bond valuation, equity research analyst.ppt

Briefly about bond valuation

1. VALUATION

2. Let us understand the concept of valuation
Investment
Real Assets
Land, Building, Machinery
Financial Assets
Shares, Bonds Etc
How do you decide the price at what price these assets
can be purchased ?

3. Real estate investment in Bangalore
•You expect that a plot value in Koramangla,
Bangalore is on steady rise.
•A 10 x10 square feet plot near Forum Mall,
purchased now can be sold for Rs 10,00,000
after 5 years.
•As a real estate owner, if you expect a
return of 20 %, What is the maximum price
you can pay for the plot.

4. Rs 10,00,000
5 years
20 %
?
5 years
20 %
Rs 10,00,000
(1.20)
5
4,02,000

5. Real estate investment in Bangalore
•You expect that a residential flat in
Koramangla, Bangalore can be let out for
rent @ Rs 60,000 per annum.
•The same flat, purchased now can be sold
for Rs 10,00,000 after 5 years.
•As a real estate owner, if you expect a
return of 20 %, What is the maximum price
you can pay for the plot.

6. 0 1 2 3 4 5
60,000 60,000 60,000 60,000 60,000 +
10,00,000
?

7. What do you understand from these
two examples ?
•The value of an asset is equal to the present
value of its future cash flows.
•The PV is the tool which we are going to
use for the purpose of bond valuation

8. • A Bond represents a contract under which a borrower
promises to pay interest and principal on specific dates
to the holders of the bond.
•Coupon
•Maturity date and Maturity
•Redemption premium
•Call option
•Put option
•Basis point

9. Bonds are issued by the Central Government,
State Governments, financial institutions, public
sector undertakings.

10. •Face value
•Coupon
•Maturity date and Maturity
•Redemption premium
•Call option
•Put option
•Basis point
BOND TERMINOLOGY

11. TYPES OF BOND
•Bonds with maturity
•Pure discount bonds
•Perpetual bonds

13. Types of yield
•1.Coupon (Nominal) yield
•2.Current Yield
•3.Yield to Maturity
•4.Realized Yield

14. Coupon yield
•Coupon yield is the rate of interest of a
bond, which is on the face value.
•Face value = Rs 1000
•Rate of interest = 8 %
•Amount of interest = Rs 80
•Maturity = 5 years
•Coupon yield = 8 %
•Coupon yield = rate of interest x face value

15. Current Yield
•Current yield is the annual interest divided by the
bond’s current value.
–Current yield = annual interest/purchase price

•Example: The annual interest is Rs 60 on the
current investment of Rs 883.40. Therefore, the
current rate of return or the current yield is:
60/883.40 = 6.8 per cent.
•Current yield does not account for the capital gain
or loss.

16. Current yield
•Face value = Rs 1000
•Purchase price = Rs 800
•Coupon rate = 8 %
•Current yield = Rs 80 X 100 = 10 %
• 800

17. Yield to Maturity
•What would be the return, if you buy any
bond and hold it till the maturity period ?
•Here you are entitled to get interest for
every year and principal amount when it is
repaid at the maturity period.

18. Yield to Maturity
•The yield-to-maturity (YTM) is the
measure of a bond’s rate of return that
considers both the interest income and any
capital gain or loss. YTM is bond’s internal
rate of return.
•Current yield does not take into account the
difference between the purchase of the bond
and the principal repayment at maturity.

19. Yield to maturity
Method 1
•Face value = Rs 1000
•Purchase price = Rs 800
•Coupon rate = 8 %
•Maturity = 5 years
Yield to Maturity = Coupon + Prorated discount
(Face Value + Purchase price) / 2
YTM = 80 + 40 x 100 = 13.3 %
(1000 + 800) /2

20. Yield to maturity
•Face value = Rs 1000
•Purchase price = Rs 1100
•Coupon rate = 8 %
•Maturity = 5 years
Yield to Maturity = Coupon - Prorated Premium
(Face Value + Purchase price) / 2
YTM = 80 - 20 x 100 = 5.7 %
(1000 + 800) /2

21. Yield to maturity
Method 2
•The yield to maturity of a bond is the
interest that equates the present value of the
cash inflows to the present values of cash
outflows. (IRR)
•Internal rate of return for a stream of cash
flows on a bond is known as the yield to
maturity.

22. Basic principle in IRR
0 4
100 146
Interest is compounded annually
What is the compounded annual rate of return ?

23. Basic principle in IRR
-100 146
@ 10 % interest rate compounded annually
0 1 2 3 4
110 121 133
If you deposit Rs 100 now and get Rs 146 after 4 years the rate of
Return associated with your investment is 10 % ( yield on your
Investment or true rate of return). At 10 % discount rate the present
Value of cash inflow is equal to the present value of cash outflow.
Now you can understand that the discount rate that equates the
Present value of cash inflow to the present value of cash outflow
Is the internal rate of return.
IRR is the annualized rate of return on investment

24. - 100 121 133 146 161
0 1 2 4 53
110
110
(1.10)
1
121
(1.10)
2
133
(1.10)
3
146
(1.10)
4
161
(1.10)
5
Empirical testing of IRR
100
100
100
100
100

25. - 100 121 133 146 161
0 2 4 53
121
(1.10)
2
133
(1.10)
3
146
(1.10)
4
161
(1.10)
5
Empirical testing of IRR
100
100
100
100

26. - 100 133 146 161
0 4 53


133
(1.10)
3
146
(1.10)
4
161
(1.10)
5
Empirical testing of IRR
100
100
100

27. 146 161
0 1 2 4 53


146
(1.10)
4
161
(1.10)
5
Empirical testing of IRR
100
100
- 100

28. What is IRR ?
•IRR is the discount rate at which the present
value of cash inflow is equal to the present
value of cash outflow.

29. Case 1
•Suppose that the market price of 6 % BOB
bond is Rs 883.40
•Face value = Rs 1000
•Maturity period = 5 years
•Redeemable value = Rs 1000
•Calculate the current yield and yield to
maturity.

30. Case 1
0 1 2 3 4 5
-883.40 60 60 60 60 60 +1000

60
(1+k)
1 60
(1+k)
2 60
(1+k)
3 60
(1+k)
4
1060
(1+k)
5
NPV = 0
K = ?

31. Face value 1000
Interest rate 6%
Year 0 1 2 3 4 5
Current price -883.4
Interest 60 60 60 60 60
Maturity value 1000
Cash flow -883.4 60 60 60 60 1060
Yield to Maturity
Calculation of YTM / IRR using excel sheet
=IRR(B7:G7)
Type here
A B C D E F G
1
2
3
4
5
6
7

32. Face value 1000
Interest rate 6%
Year 0 1 2 3 4 5
Current price -883.4
Interest 60 60 60 60 60
Maturity value 1000
Cash flow -883.4 60 60 60 60 1060
Yield to Maturity 9%

33. Consider a bond with face value of Rs 100,an
annual coupon of 12.5 % redeemable at par on
1/10/07, selling at Rs 80.60 on 1/10/04. What is
the return earned by the investor, who buys the
bond on 1/10/04 and holds it till maturity?

34. 0 1 2 3
04 05 06 07
-80.60 12.50 12.50 12.50 + Rs 100
12.50 12.50 112.50
------- -------- ----------
(1+k)
1
(1+k)
2
(1+k)
3

35. Consider a bond with an annual coupon of 12.5 % redeemable
on 1/10/07 selling at Rs 80.60 on 1/10/04. What is the return
earned by the investor, who buys the bond on 1/10/04 and
holds it till maturity?
Date1/10/041/10/051/10/061/10/07
Cash
flow
- 80.6012.5012.50112.50

36. Solution
Date 1/10/041/10/051/10/061/10/07
Cash flow-80.60 12.50 12.50 112.50
PV of cash
flow at 22 %
80.60 10.25 8.40 61.95
Net Present Value = 0
Yield to Maturity = 22 %

37. Yield Curve
70 75 80 85 90 95 100 105 110 115 120
8.0
7.5
7.0
6.0
5.5
3.5
Bond Price
Coupon rate
YTM

38. Realized yield to Maturity
•YTM assumes that the cash flows received
are reinvested at a rate equal to the yield to
maturity
•It is necessary to define the future
reinvestment rate and calculate the Realized
rate of return

39. Consider a Rs 1000 par value bond carrying an
interest rate of 15 % (payable annually) and
maturity after 5 years. The present market price of
this bond is Rs 850.The reinvestment rate
applicable to the future cash flows of this bond is
16 %. Calculate the realized yield to maturity.

40. Solution
Anl
interest
150 150 150 150 150
Re inv
period
4 3 2 1 0
Com @
16 %
1.811.561.351.161.00
Mv 271.5234.0202.5174.0150
TMV 2032

41. Realized yield
Present market price (1+r)
5
= Future value
850(1+r)
5
= 2032
(1+r)
5
= 2032/850 = 2.391
r = 19 %

42. Yield to Call
•For calculating the yield to call, the call period
would be different from the maturity period
and the call (or redemption) value could be
different from the maturity value.
•Example: Suppose the 10% 10-year Rs 1,000
bond is redeemable (callable) in 5 years at a
call price of Rs 1,050. The bond is currently
selling for Rs 950.The bond’s yield to call is
12.7%.
  
5
5
1
100 1,050
950
1 YTC 1 YTC
t
t
 
 


43. Bond with Maturity
Bond value = Present value of interest + Present
value of maturity value:

0
1
INT
(1 ) (1 )
n
t n
t n
t d d
B
B
k k

 
 


44. Bond Value and Amortisation of
Principal
•A bond (debenture) may be amortised every year,
i.e., repayment of principal every year rather at
maturity.
•The formula for determining the value of a bond or
debenture that is amortised every year, can be
written as follows:
–Note that cash flow, CF, includes both the interest and
repayment of the principal.
0
1(1 )
n
t
t
t d
CF
B
k





45. Pure Discount Bonds
•Pure discount bond do not carry an explicit
rate of interest. It provides for the payment of
a lump sum amount at a future date in
exchange for the current price of the bond.
The difference between the face value of the
bond and its purchase price gives the return or
YTM to the investor.

46. Pure Discount Bonds
•Example: A company may issue a pure
discount bond of Rs 1,000 face value for
Rs 520 today for a period of five years.
The rate of interest can be calculated as
follows:
 
 
5
5
1/5
1,000
520
1 YTM
1,000
1 YTM 1.9231
520
1.9231 1 0.14 or 14%i


  
  

47. Pure Discount Bonds
•Pure discount bonds are called deep-
discount bonds or zero-interest bonds or
zero-coupon bonds.
•The market interest rate, also called the
market yield, is used as the discount rate.
• Value of a pure discount bond = PV of the
amount on maturity:
 
0
1
n
n
d
M
B
k



48. Perpetual Bonds
•Perpetual bonds, also called consols, has an
indefinite life and therefore, it has no maturity
value. Perpetual bonds or debentures are
rarely found in practice.

49. Perpetual Bonds
•Suppose that a 10 per cent Rs 1,000 bond will
pay Rs 100 annual interest into perpetuity. What
would be its value of the bond if the market yield
or interest rate were 15 per cent?
•The value of the bond is determined as follows:
0
INT 100
Rs 667
0.15
d
B
k
  