Finance School of management Bond prices fall as the interest Rates rise .Write the pv of the fixed-income security as the sum terms Pv pmt.* 1+i 1+/+pm2*/1)2 my*/1 +.+Dmt.,* 1+i 1+1/+Pm1*/ 1+i uesTc
6 Finance School of Management Bond Prices Fall as the Interest Rates Rise ❖ Write the PV of the fixed-income security as the sum terms n n n n n j j j i pmt i pmt i pmt i pmt i PV pmt + + + + + + + + = + = − − = 1 1 * 1 1 ... * 1 1 * 1 1 * 1 1 * 1 1 2 2 1 1 1
Finance School of management The Difficulty of Valuation of Known Cash Flows g We do not know usually which discount rate to use in the present value formula Is it correct to use the interest rate corresponding to a three-year maturity in valuing the three-year annuity in the previous example uesTc
7 Finance School of Management The Difficulty of Valuation of Known Cash Flows ❖ We do not know usually which discount rate to use in the present value formula. ❖ Is it correct to use the interest rate corresponding to a three-year maturity in valuing the three-year annuity in the previous example?
Finance School of management US Treasury yiled curve Jan 97 7.00 0>N= 6.00 Years to Maturity uesTc
8 Finance School of Management US Treasury Yiled Curve, Jan 97 4.50 5.00 5.50 6.00 6.50 7.00 7.50 0 5 10 15 20 25 30 Years to Maturity Annualized Yield (%)
Finance School of management The Basic Building Blocks: Pure Discount bonds The difficulties of finding equivalent fixed-income securities, or comparables and making adjustments for differences Any fixed-income security can be decomposed into a series of known payments at different time points in the future Pure discount bonds(zero-coupon bonds ): Promising a single payment of cash at the maturity date (in the future) uesTc
9 Finance School of Management The Basic Building Blocks: Pure Discount Bonds ❖ The difficulties of finding equivalent fixed-income securities, or comparables and making adjustments for differences. ❖ Any fixed-income security can be decomposed into a series of known payments at different time points in the future. ❖ Pure discount bonds (zero-coupon bonds): Promising a single payment of cash at the maturity date (in the future)
Finance School of management Pure Discount bonds The pure discount bond is an example of the present value of a lump sum equation we analyzed in Chapter 4 Solving this, the yield-to-maturity on a pure discount bond is given by the relationship F F=P1+ iy P uesTc 10
10 Finance School of Management Pure Discount Bonds ❖ The pure discount bond is an example of the present value of a lump sum equation we analyzed in Chapter 4. ❖ Solving this, the yield-to-maturity on a pure discount bond is given by the relationship: (1 ) 1 1 − = + = n n P F F P i i