bonds valuation and ytm


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Yield to maturity and yield to call.


Page 1: Bonds Valuation and Ytm
Page 2: Bonds Valuation and Ytm

What is bond and bond valuation?

• Bond valuation is the process of determining the fair price/theoretical price/intrinsic value of a bond.

• Bond (also term as debenture) is long term loan (Instrument of debt) which pay periodical interest and also principal amount upon maturity

Page 3: Bonds Valuation and Ytm

Basic bond related term • a. Face Value/Par Value: It is the value stated on the face of the bond. Unless otherwise stated, bond is

assumed to be issued at face value/par value. The face value/par value may be Rs.100 or Rs.1,000 depending upon the question.

• b. Redemption value: • The value which the bond holder will get on maturity is called redemption

value. If no information about redeemable value is given, the bond is always assumed to be redeemed at par value. Otherwise it is redeemed at redeemable value.

• c. Coupon Rate: • A bond carries a specific interest rate known as the coupon rate. The

interest may be paid annually, semi-annually or even monthly. • Interest payable to bond holder = Par value of bond Coupon rate

Page 4: Bonds Valuation and Ytm

Value of bond • Concept for valuation: • Suppose Mr. X want to invest in any of the following companies.

All these companies pay back the same amount (Say 110) at end of the year 1. How much will Mr. X invest now in these companies so that he will get exact as he want?

Page 5: Bonds Valuation and Ytm

• For example suppose you have 1,00,000 surplus today and you want to lend it. Two persons, one is student and another is CA, are approached for it @10% interest rate. What will you do?

• Obviously you will provide loan to CA @ 10% because you fill low risk. But if you provide loan to “UNKNOWN” you will probably charge high interest rate because you fill high risk.

• - It means Low risk low return and high risk high return

Page 6: Bonds Valuation and Ytm

Calculation of Value of investment: 1. Government company:

• It means, if Mr. X invest 100 today in Government Company then he will get 10% return from this investment.

• Verification: interest = 110-100 = 10

Page 7: Bonds Valuation and Ytm

Company X:

It means, if Mr. X invest 98.22 today in Company X then he will get 12% return from this investment. Verification: interest = 110-98.22 = 11.78

Page 8: Bonds Valuation and Ytm

Company Y:

It means, if Mr. X invest 95.65 today in Company Y then he will get 15% return from this investment. Verification: interest = 110 - 95.65 = 14.35

Page 9: Bonds Valuation and Ytm

• The value of investment will depend upon the “required return” and “cash inflow”. If you want more return then you will invest lesser amounts today and if you want lesser return then you will invest more amounts today for the same future inflow.

• -Investment value today = PV of future inflow

Page 10: Bonds Valuation and Ytm

Value of bond • It is the amount which the investor is willing to pay today to

purchase the bond. It is also known as current value of bond/present value of bond/intrinsic value of bond/theoretical value of bond/equilibrium value of bond.

• Value of bond (B0) = PV of future inflow • [Where inflow will be the future interest and maturity value]

Page 11: Bonds Valuation and Ytm

The value of the bond is depends upon the investor- that how much the Investor want to invest in that bond.

”10% bond” means company provides interest year by year @ 10% on face value of bond for life of the bond. (i.e. coupon rate is 10%). which is cash inflow for Mr. X.

Required return 12% means Mr. X discount above cash inflow @ 12%. If question does not specify the Required return the coupon rate is assumed to be discount rate.

Page 12: Bonds Valuation and Ytm

Value of bond: a. Annual equal interest bond:

• It is the bond on which investors are entitled to get annual interest at fixed rate and also get maturity value at end of the bond life (i.e. on maturity date)

• Value of annual interest bond (B0)

• Where: PVIFA (YTM, Life) = Sum of PV factor at YTM rate for specific period (i.e. life)

• PVIF (YTM, Life) = PV factor at YTM rate for specific period (i.e. life)

Page 13: Bonds Valuation and Ytm

b. Value of Zero coupon bond:

• Zero coupon bonds are those bonds on which investors are not allowed to any interest but are entitled only to repayment of principal amount on the maturity period.

• Value of Zero coupon bond (B0) =

Page 14: Bonds Valuation and Ytm

c. Value of Perpetual bond:

• Perpetual bond are those bonds on which interest is paid forever i.e. up to infinity period. In other word we can say that the perpetual bonds are irredeemable bond.

• Value of perpetual bond (B0)

Page 15: Bonds Valuation and Ytm

d. Value of Semi-annual interest bond

• Semi-annual interest bond are those bond which pay interest semi-annually (i.e. on every 6 month)

• Value of Semi-annual interest bond (B0)

Page 16: Bonds Valuation and Ytm

Return or yield • (a) Current yield: • The rate of return over next one year on the

amount invested is called current yield.

(b) Holding period return: - The holding period is the investment period and return over this period is known as holding period return. - It is the % return of total holding period and not for one year period.

Page 17: Bonds Valuation and Ytm

c) Yield to maturity(YTM)/Annual Redemption Yield:

• - It is the available rate of return from bond if it is purchased and hold till maturity period.

• - It is similar to IRR. Also known as available rate of return from bond

• - Yield to maturity would be calculated by using linear interpolation between two different rates. However, before interpolation we calculate approximate rate to find the range of two different rates, so that we can save our time which we will waste in trial and error method to find one higher rate & another lower rate.

Page 18: Bonds Valuation and Ytm

• Suppose, a bond pays 80 per year as interest and 1000 at maturity. A person invested 930 in such a bond. What is YTM and what does it mean?

YTM is such discount rate at which PV of future inflow of bond will equal to the amount invested in such bond (i.e. PV of outflow)

In other word, we can say at this discount rate (YTM) PV of future inflow is equal to PV of outflow (i.e. NPV = 0) -

Page 19: Bonds Valuation and Ytm

• If we can solve the equation written below, then we will get YTM directly,

• 930 =• - But we cannot solve above equation easily.

Hence, to calculate YTM, we have to assume any rate in place of YTM on TRIAL AND ERROR method. But it is not necessary that the calculated value will arrive to 930 at the rate assumed.

• - Hence we have to make interpolation of two different rates to reach at 930 values.

Page 20: Bonds Valuation and Ytm

• Concept of interpolation: • Assume rate of YTM as 7%, then PV of inflows = 1041 (from above expression) • Assume rate of YTM as 8%, then PV of inflows = 1000 (from above expression) • Assume rate of YTM as 9%, then PV of inflows = 961 (from above expression)

• Assume rate of YTM as 10%, then PV of inflows = 924 (from above expression) • But we need such YTM rate at which PV of inflows = 930. We know that the

required rate is between 9% and 10%. • How it will be calculated? • - It will be calculated by interpolating 9% and 10%

Page 21: Bonds Valuation and Ytm

PV of cash inflow has inverse relationship with discount rate.

If discount rate increases PV of inflow will be decreases If discount rate decreases PV of inflow will be

increases It can be understand by following relationship

PV of inflow = If we divide anything by higher figure, the resultant

figure will be lower and If we divide anything by lower figure the resultant figure

will be higher.

Page 22: Bonds Valuation and Ytm

d) Yield to call (YTC) • It is available rate of return from bond if it purchased and hold till call period. • It is also similar to IRR or YTM • Call feature allow the bond issuer to call in the bond and repay them at a pre-

determined price before maturity. • Bond issuers use this features to protect themselves from paying more interest. • Example: • - Suppose IDBI had issued 16 Years 1000 bonds 10 year ago @14% p.a. But now

interest rate in market is around 9% to 10%. • - If the issuer wants to take the benefit of the call features, it will call back the

earlier issued bonds and re-issue it @9% p.a. • - The new proceeds from new bonds may be used to re-pay the existing bonds.

In this way IDBI now enjoy lower cost for its borrowed money. • - Some bonds offer “call protection” i.e. it would guarantied not to be called

before maturity period and it will affect the “bond price”