Download - Ch 01 Bond Pricing - Ready-To-Build
Annual Payments
Inputs
Number of Periods to Maturity (T) 8 8
Face Value (PAR) $1,000 20
Discount Rate / Period (r) 3.25% 6
Coupon Payment (PMT) $35.00 7
Bond Price using a TimelinePeriod 0 1 2 3 4 5 6 7 8
Cash FlowsPresent Value of Cash FlowsBond Price
Bond Price using the FormulaBond Price (P)
Bond Price using the PV FunctionBond Price
BOND PRICING
1 1
1
T
T
PMT r PARP
r r
A B C D E F G H I J
1
234567
8
9
1011
12
13
1415161718192021222324252627282930313233343536
EAR, APR, & Foreign Currencies Currency: US Dollar $1.00
Currency Number 4 Inputs (Select from below)
Rate Convention 2 Annual Percentage Rate 1 = Chinese Yuan
Annual Coupon Rate 4.00% 8 2 = European Euro € 0.6805
Yield to Maturity (Annualized) 1.74% 3 3 = Indian Rupee IDR 39.30
Number of Payments / Year 2 2 4 = US Dollar $1.00
Number of Periods to Maturity (T) 8 8
Face Value (PAR) $1,000 20
OutputsDiscount Rate / Period (r)Coupon Payment (PMT)
Bond Price using a TimelinePeriod 0 1 2 3 4 5 6 7 8Time (Years)Cash FlowsPresent Value of Cash FlowsBond Price
Bond Price using a FormulaBond Price
Bond Price using a FunctionBond Price
Bond Price using the PRICE Function (under APR)Bond Price
Yield to Maturity (Annualized) 1.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0% 10.0% 11.0% 12.0% 13.0% 14.0% 15.0% 16.0% 17.0% 18.0% 19.0% 20.0%
Data Table: Sensitivity of Bond Price to Discount Rate / PeriodInput Values for Discount Rate / Period
Output Formula:Bond Price
Bond Pricing By Calendar TimeCalendar Time (Years) 0 0.5 1 1.5 2 2.5 3 3.5 4Time to Maturity (Years) 4 3.5 3 2.5 2 1.5 1 0.5 0Number of Periods to Maturity (T)Bond Price of Coupon BondBond Price of Par Bond
BOND PRICINGExch Rate
$1.00 =
¥7.3790
)8 (Create the bond price Data Table. Select the range B64:V65, click on
Data | Data Tools | What-If Analysis | Data Table , enter B12 in the Row Input Cell ,
and click on OK.
0.00
2.00
4.00
6.00
8.00
10.00
12.00Bond Price By Yield To Maturity
Yield To Maturity
Bond
Pric
e
0 0.5 1 1.5 2 2.5 3 3.5 40.00
2.00
4.00
6.00
8.00
10.00
12.00Bond Pricing by Calendar Time
Calendar Time (Years)
Bo
nd
Pri
ce
E
A B C D E F G H I J K L M N O P Q R S T U V
1
23
4
5
6
7
8
9
10111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061
62
63646566676869707172737475767778798081828384858687888990
Duration and Convexity
Inputs
Rate Convention 2 Annual Percentage Rate
Annual Coupon Rate 4.00% 8
Yield to Maturity (Annualized) 1.74% 3
Number of Payments / Year 2 2
Number of Periods to Maturity (T) 8 8
Face Value (PAR) $1,000 20
OutputsDiscount Rate / Period (r)Coupon Payment (PMT)
Bond Duration using a TimelinePeriodTime (Years)Cash FlowsPresent Value of Cash FlowsBond Price using a TimelineWeightWeight * TimeDuration using a TimelineModified Duration using a Timeline
Bond Duration using a FormulaDuration (D) using a FormulaModified Duration using a Formula
Bond Duration using a Function (under APR)Duration using a FunctionModified Duration using a Function
Bond ConvexityWeight * (Time^2+Time)Convexity using a TimelineConvexity using a Formula
BOND PRICING
EAR APR
1 /1
1 1T
r T CR NOP rrD
r NOP CR r r NOP
1
2 32
2 2
1 1 2
1 1 2 3 21
1
T
T
CR r r NOP
CR r NOP T T r NOP T r NOP T NOP Tr
r NOP CR r CR r NOP
1
2 32
2 2
1 1 2
1 1 2 3 21
1
T
T
CR r r NOP
CR r NOP T T r NOP T r NOP T NOP Tr
r NOP CR r CR r NOP
Currency: US Dollar $1.00
Currency Number 4 (Select from below)
1 = Chinese Yuan
2 = European Euro € 0.6805
3 = Indian Rupee IDR 39.30
4 = US Dollar $1.00
Exch Rate $1.00 =
¥7.3790
1 /1
1 1T
r T CR NOP rrD
r NOP CR r r NOP
1
2 32
2 2
1 1 2
1 1 2 3 21
1
T
T
CR r r NOP
CR r NOP T T r NOP T r NOP T NOP Tr
r NOP CR r CR r NOP
1
2 32
2 2
1 1 2
1 1 2 3 21
1
T
T
CR r r NOP
CR r NOP T T r NOP T r NOP T NOP Tr
r NOP CR r CR r NOP
Price Sensitivity
Inputs Annual Percentage Rate
Rate Convention 2
Annual Coupon Rate (CR) 4.00% 8
Yield to Maturity (Annualized) 1.74% 3
Number of Payments / Year (NOP) 2 2
Number of Periods to Maturity (T) 8 8
Face Value $1,000 20
OutputsDiscount Rate / Period (r) 0.9%Coupon Payment $20
Chart OutputsYield to Maturity (Annualized) 0.50% 1.00% 1.50% 2.00% 2.50%Discount Rate / PeriodChange in Yield to MaturityActual Bond PriceCurrent Bond PriceActual Percent Change in PriceModified DurationDuration ApproximationConvexityDuration and Convexity Approx.
BOND PRICING
0.0% 200.0% 400.0% 600.0% 800.0% 1000.0% 1200.0%
0%
200%
400%
600%
800%
1000%
1200%
Price Sensitivity
Actual Percent Change in Price
Duration Approximation
Duration and Convexity Approx.
Change in Yield To MaturityP
erc
en
t C
ha
ng
e in
Pri
ce
1 /1
* 11 1
T
r T CR NOP rrD r
r NOP CR r r NOP
EAR APR
1
2 32
2 2
1 1 2
1 1 2 3 21
1
T
T
CR r r NOP
CR r NOP T T r NOP T r NOP T NOP Tr
r NOP CR r CR r NOP
1
2 32
2 2
1 1 2
1 1 2 3 21
1
T
T
CR r r NOP
CR r NOP T T r NOP T r NOP T NOP Tr
r NOP CR r CR r NOP
Currency: US Dollar $1.00
Currency Number 4 (Select from below)
1 = Chinese Yuan
2 = European Euro € 0.6805
3 = Indian Rupee IDR 39.30
4 = US Dollar $1.00
3.00% 3.50% 4.00% 4.50% 5.00% 5.50% 6.00% 6.50%
Exch Rate $1.00 =
¥7.3790
0.0% 200.0% 400.0% 600.0% 800.0% 1000.0% 1200.0%
0%
200%
400%
600%
800%
1000%
1200%
Price Sensitivity
Actual Percent Change in Price
Duration Approximation
Duration and Convexity Approx.
Change in Yield To Maturity
Pe
rce
nt
Ch
an
ge
in P
ric
e
1
2 32
2 2
1 1 2
1 1 2 3 21
1
T
T
CR r r NOP
CR r NOP T T r NOP T r NOP T NOP Tr
r NOP CR r CR r NOP
1
2 32
2 2
1 1 2
1 1 2 3 21
1
T
T
CR r r NOP
CR r NOP T T r NOP T r NOP T NOP Tr
r NOP CR r CR r NOP
Immunization
Inputs
Rate Convention 2 Annual Percentage Rate
Yield to Maturity (Annualized) 1.74%
Number of Payments / Year 2
Bond 1 1.50% 4 $1,000 1,783 Bond 2 2.00% 8 $1,000 2,042 Bond 3 0.90% 2 $1,000 0 Bond 4 1.50% 4 $1,000 0 Bond 5 1.90% 6 $1,000 0 Bond 6 2.30% 8 $1,000 0 Bond 7 1.90% 6 $1,000 0 Bond 8 2.30% 8 $1,000 0
OutputsDiscount Rate / Period (r)
Bond Present Value, Duration, and Convexity using a TimelinePeriod 0 1 2 3Time (Years) 0.0 0.5 1.0 1.5Liabilities $0 $0 $0 Present Value of LiabilitiesTotal Present Value of LiabilitiesWeightWeight * TimeDuration of LiabilitiesModified Duration of LiabilitiesWeight * (Time^2+Time)Convexity of Liabilities
Assets Bond 1 $0 $0 $0 Bond 2 $0 $0 $0 Bond 3 $0 $0 $0 Bond 4 $0 $0 $0 Bond 5 $0 $0 $0 Bond 6 $0 $0 $0 Bond 7 $0 $0 $0 Bond 8 $0 $0 $0 Total Assets $0 $0 $0 Present Value of AssetsTotal Present Value of AssetsWeightWeight * TimeDuration of AssetsModified Duration of AssetsWeight * (Time^2+Time)Convexity of Assets
BOND PRICING
Annual Coupon Rate
Number of Periods to
Maturity (T)Face Value
(PAR)Number of
Bonds
EAR APR
DifferencesTotal Assets - LiabilitiesPV of Assets - PV of LiabilitiesDuration of Assets - Duration of LiabConvexity of Assets - Convexity of Liab
To solve the first problem when there is a single liability to immunize
To solve the second problem when there is a series of liabilities to immunize
To solve the third problem when there is a series of liabilities to immunize with cash flow matching
Currency: US Dollar $1.00
4 5 6 7 82.0 2.5 3.0 3.5 4.0$0 $0 $4,000,000 $0 $0
$1,782,856 $0 $0 $0 $0 $0 $0 $0 $0 $2,041,788 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0
$1,782,856 $0 $0 $0 $2,041,788
Exch Rate $1.00 =
Coupon Payment (PMT)
Currency Number 4 (Select from below)
1 = Chinese Yuan
2 = European Euro € 0.6805
3 = Indian Rupee IDR 39.30
4 = US Dollar $1.00
¥7.3790
Currency: US Dollar $1.00
Inputs Annual Percentage Rate
Rate Convention 2 Annual Coupon Rate 4.00%Yield to Maturity (Annualized) 1.74%Number of Payments / Year 2 (1) Number of Periods to Maturity (T) 8 (2) Face Value (PAR) $1,000 (3) Discount Rate / Period (r) 0.87%(4) Coupon Payment (PMT) $20.00 (5) Bond Price (P) $1,086.96
(1) Number of Periods to Maturity (T) from the other four variablesNumber of Periods to Maturity using NPER Function
(2) Face Value (PAR) from the other four variablesFace Value using the FV FunctionFace Value using the Formula
(3) Discount Rate / Period (r) from the other four variablesDiscount Rate / Period using the RATE Function
(4) Coupon Payment (PMT) from the other four variablesCoupon Payment using the PMT FunctionCoupon Payment using the Formula
(5) Bond Price (P) from the other four variablesBond Price using the PV FunctionBond Price using the Formula
BOND PRICINGSystem of Five Bond
VariablesExch Rate
$1.00 =
EAR
APR
1 1
1
T
TPMT r
PAR P rr
1
1 1
T
T
P PAR rPMT
r r
1 1
1
T
T
PMT r PARP
r r
A B C D E F G H I J
1
23
4
56789101112131415161718192021222324252627282930313233343536373839404142