determinant of bond
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Transcript of 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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