determinant of bond

8/13/2019 determinant of bond

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What is Bond ?

A long-term debt instrument in which a borroweragrees to make payments of principal and interest,

on specific dates, to the bond holders.

Bonds are issued when companies want to borrow

smaller amounts of money from numerous lenders.

Buying a bond means you are lending out your

money


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Sample of Bond


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Bondholders

bond

Capital

(RM)

Coupon interest

(periodically)

(RM)

Par Value

(at maturity date)

Firm A

Receive interest

payments until the

term ends


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Bond Characteristics


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Present Value of Bond = Present value annuity of interest payments

+ Present value of principal repayment

or

Present Value of Bond = I (PVA) + P (PV)k%n k%n

Formula


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I and k should be devided by 2 or 4 n should times 2 or 4

I

K

N

P

= Interest payment / coupon payment

= Market interest rate / required rate of return

on the bond

= No. of years to maturity

= Principal Payment / Par or maturity value

Usually RM 1000

KEY FEATURES OF BONDS


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Assume that you purchased a bond with 15 years remainingto maturity with 15% coupon rate. The interest payment ispaid annually and also assume that par value is RM 1000. Ifthe required rate of return on bonds of this risk andmaturity is 15%, what will the bond sell for?

Value of Bond = I (PVA) + P (PV)k%n k%n

= 15% (1000) (PVA) + 1000 (PV)

15%, 15 15%, 15= 150 (5.847) + 1000 (0.123)

= 877.05 + 123

= RM 1000.05 ~ RM 1000

EXAMPLE


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INPUTS

OUTPUT

N I/Y PMTPV FV

15 15 150 1000

-1000

CPT PV=

METHOD 2 CALCULATOR


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Assume that you purchased a bond with 15years remaining to maturity with 15% coupon

rate. The interest payment is paid annually and

also assume that par value is RM 1000. If the

required rate of return on bonds of this risk andmaturity is 15%, what will the bond sell for?

What would be the bondsvalue after one year

if the required rate of return were down to 10%or up to 20% respectively?

CONT.


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Value of Bond = 150 (PVA) + 1000 (PV)10%, 14 10%, 14

= 150 (7.367) + 1000 (0.263)

= 1150.05 + 263= RM 1413.05 (at premium)

Value of Bond = 150 (PVA) + 1000 (PV)20%, 14 10%, 14= 150 (4.611) + 1000 (0.078)= 691.65 + 78

= RM 769.65 (at discount)

EQUATION 1

EQUATION 2


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INPUTS

OUTPUT

N I/Y PMTPV FV

14 20 150 1000

-769.47

CPT PV=


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Mr. Azmin purchased a bond with 10 years remaining tomaturity with 10% coupon rate. The interest payment is

paid annually and also assume that par value is RM 1000.

If the required rate of return on bonds of this risk and

maturity is 10%, what will the bond sell for?

I

K

N

P

= 10% (1000)

= 10%

= 10

= RM 1000

EXERCISE 1


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Value of Bond = I (PVA) + P (PV)k%n k%n

= 10% (1000) (PVA) + 1000 (PV)10%, 10 10%10

= 100 (6.1446) + 1000 (0.3855)

= 614.46 + 385.50

= RM 999.96

METHOD 1 : FORMULA


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INPUTS

OUTPUT

N I/Y PMTPV FV

10 10 100 1000

-1000

CPT PV=


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Mr. Azmi purchased a bond with 10 years remaining to

maturity with 10% coupon rate. The interest payment is

paid annually and also assume that par value is RM 1000. If

the required rate of return on bonds of this risk and

maturity is 10%, what will the bond sell for?

What would be the bonds value after two years if the

required rate of return were down to 5% or up to 15%

respectively?


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Value of Bond = 10% (1000) (PVA) + 1000 (PV)5%, 8 5%, 8= 100 (6.4632) + 1000 (0.6768)

= 646.32 + 676.80

= RM 1323.12 (at premium)

I

K

N

P

= 10% (1000)

= 5%

= 8

= RM 1000

EQUATION 1 METHOD 1 FORMULA


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I

K

N

P

= 10% (1000)

= 5%

= 8

= RM 1000

INPUTS

OUTPUT

N I/Y PMTPV FV

8 5 100 1000

-1323.16

EQUATION 1 METHOD 2 CALCULATOR


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Value of Bond = 10% (1000) (PVA) + 1000 (PV)15%, 8 51%, 8= 100 (4.4873) + 1000 (0.3269)

= 448.73 + 326.90

= RM 775.63 (at discount)

I

K

N

P

= 10% (1000)

= 15%

= 8

= RM 1000

EQUATION 1 METHOD 1 FORMULA


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I

K

N

P

= 10% (1000)

= 15%

= 8

= RM 1000

INPUTS

OUTPUT

N I/Y PMTPV FV

8 15 100 1000

-775.63

EQUATION 2 METHOD 2 CALCULATOR


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Sell at Par Value Sell at Premium Sell at Discount

Whenever the

required rate of is

equal to the

coupon rate

Whenever the

required rate of

return is lower than

the coupon rate

Whenever the

required rate of

return than the

coupon return is

higher rate

I = K I > K I < K

10% = 10% 10% > 5% 10% < 15%

PV Bond =

RM1000

PV Bond = RM

1323.12

PV Bond = RM

775.63

INTEPRET TION


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It is another name for :-Rate of return

Internal rate of return

Market interest rate

Discount rate of return

It is the required yield expected by the

investors

There are 3 methods to calculate theYTM:-

Trial and Error

YTM formula

Calculator

YIELD-TO-MATURITY (YTM)


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Example:You were offered a 10yr, 15% coupon rate, RM1000 par value

bond at a price of RM960. What rate of interest would you

have earn if you have bought this bond and held it to

maturity?

Solution:

n = 10, I = 15%, P = 1000, Bond Price = 960, k = ?

Value of Bond = I (PV A k%n ) + P (P V k%n)

960 = 15% (1000) (PV A k% 10 ) + 1000 (PV k% 10)

TRIAL AND ERROR


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1. Type of bond: Discount Bond

2. Features: Market yield (market interest) is

greater than Coupon rate.3. k > I

Begin searching with k = 15% (because the value of

I = 15%) and higher than 15%. So now we assume the value of k as 15% and 16%.

At k = 15%, Bond Price = RM999.85

At k = 16%, Bond Price = RM951.95

RM999.85 RM960 RM951.95

k = 16k = ?k = 15%


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I + M- Value of Bond

YTM = N

( M + Value of Bond)

2

I = Coupon interest payment

M = Bond par value

N = Years

YTM FORMULA


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determinant of bond

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