Finance School of management Chapter 8. Valuation of Known Cash flows. Bonds Objective Explain the principles of bond pricing Understand the features that affect bond prices uesTc
1 Finance School of Management Objective Explain the principles of bond pricing Understand the features that affect bond prices Chapter 8. Valuation of Known Cash Flows: Bonds
Finance School of management Chapter 8 Contents Using Present Value Formulas to Value Known Flows The Basic building blocks: Pure Discount bonds Coupon Bonds, Current Yield, and Yield-To-Maturity Reading bond listings Why Yields for the Same Maturity Differ The behavior of bond prices over time uesTc
2 Finance School of Management Chapter 8 Contents ❖ Using Present Value Formulas to Value Known Flows ❖ The Basic Building Blocks: Pure Discount Bonds ❖ Coupon Bonds, Current Yield, and Yield-To-Maturity ❖ Reading Bond Listings ❖ Why Yields for the Same Maturity Differ ❖ The Behavior of Bond Prices over Time
Finance School of management Valuation and fixed-Income securities Essence of valuation process Valuation models Fixed-income securities and other contracts promising a stream of known future cash payments Bond Mortgages Pension annuities uesTc
3 Finance School of Management Valuation and Fixed-Income Securities ❖ Essence of valuation process ❖ Valuation models ❖ Fixed-income securities and other contracts promising a stream of known future cash payments – Bonds – Mortgages – Pension annuities
Finance School of management Reasons for Valuing Fixed-Income Securities To have an agreed-upon valuation procedure in setting the terms of the contracts at the outset To revaluate the securities when they are sold before maturity uesTc
4 Finance School of Management Reasons for Valuing Fixed-Income Securities ❖ To have an agreed-upon valuation procedure in setting the terms of the contracts at the outset. ❖ To revaluate the securities when they are sold before maturity
Finance School of management Using Present Value Formulas to value Known Cash flows a fixed-income security that PV= PM1-(1+i) promises to pay $100 each year for the next three years The appropriate n PV FV PMT Result discount rate is 6% 36%?0100PV=267.30 per year An hour after you PV FV PMT Result buy the security the 37%?0100PV=262.43 risk-free interest rate rises from 6% to 7%o ber year uesTc
5 Finance School of Management Using Present Value Formulas to Value Known Cash Flows ❖ A fixed-income security that promises to pay $100 each year for the next three years. ❖ The appropriate discount rate is 6% per year. ❖ An hour after you buy the security, the risk-free interest rate rises from 6% to 7% per year. i PMT i PV −n − + = 1 (1 ) n i PV FV PMT Result 3 6% ? 0 100 PV=267.30 n i PV FV PMT Result 3 7% ? 0 100 PV=262.43
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
