1. Capital Market Course 8

2. VIII. Bonds Valuation Bonds generate future cash flows  we must compare between the future flows and actual cash in hand Nominal risk free interest rate: - real risk free interest rate - inflation rate Corporate bonds have risk Interest rate is not the best approximation but 

3. VIII. Bonds Valuation For a bond having 30 years maturity, with reimbursement at the maturity, with PV = 1000 m.u. and coupon of de 80 m.u./year, paid biannual (  40 u.m/semester), if the interest rate on the market is 4%/semester (8%/year), then: In reality, the interest rate is not equal with the coupon; if the interest rate on the market is 10%/year (  5%/semester):

4. VIII. Bonds Valuation Source: Bodie, Z., A. Kane, and A. J. Marcus (2007), Essentials of Investments, 6th edition, McGraw Hill International Edition If the interest rate on the market increase, then the actual value of the future cash flows decrease,  AV decrease If the interest rate on the market change, AV changes will be lower if the time until maturity is lower

5. VIII. Bonds Valuation The AV depends also on the reimbursement method:

6. VIII. Bonds Valuation Duration (Macaulay Duration): the weighted average of the times to each coupon or principal payment made by the bond The weight for each payment time is the proportion of the total value of the bond accounted for by that payment If the valuation is made on a different date than the payment:

7. VIII. Bonds Valuation Conclusions: - Duration is only an average of the times when bond generates cash flows - Duration changes as the bond’s maturity is closer - If the coupon rate increase, the duration decrease - If the coupon rate is constant, the duration increase as the maturity increase For zero coupon bonds, the duration is the same as the maturity Source: Bodie, Z., A. Kane, and A. J. Marcus (2007), Essentials of Investments, 6th edition, McGraw Hill International Edition

8. VIII. Bonds Valuation The percentage change in a bond’s price is proportional to its duration Modified duration (Sensitivity): percentage change in the bond price due to the a 1% change in interest - Reflects the inverse correlation between the interest rate and the bond price - Increase if the duration increase - Is a measure of the bond’s exposure to interest rate volatility

9. VIII. Bonds Valuation Coupon return: Current yield: Yield to maturity: Achieved return: Holding period return: Weekend return

10. VIII. Bonds Valuation Bond’s rating: evaluation process in order to identify the risks; a classification is obtained Based on: - Coverage ratios - Leverage ratio - Liquidity ratios - Profitability ratios - Cash flow-to-debt ratio - Issuer management

11. VIII. Bonds Valuation Risk premium Term structure of interest rates The Expectation Theory The Liquidity Preference Theory The Market Segmentation Theory

12. Bibliography Anghelache G. (2004), Piaţa de capital. Caracteristici. Evoluţii. Tranzacţii, Editura Economică, Bucureşti Bodie, Z., A. Kane, and A. J. Marcus (2007), Essentials of Investments, 6th edition, McGraw Hill International Edition