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Kristelle Joyce A. Borres BSBA – 4 Financial Management

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Kristelle Joyce A. BorresBSBA – 4 Financial Management

THE ANALYSIS AND VALUATION OF BONDS

The fundamentals of bond valuation• Value of bonds can be described I terms of dollars value or the rates of

return they promise under some set of assumptions.

Present Value Model Formula:

Pm = the current market price of the bondn = the number of years to maturityCi = the annual coupon payment for bond i.i = the prevailing yield to maturity for this bond issue.Pp = the par value of the bond.

COMPUTATION:

Present value of interest payments \$40 x 17.1591 = \$686.36 Present value of principal payments \$1,000 x 0.1420 = 142.00 TOTAL VALUE OF THE BOND AT 10% = \$828.36

THE YIELD MODEL

THE YIELD MODEL

• Instead of determining the value of a bond in dollar term, investors often prices bonds in terms of yields.• Yields – the promise return of bonds under certain assumptions.

FORMULA:

NOMINAL YIELD

• Is the coupon rate of a particular issue.

• A bond with an 8% coupon has an 8% nominal.

CURRENT YIELD

CURRENT YIELD

• Can be computed by using the present value model with semi-annual compounding.

FORMULA:• CY = Ci/Pm

where:

CY = Current yieldCi = annual coupon payment for bondPm = current market price of the bond.

COMPUTING THE PROMISED YIELD TO MATURITY

COMPUTING THE PROMISED YIELD TO MATURITY

• can be computed by using the present value model with semi-annual compounding.

• FORMULA:

COMPUTATION:

900 =

= 40 (18.2574) + 1000 (0.1702) = 900

YTM for a ZERO COUPON BOND

YTM for a zero coupon bond

• In several instances, we have discussed the existence of zero coupon bonds that only have the one cash inflow at maturity.• It means that the calculation of the single cash flow of YTM is

substantially easier as shown by the following example.

FORMULA:\$311.80 = 20

PROMISED YIELD TO CALL

PROMISED YIELD TO CALL

• Although investors used promised YTM to value most bonds, they must the return on certain bonds with a different measure – the promised yield to call (YTC).

FORMULA:

Where:Pm = current market price of the bond Ci = annual coupon payment of bond iNc = number of years to first call date.Pc = call price of the bond.

COMPUTING PROMISED YIELD TO CALL

Computing the Promised yield to Call

• Again, the present value method assumes that you hold the bond until the first call date and that you reinvest all coupon payments at the YTC rate.• Yield to call is calculated using a variation of Equation. 18.1• To compute the YTC by the present value method, we would just add

the semiannual present value equation to give.

FORMULA:

Where:

Pm = the current market price of the bondCi = the annual coupon payment of Bond Inc = the number of years to first call datePc = the call price of the bond

REALIZED (HORIZON) YIELD

REALIZED (HORIZON) YIELD

• The final measure of bond yield, realized yield or horizon yield (i,.e the actual return over a horizon period) measures the expected rate of return of a bond that you anticipate to selling prior to its maturity.

Computing Realized (Horizon) Yield

Computing Realized (Horizon) Yield

• The realized yields over a horizon holding period are variations on the promised yield equations. • The substitutions of Pf (future selling price) and hp into the present

value model provide the following realized yield model:

• Municipal bonds, treasury issues, and many agency obligations possess one common characteristics: their interest income is partially or fully tax-exempt.

• To compute the FTEY, we determine the promised yield on a tax-exempt,bond using one of the yields formulas and then adjust the computed yield to reflect the rate of return that must be earned on a fully taxable issue.

FORMULA: FTEY =

i = the promised yield on the tax-exempt bond.T = the amount and type of tax-exemption.

WHAT DETERMINES INTEREST RATE?

WHAT DETERMINES INTEREST RATE?

• Interest rates and yields are the same.

They are different terms for the same concept.

• The inverse relationship between bond prices and interest rate is when interest rates decline, the prices of bonds increases; when interest rate arises, there is a decline in bond prices.

FORECASTING INTEREST RATES

• The ability to forecast interest rates and changes in these rates is critical to successful bond investing. • Like any price, they are determined by the supply and demand for

these funds. • On the one side, investors are willing to provide funds (the supply) at

prices based on their require rates of return on a particular borrower.• On the other side, borrowers need funds (the demand) to support

budget deficits (gov’t) to invest in capital projects (corporations) or to acquire durable goods or homes.• Although lenders and borrowers have some fundamental factors that

determine supply and demand curves, the prices for these funds also affected for short period by events that shift the curves.• Detailed forecasting of interest rates is a very complex task that is best

left to professional economists.

FUNDAMENTALS DETERMINANTS OF INTEREST RATES

• As you would expect, bond prices increased dramatically during periods when market interest rates dropped, and some bond investors experienced very attractive returns.• In contrast, some investors experienced substantial losses during

periods when interest rates increased.• Essentially, the factors causing interest rates (i ) to rise or fall are

described by following model:i = RFR + I + RP

Where:RFR = the real risk-free rate of interestI = the expected rate of inflationRP = the risk premium

EFFECT OF ECONOMIC FACTORS

• The real risk-free rate of interest (RFR) is the economic cost of money, that is, the opportunity cost necessary to compensate individuals for forgoing consumption.

• The expected rate of inflation is the other economic influence on interest rate.

• We add the expected level of inflation to the real risk-free rate to specify the nominal RFR, which is a market rate like the current rate on gov’t T-bills.

• To sum up, one way to estimate the nominal RFR is to begin with the real growth rate of the economy, adjust for short-run ease or tightness in the capital market, and then adjust this real rate of interest for the expected rate of inflation.

The Impact of Bond Characteristics

• The interest rate of a specific bond issue is influenced by factors that affect the nominal RFR but also by the unique issue characteristics of the bond that influences the bonds risk premium (RP).

Bond separate the risk premium into four components:

1. The quality of the issue as determined by its risk of default relative to other bonds.

2. The term to maturity of the issue, which can affect price volatility.3. Indenture provisions, including collateral, call features, and sinking-fund

provisions.4. Foreign bond risk, including exchange rate risk and country risk.

• Of the four factors, quality and maturity have the greatest impact on the risk premium for domestic bonds, while exchange rate risk are important components of risk for non-US bonds.