# Bond by wanghonghx

VIEWS: 13 PAGES: 14

• pg 1
```									                    Bond Valuation
Coverage
 Terms

 Calculations
 Bond Price and coupon
 Bond Yield

 Bond Price Relationship
 Price, Coupon rate, Interest rate, Maturity

1
Issuer and Holder

Price of Bond

Bond                                            Bond
Issuer                                           Holder
Periodic Coupon
Payments
Paid out

+
Principal Amount

2
Bond Price

Price of Bond

Bond                                         Bond
Issuer                                        Holder
Periodic Coupon
Payments
Paid out

+
Principal Amount

3
Bond Price
Because what you paid should be what you get, therefore;

Periodic Coupon
Payments
Price of Bond

+
Principal Amount

OR

Vb = PV of expected periodic coupon payment + PV of bond’s principal

4
Bond Terminology (1)
 Price (Vb)
 Value or price of bond
 Par Value
 The stated value, face value, principal, or maturity value
 Usually, par = \$1,000
 Coupon Interest Payment (C)
 Issuer pays a specified \$ amount of interest each year
according to the stated coupon rate written on the bond
 Ex. A 6-year bond offers 10% interest rate compounded annually
 The periodic coupon payment would be \$1,000 x 10% = \$100
 Because the interest is compounded annually, our periodic payment
will be \$100/1 or \$100 yearly

5
Bond Terminology (2)
 Rate of Return (Kb)
 Return required by investors on bonds or investments with
comparable risk.
 Maturity Date
 The date when the principal of bond must be repaid
 Current Yield
 An annualized return of bond
 Ignore capital gain/loss and time value of money
 Yield to Maturity (YTM)
 An ANNUAL RETURN if investors hold bonds till maturity
 The interest rate that will make the present value of all
cash flows equal to the price of the bond.
6
Bond Calculations
 1A) A 20-yr 10% annual coupon bond with a par value of
\$1,000 and the required yield on this bond is 14%.
Vb = C(PVA 14%, 20) + M(PV14%, 20)
= 100 x 6.6231 + 1,000 x 0.0728
= 662.31 + 72.8
= \$735.11

 1B) A 20-yr 10% annual coupon bond with a par value of
\$1,000 and the required yield on this bond is 8%.

 1C) A 20-yr 10% annual coupon bond with a par value of
\$1,000 and the required yield on this bond is 10%.

7
Bond Calculations
 2A) A 20-yr 10% semi-annual coupon bond with a par value
of \$1,000 and the required yield on this bond is 14%.
Vb = C(PVA 7%, 40) + M(PV 7%, 40)
= (100/2) x 13.3317 + 1,000 x 0.0668
= 666.59 + 66.8
= \$733.39

 2B) A 20-yr 10% semi-annual coupon bond with a par value
of \$1,000 and the required yield on this bond is 8%.

 2C) A 20-yr 10% semi-annual coupon bond with a par value
of \$1,000 and the required yield on this bond is 10%.

8
Bond Relationships
 Yield – Price (Inverse relationship)

Yield     > Price

 Yield – Coupon – Price
if kb ,> coupon rate = sold at discount
if kb ,< coupon rate = sold at premium
if kb ,= coupon rate = sold at par

If you give us more than what we want, we will pay you more
Or coupon rate higher than required return.
9
Bond Relationship
 Bond with more frequent coupon payments
20-Yr with 10% coupon                        20-Yr with 10% coupon
yield = 14%                                  yield = 8%
Annually                                 Annually
20       100     14% 662.3131            20         100         8% 981.8147
1000         72.76172                      1000            214.5482
735.0748                                      1196.363
Semi-annually                            Semi-annually
40         50      7% 666.5854           40           50       4.0% 989.6387
1000         66.78038                      1000             208.289
733.3658                                      1197.928
Quarterly                                Quarterly
80        25    3.50% 668.7194           80          25       2.0% 993.6128
1000          63.79285                     1000            205.1097
732.5122                                     1198.723

Monthly                                  Monthly
240        8.33   1.17% 670.1402         240          8.33     0.67% 996.2858
1000          61.80367                     1000            202.9714
731.9439                                     1199.257
10
Yield-to-Maturity
 Calculating YTM
 Trial and Error
 Use financial calculators
 Use software functions
 Use formulas (approximation)

YTM - The interest rate that will make the present value of all
cash flows equal to the price of the bond.

11
YTM vs. Current Yield
 YTM - the interest rate that       Current Yield - an
will make the present value         annualized return of bond
of all cash flows equal to         Good for person who only
the price of the bond               concern about annual
 Good for person who                 income because:
concern about total return            Consider only one source of
because:                               bond income – annual coupon
 Consider two sources of bond        payment
income                             Ignore potential capital gain or
 Take into account time value        loss at maturity
of money                           Ignore time value of money

12
Bond Relationship Summary
 Yield – Price (Inverse relationship)

Yield    > Price

 Yield – Coupon – Price
if kb ,> coupon rate = sold at discount
if kb ,< coupon rate = sold at premium
if kb ,= coupon rate = sold at par
 YTM – CY – Price
 If YTM>CY = Discount (capital gain is received)
 If CY>YTM = Premium (ignore capital loss at maturity)
13
Price vs. Value
 Undervalue vs Overvalue
 A bond is undervalued when the market price is
lower than the bond value (or calculated value