%

Price after one year = Coupen rate * PVAF(r, n) + Face value * PVIF(r, n)

                           = ( 100 * 6% * 6/12 ) * PVAF( 4.88%/2, 7 * 2 ) + 100* PVIF( 4.88%/2, 7 * 2 )

                           = 3 * PVAF( 2.44%, 14 ) + 100 * PVIF( 2.44%, 14 )

                           = 3 * [ 1/1.0244 + 1/1.0244² + ...... + 1/1.0244¹⁴ ] + 100000 * 1/1.0244¹⁴

                           = 3 * 11.7397 + 100 * 0.7136

                           = 35.22 + 71.36

                           = $ 106.58

Price after one year shall be $ 106.58 Answer