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# 07 bond evaluation 02

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### 07 bond evaluation 02

1. 1. Portfolio Management LECTURE SEVEN Bond Evaluation Prepared By: Noorulhadi QureshiLecturer Govt College of Management Sciences 1 Peshawar
2. 2. Bonds• A bond is a tradable instrument that represents a debt owed to the owner by the issuer. Most commonly, bonds pay interest periodically (usually semiannually) and then return the principal at maturity.• Most corporate, and some government, bonds are callable. That means that at the company’s option, it may force the bondholders to sell them back to the company. Ordinarily, there are restrictions on the timing of the call and the amount that must be paid. 2
3. 3. • Par or Face Value:The amount of money hat is paid to the bond holder at maturity. i.e. its generally represent the amount of money borrowed by the bond issuer. 3
4. 4. Bond Return• Bond Return can be calculated and expressed in different ways. It is necessary to understand the meaning of each of these expressions.• Coupon rate: It is the nominal rate of interest fixed and printed on the bond certificate. It is calculate on the face value of the bond. For example if the coupon rate on a bond of face value of Rs. 1000 is 12%, Rs. 120 would be payable by the company to the bondholder annually till maturity. And amount Rs. 120 is known coupon payment. 4
5. 5. Current yieldBond may be trader at secondary market at different price from face value. The current yield relates the annual interest receivable on a bond to its current market price. For example if a bond face value is Rs. 1000 with coupon rate of 12% and current selling for Rs. 800, the current yield would be Current yield may be In higher than coupon if CurrentYield = .100 bond trader at discount Po and may be low if In= annual interest traded at premium Po= Current market price 120 CurrentYield = x100 800 5 CurrentYield = 15%
6. 6. Spot Interest RateZero Coupon bond is special type of bond which does not pay annual interest. The return on bond is in the form of discount on issue of the bond. Or example , two year bond of face value is Rs. 1000 at discount for Rs. 797.19 with no coupon or with no annual interest. This type of bond is also called pure discount bond or deep discount bond. And it is calculated asDiscounted Price= (Face value)/(1+k)n(1+k)n =(Face value)/ Discounted Price K = n FaceValue / Di csc ount Pr ice − 1 6
7. 7. Spot Interest Rate (con’t)Consider a zero coupon bond whose face value is Rs. 1000 and maturity period is 5 year. If the issue rice of the bond is Rs. 519.37, what is spot interest rate. K = n FaceValue / Di csc ount Pr ice −1 K = 5 1000 / 519.37 −1 K = 14% 7
8. 8. Bond• Maturity date: The maturity date represent on which the bond is mature and repaid to the bond holder: 8
9. 9. Yield to Maturity• The compounded rate of return an investor expected to receive from bond purchased at the current market price and held to n maturity: Ct MP = ( ∑ TV (1 + YTM )t )+( (1 + YTM )n ) MP is the current market price of the bond Ct is the cash inflow from the bond throughout the holding period TV is the terminal cash inflow received at the end of the holding period. 9
10. 10. YTM (con’t)• A bond face value with Rs. 1000 and coupon rate is 15%, market price is Rs. 900 with five years maturity period, n ∑ MP = ( Ct (1 + YTM )t )+( TV (1 + YTM )n ) It will be on the basis on trail and error, assuming 20% YTM, the value of if calculated, is 850.49, so the value is less the market value so this rate to be reduced with another assumption i.e 18% rate is inserted in equation, it gives Rs. 906.18 Now to calculate YTM HigheCalculatedValue − MPYTM = LowerRate + ( HigherRate − LowerRate) HighCacultedValue − LowerCalculatedValue 906.18 − 900 YTM = 18 + (20 −18) 906.18 − 850.49 YTM = 18.22 10
11. 11. YTM(alternative way Approx)To avoid trail and error which tedious calculation, YTM maturity canbe calculated approximately asI is annual interest=150MV is maturity value and=1000MP is market price, and =900n is holding period to maturity= 5 I +( MV −MP) / n YTM = ( MV +MP) / 2 150 +(1000 −900) / 5 YTM = (1000 +900) / 2 150 +20 YTM = 950 YTM =0.1789or17.89% 11
12. 12. Bond Price • Bond price refers to the Present value of Bond. CFt It MV Po = ∑ Po = ∑ + (1 + k )t (1 + K )t (1 + K )tPo = Present value, It is the annual interest, MV is maturity value, n is thenumber of year to maturity and k is the appropriate discount rate.Let a bond face value is Rs. 1000 issued five years ago at coupon rate of 10%the had had a maturity period of 10 years, so five years are more left fromtoday to maturity the current market rate is 14% the present value would be 12
13. 13. Calculating the Value of a Bond• There are two types of cash flows that are provided by a bond investments: – Periodic interest payments (usually every six months, but any frequency is possible) – Repayment of the face value (also called the principal amount, which is usually \$1,000) at maturity• The following timeline illustrates a typical bond’s cash flows: 1,000 100 100 100 100 100 0 1 2 3 4 5 13
14. 14. Calculating the Value of a Bond (cont.)• We can use the principle of value additivity to find the value of this stream of cash flows• Note that the interest payments are an annuity, and that the face value is a lump sum• Therefore, the value of the bond is simply the present value of the annuity-type cash flow and the lump sum: 14
15. 15. Bond Terminology• There are several terms with which you must be familiar to solve bond valuation problems: – Coupon Rate - This is the stated rate of interest on the bond. It is fixed for the life of the bond. Also, this rate time the face value determines the annual interest payment amount. – Face Value - This is the principal amount (nominally, the amount that was borrowed). This is the amount that will be repaid at maturity – Maturity Date - This is the date after which the bond no longer exists. It is also the date on which the loan is repaid and the last interest payment is made. 15
16. 16. Bond Valuation: An Example• Assume that you are interested in purchasing a bond with 5 years to maturity and a 10% coupon rate. If your required return is 12%, what is the highest price that you would be willing to pay? 1,000 100 100 100 100 100 0 1 2 3 4 5 16
17. 17. Some Notes About Bond Valuation• The value of a bond depends on several factors such as time to maturity, coupon rate, and required return• We can note several facts about the relationship between bond prices and these variables (ceteris paribus): – Higher required returns lead to lower bond prices, and vice-versa – Higher coupon rates lead to higher bond prices, and vice versa – Longer terms to maturity lead to lower bond prices, 17 and vice-versa
18. 18. Bond Risk1. Default Risk:Default risk refers to the possibility that a company may fail to pay the interest rate or principal amount on maturity date3. Interest Rate RiskInterest rate risk refers to variation of market interest rate or discount rate compare to coupon rate. 18
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