[XLS]people.highline.edu · Web viewEffective Annual Yield = (1+YTM/n)^n -1 = Words: Bond Value =...

Milk Price now $3.39 Number of milk cartons bought 100Total price (Buying power = 100 cartons)

Amount now in bank $339.00 APR (n=1) = R = Nominal 10% RBank amount in 1 year

Milk price in 1 year $3.56 Milk Inflation = 3.56/3.39 -1 = h hCan you buy 10.00% more (Number of cartons)? 110How many can you buy today = $372.90/3.56 =

1 Change in Buying Power =

2 Real Rate = r = r = (1+R)/(1+h)-1 =Real Rate of return is = how much more can we buy with our money!!!

Change in buying power

Milk Price now $3.39 Number of milk cartons bought 100Total price (Buying power = 100 cartons) $339.00

Amount now in bank $339.00 APR (n=1) = R = Nominal 10% RBank amount in 1 year $372.90

Milk price in 1 year $3.56 Milk Inflation = 3.56/3.39 -1 = h 5.0147% hCan you buy 10.00% more (Number of cartons)? 110How many can you buy today = $372.90/3.56 = 104.7472

1 Change in Buying Power = 0.0474719

2 Real Rate = r = 4.7472% r = (1+R)/(1+h)-1 =Real Rate of return is = how much more can we buy with our money!!!

Change in buying power

Nominal Rate = (Annual Rate, n = 1) 0.12 RInflation 0.06 h

3 Change in buying power = Real Rate r





Just like the stock market, going up looks bigger than going down (going down you can only loose 100%, but up can be bigger than 100%)


3 Change in buying power = Real Rate 0.056603774 r


4 Change in buying power = Real Rate -0.004926108 r


5 Change in buying power = Real Rate 0.00495050 r

Just like the stock market, going up looks bigger than going down (going down you can only loose 100%, but up can be bigger than 100%)

6 Point of View: Bond Issuer 8 Point of View: Bondholder #1 10Interest Only - Coupon Bond Interest Only - Coupon BondBond Issue Date 1/1/2010 Day #1 buys bond 1/1/2010Face Value = FV ($1,000.00) Face Value = FV $1,000.00 i = Coupon Rate 10.00% i = Coupon Rate 10.00%n 2 n 2x 3 x 3i/n i/nx*n x*nPMT Coupon PMT PMTYTM 11.00% YTM 11.00%YTM/n YTM/nPV PVcheck: check:

7 Point of View: Bond Issuer 9 Point of View: Bondholder #1Deep Discount - Zero Coupon Bonds Deep Discount - Zero Coupon BondsFace Value = FV ($1,000.00) Face Value = FV $1,000.00 i = Coupon Rate 10.00% i = Coupon Rate 10.00%n 2 n 2x 3 x 3i/n 0.00% i/n 0.00%x*n 0 x*n 0YTM 11.00% YTM 11.00%YTM/n 0.00% YTM/n 0.00%PV PVcheck: check:

Interest Only - Coupon BondDay #2 buys bond 1/1/2012Face Value = FV $1,000.00 i = Coupon Rate 10.00%n 2x 1i/nx*nPMT Coupon PMTYTM 9.00%YTM/nPVcheck:

Point of View: Bondholder #2 (This person buys the bond from

Bondholder #1)

6 Point of View: Bond Issuer 8 Point of View: Bondholder #1 10Interest Only - Coupon Bond Interest Only - Coupon BondBond Issue Date 1/1/2010 Day #1 buys bond 1/1/2010Face Value = FV ($1,000.00) Face Value = FV $1,000.00 i = Coupon Rate 10.00% i = Coupon Rate 10.00%n 2 n 2x 3 x 3i/n 5.00% i/n 5.00%x*n 6 x*n 6PMT Coupon PMT ($50.00) PMT $50.00 YTM 11.00% YTM 11.00%YTM/n 5.50% YTM/n 5.50%PV $975.02 PV ($975.02)check: $975.02 check: ($975.02)

7 Point of View: Bond Issuer 9 Point of View: Bondholder #1Deep Discount - Zero Coupon Bonds Deep Discount - Zero Coupon BondsFace Value = FV ($1,000.00) Face Value = FV $1,000.00 i = Coupon Rate 10.00% i = Coupon Rate 10.00%n 2 n 2x 3 x 3i/n 5.00% i/n 5.00%x*n 6 x*n 6YTM 11.00% YTM 11.00%YTM/n 5.50% YTM/n 5.50%PV $725.25 PV ($725.25)check: $725.25 check: ($725.25)

Interest Only - Coupon BondDay #2 buys bond 1/1/2012Face Value = FV $1,000.00 i = Coupon Rate 10.00%n 2x 1i/n 5.00%x*n 2PMT Coupon PMT $50.00 YTM 9.00%YTM/n 4.50%PV ($1,009.36)check: ($1,009.36)

Point of View: Bondholder #2 (This person buys the bond from

Bondholder #1)

Interest Only - Coupon BondBond Price = PV -1,009.36FV = Face Value $1,000.00 PMT = Coupon PMT $50.00 Years To Maturity 1n = assumed to be semi-annual = 2Total Number of PeriodsYTM/nYTM checkEffective Annual Yield

Point of View: Bondholder #2 (This person buys the bond from Bondholder #1)

Interest Only - Coupon BondBond Price = PV -1,009.36FV = Face Value $1,000.00 PMT = Coupon PMT $50.00 Years To Maturity 1n = assumed to be semi-annual = 2Total Number of Periods 2YTM/n 4.50%YTM 9.00% checkEffective Annual Yield 9.2025% 0.092025

Point of View: Bondholder #2 (This person buys the bond from Bondholder #1)

1 Year 10% Coupon Bond is priced at 100.936%

1 Year 10% Coupon Bond is priced at 100.936%

Years To Maturity 1n 2Total Periods 2Face 1000Coupon Rate 10%Interest PMT = Coupon PMT 50Quoted Price 1.00936Price = PV -1009.36YTM/n 4.50%YTM 0.0900035406Effective Annual Rate 0.0920286999

Point of View = Bond Issuer Face Value = FV = $1,000.00Maturity = years = x = 30n = 2Coupon Rate = 6.00%Coupon Rate/n = 3.00%Semiannual Coupon Payment = $30.00Total # of Coupon Payments = 60YTM/n = 3.00%

YTM = 6.00% YTM = Coupon RateBond Price = PV = 1,000.00 Par

YTM and Price move in opposite Directions

Point of View = Bond Issuer Face Value = FV = $1,000.00Maturity = years = x = 30n = 2Coupon Rate = 6.00%Coupon Rate/n = 3.00%Semiannual Coupon Payment = $30.00Total # of Coupon Payments = 60YTM/n = 1.00%

YTM = 2.00% YTM < Coupon RateBond Price = PV = 1,899.10 Premium

YTM Discount Rate Bond Price0.04 $1,347.610.05 $1,154.540.06 $1,000.000.07 $875.280.08 $773.770.09 $690.43

0.1 $621.410.11 $563.750.12 $515.160.13 $473.850.14 $438.430.15 $407.83

YTM and Price move in opposite Directions

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16$0.00

$200.00

$400.00

$600.00

$800.00

$1,000.00

$1,200.00

$1,400.00

$1,600.00Bond Price

YTM Discount Rate

Bond

Pric

e

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16$0.00

$200.00

$400.00

$600.00

$800.00

$1,000.00

$1,200.00

$1,400.00

$1,600.00Bond Price

YTM Discount Rate

Bond

Pric

e

Years To Maturity 10n 2Coupon Rate 6%Coupon Rate/n 3%YTM 6%YTM/n 0.03Total Periods 20Coupon PMT -$30.00Face -$1,000.00PV = Price

Years To Maturity 10n 2Coupon Rate 6%Coupon Rate/n 3%YTM 7%YTM/n 0.035Total Periods 20Coupon PMT -$30.00Face -$1,000.00PV = Price $928.94 Discount

YTM (Market) Rate For Similar Securities6% 8% 10.0%

Coupon Rate On Bond (Used To Calculate Interest PMT)8% 8% 8.0%

Record Bond At Premium

Record Bond Without Pre. Or Dis.

Record Bond At Discount

Selling Price For Bond

Below 1.00(Example: 93 or

0.93 or 93%)

1.00(Example: 100 or

1.00 or 100%)

Above 1.00(Example: 107 or

1.07 or 107%)

Record Bond At Discount

Record Bond With No Premium Or

DiscountRecord Bond At

Premium

Years To Maturity 10n 2Coupon Rate 6%Coupon Rate/n 3%YTM 7%YTM/n 0.035Total Periods 20Coupon PMT -$30.00Face -$1,000.00PV = Price $928.94

Period Coupon YTM Interest Principal Addition Carrying Balance YTM0123456789

1011121314151617181920

Years To Maturity 10n 2Coupon Rate 6%Coupon Rate/n 3%YTM 5%YTM/n 0.025Total Periods 20Coupon PMT -$30.00Face -$1,000.00PV = Price $1,077.95

Period Coupon YTM Interest Pricipal Addition Carrying Balance YTM0 $1,077.95 1 $30.00 $26.95 ($3.05) $1,074.89 0.0252 $30.00 $26.87 ($3.13) $1,071.77 0.0253 $30.00 $26.79 ($3.21) $1,068.56 0.0254 $30.00 $26.71 ($3.29) $1,065.28 0.0255 $30.00 $26.63 ($3.37) $1,061.91 0.0256 $30.00 $26.55 ($3.45) $1,058.45 0.0257 $30.00 $26.46 ($3.54) $1,054.92 0.0258 $30.00 $26.37 ($3.63) $1,051.29 0.0259 $30.00 $26.28 ($3.72) $1,047.57 0.025

10 $30.00 $26.19 ($3.81) $1,043.76 0.02511 $30.00 $26.09 ($3.91) $1,039.85 0.02512 $30.00 $26.00 ($4.00) $1,035.85 0.02513 $30.00 $25.90 ($4.10) $1,031.75 0.02514 $30.00 $25.79 ($4.21) $1,027.54 0.02515 $30.00 $25.69 ($4.31) $1,023.23 0.02516 $30.00 $25.58 ($4.42) $1,018.81 0.02517 $30.00 $25.47 ($4.53) $1,014.28 0.02518 $30.00 $25.36 ($4.64) $1,009.64 0.02519 $30.00 $25.24 ($4.76) $1,004.88 0.02520 $30.00 $25.12 ($4.88) $1,000.00 0.025

Years To Maturity 10 Date Description DR CRn 2Coupon Rate 6%Coupon Rate/n 3%YTM 7%YTM/n 0.035Total Periods 20Coupon PMT -$30.00Face -$1,000.00PV = Price $928.94

Period Coupon Carrying Balance YTM0 $928.94 1 $30.00 $32.51 $2.51 $931.45 0.0352 $30.00 $32.60 $2.60 $934.05 0.0353 $30.00 $32.69 $2.69 $936.74 0.0354 $30.00 $32.79 $2.79 $939.53 0.0355 $30.00 $32.88 $2.88 $942.41 0.0356 $30.00 $32.98 $2.98 $945.40 0.0357 $30.00 $33.09 $3.09 $948.49 0.0358 $30.00 $33.20 $3.20 $951.68 0.0359 $30.00 $33.31 $3.31 $954.99 0.035

10 $30.00 $33.42 $3.42 $958.42 0.03511 $30.00 $33.54 $3.54 $961.96 0.03512 $30.00 $33.67 $3.67 $965.63 0.03513 $30.00 $33.80 $3.80 $969.43 0.03514 $30.00 $33.93 $3.93 $973.36 0.03515 $30.00 $34.07 $4.07 $977.42 0.03516 $30.00 $34.21 $4.21 $981.63 0.03517 $30.00 $34.36 $4.36 $985.99 0.03518 $30.00 $34.51 $4.51 $990.50 0.03519 $30.00 $34.67 $4.67 $995.17 0.03520 $30.00 $34.83 $4.83 $1,000.00 0.035

YTM Interest

Pricipal Addition

Years To Maturity 10 Date Description DR CRn 2 1/1/2010 Cash $928.94 Coupon Rate 6% Discount On BP $71.06 Coupon Rate/n 3% Bonds Payable $1,000.00YTM 7%YTM/n 0.035 7/1/2010 Interest Expense $32.51Total Periods 20 Cash $30.00Coupon PMT -$30.00 Discount On BP $2.51 Face -$1,000.00PV = Price $928.94

Period Coupon Carrying Balance YTM0 $928.94 1 $30.00 $32.51 $2.51 $931.45 0.0352 $30.00 $32.60 $2.60 $934.05 0.0353 $30.00 $32.69 $2.69 $936.74 0.0354 $30.00 $32.79 $2.79 $939.53 0.0355 $30.00 $32.88 $2.88 $942.41 0.0356 $30.00 $32.98 $2.98 $945.40 0.0357 $30.00 $33.09 $3.09 $948.49 0.0358 $30.00 $33.20 $3.20 $951.68 0.0359 $30.00 $33.31 $3.31 $954.99 0.035

10 $30.00 $33.42 $3.42 $958.42 0.03511 $30.00 $33.54 $3.54 $961.96 0.03512 $30.00 $33.67 $3.67 $965.63 0.03513 $30.00 $33.80 $3.80 $969.43 0.03514 $30.00 $33.93 $3.93 $973.36 0.03515 $30.00 $34.07 $4.07 $977.42 0.03516 $30.00 $34.21 $4.21 $981.63 0.03517 $30.00 $34.36 $4.36 $985.99 0.03518 $30.00 $34.51 $4.51 $990.50 0.03519 $30.00 $34.67 $4.67 $995.17 0.03520 $30.00 $34.83 $4.83 $1,000.00 0.035

YTM Interest

Pricipal Addition

Years To Maturity 10 Date Description DR CRn 2Coupon Rate 6%Coupon Rate/n 3%YTM 5%YTM/n 0.025Total Periods 20Coupon PMT -$30.00Face -$1,000.00PV = Price $1,077.95

Period Coupon Carrying Balance YTM0 $1,077.95 1 $30.00 $26.95 ($3.05) $1,074.89 0.0252 $30.00 $26.87 ($3.13) $1,071.77 0.0253 $30.00 $26.79 ($3.21) $1,068.56 0.0254 $30.00 $26.71 ($3.29) $1,065.28 0.0255 $30.00 $26.63 ($3.37) $1,061.91 0.0256 $30.00 $26.55 ($3.45) $1,058.45 0.0257 $30.00 $26.46 ($3.54) $1,054.92 0.0258 $30.00 $26.37 ($3.63) $1,051.29 0.0259 $30.00 $26.28 ($3.72) $1,047.57 0.025

10 $30.00 $26.19 ($3.81) $1,043.76 0.02511 $30.00 $26.09 ($3.91) $1,039.85 0.02512 $30.00 $26.00 ($4.00) $1,035.85 0.02513 $30.00 $25.90 ($4.10) $1,031.75 0.02514 $30.00 $25.79 ($4.21) $1,027.54 0.02515 $30.00 $25.69 ($4.31) $1,023.23 0.02516 $30.00 $25.58 ($4.42) $1,018.81 0.02517 $30.00 $25.47 ($4.53) $1,014.28 0.02518 $30.00 $25.36 ($4.64) $1,009.64 0.02519 $30.00 $25.24 ($4.76) $1,004.88 0.02520 $30.00 $25.12 ($4.88) $1,000.00 0.025

YTM Interest

Pricipal Addition

Years To Maturity 10 Date Description DR CRn 2 1/1/2010 Cash $1,077.95 Coupon Rate 6% Premium On BP $77.95 Coupon Rate/n 3% Bonds Payable $1,000.00YTM 5%YTM/n 0.025 7/1/2010 Interest Expense $26.95Total Periods 20 Premium On BP $3.05 Coupon PMT -$30.00 Cash $30.00Face -$1,000.00PV = Price $1,077.95

Period Coupon Carrying Balance YTM0 $1,077.95 1 $30.00 $26.95 ($3.05) $1,074.89 0.0252 $30.00 $26.87 ($3.13) $1,071.77 0.0253 $30.00 $26.79 ($3.21) $1,068.56 0.0254 $30.00 $26.71 ($3.29) $1,065.28 0.0255 $30.00 $26.63 ($3.37) $1,061.91 0.0256 $30.00 $26.55 ($3.45) $1,058.45 0.0257 $30.00 $26.46 ($3.54) $1,054.92 0.0258 $30.00 $26.37 ($3.63) $1,051.29 0.0259 $30.00 $26.28 ($3.72) $1,047.57 0.025

10 $30.00 $26.19 ($3.81) $1,043.76 0.02511 $30.00 $26.09 ($3.91) $1,039.85 0.02512 $30.00 $26.00 ($4.00) $1,035.85 0.02513 $30.00 $25.90 ($4.10) $1,031.75 0.02514 $30.00 $25.79 ($4.21) $1,027.54 0.02515 $30.00 $25.69 ($4.31) $1,023.23 0.02516 $30.00 $25.58 ($4.42) $1,018.81 0.02517 $30.00 $25.47 ($4.53) $1,014.28 0.02518 $30.00 $25.36 ($4.64) $1,009.64 0.02519 $30.00 $25.24 ($4.76) $1,004.88 0.02520 $30.00 $25.12 ($4.88) $1,000.00 0.025

YTM Interest

Pricipal Addition

Bond Face Value = FV = -$1,000.00Coupon Payment -$100.00Coupon Rate = 10.00%n = 1

1 30YTM Time To Maturity

years = 1 years = 305%

10%15%20% The Longer The Maturity, The More YTM Affects Bond Price

The Longer The Maturity, The More YTM Affects Bond Price

Bond Face Value = FV = -$1,000.00Coupon Payment -$100.00Coupon Rate = 10.00%n = 1

1 30YTM Time To Maturity

years = 1 years = 305% $1,047.62 $1,768.62

10% $1,000.00 $1,000.00 15% $956.52 $671.70 20% $916.67 $502.11 The Longer The Maturity, The More YTM Affects Bond Price

5% 10% 15% 20%$0.00

$200.00 $400.00 $600.00 $800.00

$1,000.00 $1,200.00 $1,400.00 $1,600.00 $1,800.00 $2,000.00

$1,047.62 $1,000.00 $956.52 $916.67

$1,768.62

$1,000.00

$671.70 $502.11


years = 1years = 30

YTM

Bond

Val

ue


5% 10% 15% 20%$0.00

$200.00 $400.00 $600.00 $800.00

$1,000.00 $1,200.00 $1,400.00 $1,600.00 $1,800.00 $2,000.00

$1,047.62 $1,000.00 $956.52 $916.67

$1,768.62

$1,000.00

$671.70 $502.11


years = 1years = 30

YTM

Bond

Val

ue

Years To Maturity = 10YTM Rate Start 5.00%YTM Rate Increment = 5.00%Bond Face Value = FV = $ 1,000.00 n = 1

The Lower The Coupon Rate, The More YTM Affects Bond PriceCoupon Rate = 0.02 0.05

YTM 2.00% Coupon Rate 5.00% Coupon Rate Difference5.0% $0.00

15.0% $0.00 20.0% $0.00 25.0% $0.00

Loss in value from: 0.05 to 0.25

Proportionally larger FV causes lower PV than Higher Coupon

Bond.

Higher Coupon Payments earlier are less affected by discounting than the Bond with a lower coupon rate.

Years To Maturity = 10YTM Rate Start 5.00%YTM Rate Increment = 5.00%Bond Face Value = FV = $ 1,000.00 n = 1

The Lower The Coupon Rate, The More YTM Affects Bond PriceCoupon Rate = 0.02 0.05

YTM 2.00% Coupo5.00% Coupon Rate Difference5.0% $768.35 $1,000.00 $231.65

15.0% $347.56 $498.12 $150.56 20.0% $245.36 $371.13 $125.77 25.0% $178.78 $285.90 $107.12

Loss in value from: 0.05 to -0.7673134 -0.71410065408

Proportionally larger FV

causes lower PV

than Higher Coupon Bond.

Higher Coupon Payments earlier are less affected by discounting than the Bond with a lower coupon rate.

$768.35 $347.56 $245.36 $178.78 $0.00

$200.00

$400.00

$600.00

$800.00

$1,000.00

$1,200.00

The Lower The Coupon Rate, The More YTM Affects Bond Price

5.00% Coupon Rate

2.00% Coupon Rate

YTM

Bond

Pric

e

$768.35 $347.56 $245.36 $178.78 $0.00

$200.00

$400.00

$600.00

$800.00

$1,000.00

$1,200.00

The Lower The Coupon Rate, The More YTM Affects Bond Price

5.00% Coupon Rate

2.00% Coupon Rate

YTM

Bond

Pric

e

Tax Bracket 25%Corportae Bond Pays Coupon = 5%Muni Bond Pays Coupon = 3.90%After Tax Rate For MuniAfter Tax For Corporate

Tax Bracket 25%Corportae Bond Pays Coupon = 5%Muni Bond Pays Coupon = 3.90%After Tax Rate For Muni 3.90%After Tax For Corporate 0.0375

Point of View = Bondholder'sFace Value = Par Value = $1,000.00 # of Bonds Issued = 1Total Face Value = FV =Coupon Rate = 10.00%# Compounding periods per Year = n = 2Coupon Rate/n =Periodic Coupon payments (Interest $ Amount) = PMT =Years To Maturity = x = 20Total Number of Periods = n*x =Discount Rate = Required Yield = i = YTM = 12.00%YTM/n = check:Bond Value = Bond Price = PV (using PV function) = <<Effective Annual Yield = (1+YTM/n)^n -1 = <<Words:

Point of View = Bondholder'sFace Value = Par Value = $1,000.00 # of Bonds Issued = 1Total Face Value = FV = $1,000.00 Coupon Rate = 10.00%# Compounding periods per Year = n = 2Coupon Rate/n = 5.00%Periodic Coupon payments (Interest $ Amount) = PMT = $50.00 Years To Maturity = x = 20Total Number of Periods = n*x = 40Discount Rate = Required Yield = i = YTM = 12.00%YTM/n = 0.06 check:Bond Value = Bond Price = PV (using PV function) = ($849.54) << ($849.54)Effective Annual Yield = (1+YTM/n)^n -1 = 12.36% << 0.1236

Words:

The Bond with a 10.00% coupon is priced to yield 12.00% at $849.54. This Bond is selling at a Discount. Further, the Effective Annual Yield is

12.36%.


12.36%.

Point of View = Bondholder'sFace Value = Par Value = $1,000.00 # of Bonds Issued = 1Total Face Value = FV =Coupon Rate = 8.00%# Compounding periods per Year = n = 2Coupon Rate/n =Periodic Coupon payments (Interest $ Amount) = PMT =Years To Maturity = x = 6Total Number of Periods = n*x =Discount Rate = Required Yield = i = YTM =YTM/n =Bond Value = Bond Price = ($911.37) check:Effective Annual Yield = (1+YTM/n)^n -1 = 0

Words:

check FV:$911.37

Point of View = Bondholder'sFace Value = Par Value = $1,000.00 # of Bonds Issued = 1Total Face Value = FV = $1,000.00 Coupon Rate = 8.00%# Compounding periods per Year = n = 2Coupon Rate/n = 4.00%Periodic Coupon payments (Interest $ Amount) = PMT = $40.00 Years To Maturity = x = 6Total Number of Periods = n*x = 12Discount Rate = Required Yield = i = YTM = 0.09999939824YTM/n = 4.999970%Bond Value = Bond Price = ($911.37) check:Effective Annual Yield = (1+YTM/n)^n -1 = 10.25% 0.102499

Words:


10.25%.

check FV:$1,000.00


10.25%.

15 a

15 b

15 a

15 b

The Price of a Bond and the YTM are inversely related. If the YTM goes up, the Bond Price goes down (more interest is taken out during discounting). If the YTM goes down, the Bond Price goes

up (less interest is taken out during discounting).

Bonds that sell at a Premium over Par do so because the Coupon Rate of the Bond is greater than the YTM (Bondholders are willing to pay more to get a Coupon Rate that is higher than the YTM

(market rate).Bonds that sell at a Discount compared to Par do so because the Coupon Rate of the Bond is less

than the YTM (Bondholders are only willing to pay less than par because they are getting a Coupon Rate that is lower than the YTM (market rate).

Coupon Rate > YTM ==> Sell at PremiumCoupon Rate = YTM ==> Sell at Par

Coupon Rate < YTM ==> Sell at Discount

Point of View = Bondholder'sCoupon Rate = 7.00%Years to Maturity = 20Bond Face = 1,000.00 made up numbern = 1 made up numberPMT =YTM when originally issued = 10.00% made up numberYTM today = 15.00%Price when IssuedPrice Today

Words:

Point of View = Bondholder'sCoupon Rate = 7.00%Years to Maturity = 20Bond Face = 1,000.00 made up numbern = 1 made up numberPMT = 70.00YTM when originally issued = 10.00% made up numberYTM today = 15.00%Price when Issued -744.59Price Today -499.25

Words:

Price and YTM are inversely related. If a 7.00% Coupon Bond is priced at an YTM of 15.00% that is greater than the YTM that was used to value it when it was first issued, the Price will go down. For example, If the Bond was issued at a YTM of

10.00% and it is reprice at a YTM of 15.00%, the price would go from $744.59 to $499.25.

Price and YTM are inversely related. If a 7.00% Coupon Bond is priced at an YTM of 15.00% that is greater than the YTM that was used to value it when it was first issued, the Price will go down. For example, If the Bond was issued at a YTM of

10.00% and it is reprice at a YTM of 15.00%, the price would go from $744.59 to $499.25.

Point of View = Bondholder'sFace Value = Par Value = 1000# of Bonds Issued = 1Total Face Value = FV =Coupon Rate = 7.00%# Compounding periods per Year = n = 1Coupon Rate/n =Periodic Coupon payments (Interest $ Amount) = PMT =Years To Maturity = x = 8Total Number of Periods = n*x =Discount Rate = Required Yield = i = YTM = 9.00%YTM/n = Check:Bond Value = Bond Price = PV (using PV function) = Effective Annual Yield = (1+YTM/n)^n =Words:

Point of View = Bondholder'sFace Value = Par Value = 1000# of Bonds Issued = 1Total Face Value = FV = 1000Coupon Rate = 7.00%# Compounding periods per Year = n = 1Coupon Rate/n = 7.00%Periodic Coupon payments (Interest $ Amount) = PMT = 70Years To Maturity = x = 8Total Number of Periods = n*x = 8Discount Rate = Required Yield = i = YTM = 9.00%YTM/n = 0.09 Check:Bond Value = Bond Price = PV (using PV function) = ($889.30) -889.3036Effective Annual Yield = (1+YTM/n)^n = 9.00%

Words:


9.00%.


9.00%.

Point of View = Bondholder'sFace Value = Par Value = 1000# of Bonds Issued = 1Total Face Value = FV =Coupon Rate = 10.00%# Compounding periods per Year = n = 1Coupon Rate/n =Periodic Coupon payments (Interest $ Amount) = PMT =Years To Maturity = x = 9Total Number of Periods = n*x =Discount Rate = Required Yield = i = YTM =YTM/n =Bond Value = Bond Price = ($1,145.70)Effective Annual Yield = (1+YTM/n)^n =Effective Annual Yield (Math) = 0.00%

Words:

Point of View = Bondholder'sFace Value = Par Value = 1000# of Bonds Issued = 1Total Face Value = FV = 1000Coupon Rate = 10.00%# Compounding periods per Year = n = 1Coupon Rate/n = 10.00%Periodic Coupon payments (Interest $ Amount) = PMT = 100Years To Maturity = x = 9Total Number of Periods = n*x = 9Discount Rate = Required Yield = i = YTM = 0.07696946763YTM/n = 7.696947%Bond Value = Bond Price = ($1,145.70)Effective Annual Yield = (1+YTM/n)^n = 7.70%Effective Annual Yield (Math) = 7.70%

Words:

The Bond with a 10.00% coupon is priced to yield 7.70% at $1,145.70. This Bond is selling at a Premium. Further, the Effective Annual Yield is

7.70%.

The Bond with a 10.00% coupon is priced to yield 7.70% at $1,145.70. This Bond is selling at a Premium. Further, the Effective Annual Yield is

7.70%.

Point of View = Bond Issuer'sFace Value = Par Value = 1,000.00# of Bonds Issued = 1Total Face Value = FV =Coupon Rate =# Compounding periods per Year = n = 1Periodic Coupon payments (Interest $ Amount) = PMT =Years To Maturity = x = 16Discount Rate = Required Yield = i = YTM = 7.50%Type = 0 = 0Bond Value = Bond Price = PV (using PV function) = 963.00

Point of View = Bond Issuer'sFace Value = Par Value = 1,000.00# of Bonds Issued = 1Total Face Value = FV = -1,000.00Coupon Rate = 0.0709525272# Compounding periods per Year = n = 1Periodic Coupon payments (Interest $ Amount) = PMT = -70.95Years To Maturity = x = 16Discount Rate = Required Yield = i = YTM = 7.50%Type = 0 = 0Bond Value = Bond Price = PV (using PV function) = 963.00

Point of View = Bondholder'sYears to Maturity on Contract = 15Number of Years ago that Bond Was Issued =1 1Years Left In Contract = X = 14Coupon Rate = 6.10%n = 2n *x =Coupon Rate /n =Periodic Interest PMT = PMT =Face Value = Par Value = FV = 1,000.00YTM = 5.30%YTM/n =Bond Price =

Words:

Point of View = Bondholder'sYears to Maturity on Contract = 15Number of Years ago that Bond Was Issued =1 1Years Left In Contract = X = 14Coupon Rate = 6.10%n = 2n *x = 28Coupon Rate /n = 0.0305Periodic Interest PMT = PMT = 30.50Face Value = Par Value = FV = 1,000.00YTM = 5.30%YTM/n = 0.0265Bond Price = -1,078.37

Words:The 6.10% Coupon Bond is priced to yield 5.30% at $1,078.37.

Point of View = Bond Issuer'sYears to Maturity on Contract = 15Number of Years ago that Bond Was Issued =1 2Years Left In Contract = X =Coupon Rate = 8.40%n = 2n *x =Coupon Rate /n =Periodic Interest PMT = PMT =Face Value = Par Value = FV = -1,000.00Current Bond Price (% of Par) 108.00%Current Bond Price =YTM/n =YTM = YTM/n*n =

Words:

Point of View = Bond Issuer'sYears to Maturity on Contract = 15Number of Years ago that Bond Was Issued =1 2Years Left In Contract = X = 13Coupon Rate = 8.40%n = 2n *x = 26Coupon Rate /n = 0.042Periodic Interest PMT = PMT = -42.00Face Value = Par Value = FV = -1,000.00Current Bond Price (% of Par) 108.00%Current Bond Price = 1,080.00YTM/n = 3.714889256717590000%YTM = YTM/n*n = 0.0742977851343519

Words:The 8.40% Coupon Bond with 13 years left until maturity has a YTM of 7.43%.

Nominal Rate = R = 5.70%Inflation Rate = h = 2.90%Real Rate = r = (1+R)/(1+h)-1 =Words:

Approximate r = R - h

Nominal Rate = R = 5.70%Inflation Rate = h = 2.90%Real Rate = r = (1+R)/(1+h)-1 = 0.0272108843537415

Words:

Approximate r = R - h 2.80%

The real rate (the percentage change in buying power) = r = 2.7211%.

Notice: End/Beg - 1 = Proportional Change = $1.057/$1.029 - 1

Nominal Rate = R = 13.00%Inflation Rate = h = (1+R)/(1+r)-1 =Real Rate = r = 7.00%

Words:

Nominal Rate = R = 13.00%Inflation Rate = h = (1+R)/(1+r)-1 = 5.6075%Real Rate = r = 7.00%

Words:

If the real rate (the percentage change in buying power) = r = 7.0000% and the Nominal Rate is R = .13.0000%, then the inflation rate = h = 5.6075%.

Nominal Rate = R = 17.00%Inflation Rate = h = 3.20%Real Rate = r = (1+R)/(1+h)-1 =

Words:

Nominal Rate = R = 17.00%Inflation Rate = h = 3.20%Real Rate = r = (1+R)/(1+h)-1 = 0.133720930232558Words: The real return = r = 13.3721%.

Point of View Bondholder1 Bond = Face Value $1,000.00 Coupon Rate 0.075n 2Coupon Rate/nInterest PaymentClean Price (without accrued interest) = ($915.00)Months until Interest is Paid 2Months in 1 periodPartial Interest That belongs to BuyerPart of Interest that belongs to seller of BondInvoice Price

Point of View Bondholder1 Bond = Face Value $1,000.00 Coupon Rate 0.075n 2Coupon Rate/n 0.0375Interest Payment $37.50 Clean Price (without accrued interest) = ($915.00)Months until Interest is Paid 2Months in 1 period 6Partial Interest That belongs to Buyer $12.50 Part of Interest that belongs to seller of Bond $25.00 Invoice Price ($940.00)

Total Face Value = $45,000,000.00 Years to Maturity = 20YTM = 0.075Coupon Rate = 0.075n = 1Coupon PMT =Tax Rate = 0.35Face Value = $1,000.00 Number Needed =Price of All Bonds =20 Year Repayment = Last PMT + FV =

Total Face Value = $45,000,000.00 Years to Maturity = 20YTM = 0.075Zero Couponsn = 1Zero CouponsTax Rate = 0.35Face Value = $1,000.00 Number Needed =Price of 1 Bond =20 Year Repayment = (Face Value)*Number Needed =

Total Face Value = $45,000,000.00 Total Face Value = $45,000,000.00 Years to Maturity = 20 Years to Maturity = 20YTM = 0.075 YTM = 0.075Coupon Rate = 0.075

n = 1 2Coupon PMT = $3,375,000.00 Zero CouponsTax Rate = 0.35 Tax Rate = 0.35Face Value = $1,000.00 Face Value = $1,000.00 Number Needed = $45,000.00 Number Needed = 196,217.04 Price of All Bonds = ($45,000,000.00) Price of 1 Bond = $229.34

($48,375,000.00) $196,217,044.15

PV $45,000,000.00 PV $45,000,000.00

Period Interest Balance0 $45,000,000.00 1 $1,687,500.00 $46,687,500.00 2 $1,750,781.25 $48,438,281.25 3 $1,816,435.55 $50,254,716.80 4 $1,884,551.88 $52,139,268.68 5 $1,955,222.58 $54,094,491.25 6 $2,028,543.42 $56,123,034.67 7 $2,104,613.80 $58,227,648.47 8 $2,183,536.82 $60,411,185.29 9 $2,265,419.45 $62,676,604.74

10 $2,350,372.68 $65,026,977.42 11 $2,438,511.65 $67,465,489.07 12 $2,529,955.84 $69,995,444.91 13 $2,624,829.18 $72,620,274.10 14 $2,723,260.28 $75,343,534.37 15 $2,825,382.54 $78,168,916.91 16 $2,931,334.38 $81,100,251.30 17 $3,041,259.42 $84,141,510.72 18 $3,155,306.65 $87,296,817.37 19 $3,273,630.65 $90,570,448.03 20 $3,396,391.80 $93,966,839.83

n = Semiannual required by law

20 Year Repayment = Last PMT + FV =

20 Year Repayment = (Face Value)*Number Needed =

** Bond Issuer records tax expense (cash flow benefit in) on tax return and bondholder records interest revenue (cash flow disadvantage out) on tax return.

21 $3,523,756.49 $97,490,596.32 22 $3,655,897.36 $101,146,493.68 23 $3,792,993.51 $104,939,487.19 24 $3,935,230.77 $108,874,717.96 25 $4,082,801.92 $112,957,519.89 26 $4,235,907.00 $117,193,426.88 27 $4,394,753.51 $121,588,180.39 28 $4,559,556.76 $126,147,737.16 29 $4,730,540.14 $130,878,277.30 30 $4,907,935.40 $135,786,212.70 31 $5,091,982.98 $140,878,195.67 32 $5,282,932.34 $146,161,128.01 33 $5,481,042.30 $151,642,170.31 34 $5,686,581.39 $157,328,751.70 35 $5,899,828.19 $163,228,579.89 36 $6,121,071.75 $169,349,651.63 37 $6,350,611.94 $175,700,263.57 38 $6,588,759.88 $182,289,023.45 39 $6,835,838.38 $189,124,861.83 40 $7,092,182.32 $196,217,044.15

Book answer shows rounded numbers, but calculation done on un-rounded numbers.$196,217.04

229.337875281001

Coupon Bond OUT Cash Flow Year 1:Cash Flow Benefit to Issuer $2,193,750.00

$590,625.00 Zeroes IN Cash Flow In Year 1:$612,773.44 $1,203,398.44 $635,752.44 $659,593.16 $1,295,345.60 $684,327.90 $709,990.20 $736,614.83 $764,237.89 $792,896.81 $822,630.44 $853,479.08 $885,484.54 $918,690.21 $953,141.10 $988,883.89

$1,025,967.03 $1,064,440.80 $1,104,357.33 $1,145,770.73 $1,188,737.13

** Bond Issuer records tax expense (cash flow benefit in) on tax return and bondholder records interest revenue (cash flow disadvantage out) on tax return.

Notice the cash flow for the zeroes is a cash inflow. This is because of the tax deductibility of the imputed interest expense. That is, the company gets to write off the interest expense for the year, even though the company did not have a cash flow for the interest expense. This reduces the company’s tax liability, which is a cash inflow.

During the life of the bond, the zero generates cash inflows to the firm in the form of the interest tax shield of debt. We should note an important point here: If you find the PV of the cash flows from the coupon bond and the zero coupon bond, they will be the same. This is because of the much larger repayment amount for the zeroes.

H27

Notice the cash flow for the zeroes is a cash inflow. This is because of the tax deductibility of the imputed interest expense. That is, the company gets to write off the interest expense for the year, even though the company did not have a cash flow for the interest expense. This reduces the company’s tax liability, which is a cash inflow. During the life of the bond, the zero generates cash inflows to the firm in the form of the interest tax shield of debt. We should note an important point here: If you find the PV of the cash flows from the coupon bond and the zero coupon bond, they will be the same. This is because of the much larger repayment amount for the zeroes.

$1,233,314.77 $1,279,564.08 $1,327,547.73 $1,377,330.77 $1,428,980.67 $1,482,567.45 $1,538,163.73 $1,595,844.87 $1,655,689.05 $1,717,777.39 $1,782,194.04 $1,849,026.32 $1,918,364.81 $1,990,303.49 $2,064,939.87 $2,142,375.11 $2,222,714.18 $2,306,065.96 $2,392,543.43 $2,482,263.81

Book answer shows rounded numbers, but calculation done on un-rounded numbers.book answer check:

196215.226301561

Notice the cash flow for the zeroes is a cash inflow. This is because of the tax deductibility of the imputed interest expense. That is, the company gets to write off the interest expense for the year, even though the company did not have a cash flow for the interest expense. This reduces the company’s tax liability, which is a cash inflow.

During the life of the bond, the zero generates cash inflows to the firm in the form of the interest tax shield of debt. We should note an important point here: If you find the PV of the cash flows from the coupon bond and the zero coupon bond, they will be the same. This is because of the much larger repayment amount for the zeroes.

[XLS]people.highline.edu · Web viewEffective Annual Yield = (1+YTM/n)^n -1 = Words: Bond Value =...

Documents

Transcript of [XLS]people.highline.edu · Web viewEffective Annual Yield = (1+YTM/n)^n -1 = Words: Bond Value =...