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Valuing Bonds

Chapter 4The Valuation of Long-Term SecuritiesPresented By:Syed Ahsan Aman

The Valuation of Long-Term SecuritiesDistinctions Among Valuation ConceptsTime Value of Money [Revision]Bond ValuationPreferred Stock ValuationCommon Stock ValuationRates of Return (or Yields)What is Value?Going-concern value represents the amount a firm could be sold for as a continuing operating business.Liquidation value represents the amount of money that could be realized if an asset or group of assets is sold separately from its operating organization.What is Value?(2) a firm: total assets minus liabilities and preferred stock as listed on the balance sheet.Book value represents either (1) an asset: the accounting value of an asset -- the assets cost minus its accumulated depreciation; What is Value?Intrinsic value represents the price a security ought to have based on all factors bearing on valuation.Market value represents the market price at which an asset trades.What is Time Value?We say that money has a time value because that money can be invested with the expectation of earning a positive rate of returnIn other words, a dollar received today is worth more than a dollar to be received tomorrowThat is because todays dollar can be invested so that we have more than one dollar tomorrow

6Interest Rates & Required Returns7The interest rate or required return represents the price of money.Interest rates represent the compensation that a demander of funds must pay a supplier.When funds are lent, the cost of borrowing is the interest rate.When funds are raised by issuing stocks or bonds, the cost the company must pay is called the required return, which reflects the suppliers expected level of return.The Terminology of Time ValuePresent Value - An amount of money today, or the current value of a future cash flowFuture Value - An amount of money at some future time periodPeriod - A length of time (often a year, but can be a month, week, day, hour, etc.)Interest Rate - The compensation paid to a lender (or saver) for the use of funds expressed as a percentage for a period (normally expressed as an annual rate)8AbbreviationsPV - Present valueFV - Future valuePmt - Per period payment amountN - Either the total number of cash flows or the number of a specific periodi - The interest rate per period910Introduction to the TimelineTime Value of Money (TVM) problems involve identifying the payment or receipt of cash over time.A useful tool in the analysis of these problems is the timeline illustrated below.Years or PeriodsCashflows01234CF0CF1CF2CF3CF45CF5Calculating the Future ValueSuppose that you have an extra $100 today that you wish to invest for one year. If you can earn 10% per year on your investment, how much will you have in one year?012345-100?

1112Present Value01234PresentValue5FutureValueYearsSince receiving money in the future is less valuable than having cash today, we say the the present value of a future cashflow is at a discount.Calculating the Present Value involves quantifying this discount.

Discount Factor13Testing Our IntuitionFuture ValueIncrease (Decrease) in Interest RateIncrease (Decrease) in Investment Horizon

Present ValueIncrease (Decrease) in Interest RateIncrease (Decrease) in Investment Horizon13AnnuitiesAn annuity is a series of nominally equal payments equally spaced in timeAnnuities are very common:RentMortgage paymentsCar paymentThe timeline shows an example of a 5-year, $100 annuity012345100100100100100

14THE FUNDAMENTALS & VALUATIONS OF BONDA Deeper Understanding of a Major Economic Market

16OutlineBond DefinitionsValuation of BondsYield to Maturity (YTM) Rate of ReturnInterest Rate RiskDefault Risk17What is a BOND?

A Bond is an agreement ( or financial asset ) in which an issuer is required to repay to the investor the amount borrowed plus interest over a specified period of time.

Principal borrowed by government(corporation) from investor Principal returned to investorPrincipal

Regular interest payments

17Bond Vs StockCorporate bonds differ from common stock in three fundamental ways.

Corporate BondsCommon StockRepresent a creditors claim on the corporationRepresents an ownership claim on the corporationPromised cash flows (coupons and principal) are stated in advanceAmount and timing ofdividends may changeat any timeMostly callableAlmost never callable19Example In the beginning of 1994 U.S. government borrowed $100 million at 9% yearly rate by issuing 100,000 bonds for $1,000 each. Each bond promised to pay its holder $90 (9% of $1,000) at the end of year for 10 years and repay $1,000 at the end of 2003.

$90 $90 $90 Years 1994 1995 2002 2003

You pay price of the bondcouponsprincipal+last coupon$1,000+$90=$1,09020FOUR COMPONENTS OF A BONDIssuer The organization responsible for ensuring that interest and principal payments are made to bondholder.

Principal The amount of money denominated in a specific currency that the issuer wishes to borrow and agrees to repay the investor. (Face Value, Par value, Maturity value)

Coupon (rate) The rate of interest the issuer agrees to pay the investor. Usually stated as a percentage of the Face V.

Maturity date The date on which the issuer of a bond must repay the principal due and the final interest rate payment.21Bond Valuation ???Pricing a bond is a simple two step process: 1. Define the cash flows.2. Calculate the aggregate present value of the cash flows using appropriate discount rate (r).Note: Generally discount rate IS NOT EQUAL to coupon rate!!!

c c c Years 1 2 t-1 t

You pay price of the bondcouponsprincipal+last couponFaceValue+c2122What is appropriate discount rate (r)?It is an interest rate on similar bonds on financial markets.

What does similar mean?Similar features!!! (ALL)Similar risk!!!

23Yield to Maturity (YTM)Yield to Maturity (YTM) - The single discount rate (internal rate of return) used to calculate the market price of the bond.

Reflects the required market interest rate for the bond.Assumes the bond is held to maturity.Different than the coupon rate.24Yield to Maturity (YTM)In other words:If you plan to hold the bond until maturity n years from today:The yield to maturity is the discount rate at which the bonds price is the present value of the bonds payments (coupons and face value).

YTM is the required return on the bond assuming it will be held until maturity.

25Bond Valuation (using YTM)

c c c Years 1 2 t-1 t

You pay price of the bondcouponsprincipal+last couponFaceValue+ c

26Example Five year 9% coupon bond offers these cashflows. Discount rate (YTM) is 9% . What is the present value of this bond?

$90 $90 $90 Years 1999 2000 2002 2003


28Bond ValuationUsing the Annuity Formula

Value a Bond with a combination of the Annuity and the Present Value formulas.

29ExampleSuppose investors demand an interest rate of 5 percent on a 10-year 6 percent bond. How much should investors pay to acquire the bond? (Alternatively, whats the price of the bond?)Solution: coupon rate is 6%, this means we are going to receive $60 each year for 10 years and another $1,000 in the end of year 10. The discount rate is 5%.

30Semiannual Coupon BondIn the Bond Market, most bonds make coupon payments semiannually.A bond has a coupon rate of 6 percent, with coupon payment made semiannually. This means the bond makes payment of $1,000*(6%/2)=$30 every 6 months.Accordingly, the quoted interest rate is APR and has to be compounded semiannually.31Semiannual Coupon Bond What is the value of a bond with a face value of $1000, coupon rate of 10% and maturity of 10 years? Assume semiannual coupon payments and an annual interest rate of 8% compounded semiannually.

01234520$1000$50$50$50$50$50$50Semiannual Coupon payments=(1000*0.10)/232Semiannual Coupon Bond

Semiannual payment :Present Value of Semiannual Coupon Bond:Where: r is annual discount rate (YTM)33Using Financial Functions FV=Par Yearly discount Rate = I/YR PMT PMT PMT Years 0 1 2 N PV = Price Given any four of the variables (N, I, PV, PMT,FV) your financial calculator can solve for the fifth.

34Examples$1,000 bond for 10 years with 9% interest and 9% yearly couponsPMT=90 FV=1000 N=10 I/Y=9% PV=?$1,000 bond for 5 years with 5% interest and 9% semiannual couponsPMT=45 FV=1000 N=5*2 I/Y=5/2 PV=?$1,000 bond for 10 years with 9% interest and 9% yearly coupons .What happens after five years if the interest rate changes to 5% then? 11%?

35How can we calculate YTM?Find r so present value of payments is equal to price.Use financial calculator.Example: $1,000 face value, $90 annual coupons