Bond Basics
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SOME BOND BASICS To illustrate: • Accrued interest • Bond pricing • Bond yield calculations Ultimately to ask: • Why is the yield on the Pagenet bond so much higher than that of the GE bond?
Chapter 11, Some bond basics
page 1
PAGENET BOND
Chapter 11, Some bond basics
page 2
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
B
C
D
E
F
G
H
I
PAGENET BOND Settlement date (current date) Bond coupon Price Maturity Date of last interest payment Date of next interest payment Days from last interest to settlement Days from last interest to next interest Invoice price calculation Price Accrued interest Invoice price
96.7779 0.0724 <-- Should be (8.875%/2 * 3 days / 184)*100 96.8503 Note: Bloomber calculates accrued interest based on 30 day months: =3/180*8.875/2. This gives 0.073958333
Yield calculation
Chapter 11, Some bond basics
4-Aug-97 8.875% <-- Interest paid semiannually 96.777949 1-Feb-06 1-Aug-97 1-Feb-98 3 184
Date 4-Aug-97 1-Feb-98 1-Aug-98 1-Feb-99 1-Aug-99 1-Feb-00 1-Aug-00 1-Feb-01 1-Aug-01 1-Feb-02 1-Aug-02 1-Feb-03 1-Aug-03 1-Feb-04 1-Aug-04 1-Feb-05 1-Aug-05 1-Feb-06
Payment -96.8503 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 104.4375
Yield to maturity XIRR YIELD
9.6460% <-- =XIRR(B22:B39,A22:A39) 9.4347% <-- =YIELD(B4,B7,B5,B6,100,2)
Notes XIRR is the actual IRR of the payments, taking into account the actual bond payment dates YIELD is the standardized yield assuming 30 day months (360 day years)
Current yield
9.170% <-- =B5*100/B6
page 3
GENERAL ELECTRIC CAPITAL CORP. BOND
Chapter 11, Some bond basics
page 4
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
B
C
D
E
F
G
H
I
GE BOND Settlement date (current date) Bond coupon Price Maturity Date of last interest payment Date of next interest payment Days from last interest to settlement Days from last interest to next interest
4-Aug-97 5.880% <-- Interest paid semiannually 95.0117 15-Sep-08 15-Mar-97 15-Sep-97 142 184
Invoice price calculation Price Accrued interest Invoice price
95.0117 2.2689 <-- Should be 5.880%/2 * 142 days / 184 97.2806 Note: Bloomberg calculates accrued interest based on 30 day months: =139/180*5.88/2. This gives 2.270333333
Yield calculation Date
Chapter 11, Some bond basics
Payment 4-Aug-97 15-Sep-97 15-Mar-98 15-Sep-98 15-Mar-99 15-Sep-99 15-Mar-00 15-Sep-00 15-Mar-01 15-Sep-01 15-Mar-02 15-Sep-02 15-Mar-03 15-Sep-03 15-Mar-04 15-Sep-04 15-Mar-05 15-Sep-05 15-Mar-06 15-Sep-06 15-Mar-07 15-Sep-07 15-Mar-08 15-Sep-08
-97.2806 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 102.94
Yield to maturity XIRR YIELD
6.6181% <-- =XIRR(B22:B45,A22:A45) 6.5167% <-- =YIELD(B4,B7,B5,B6,100,2)
Notes XIRR is the actual IRR of the payments, taking into account the actual bond payment dates YIELD is the standardized yield assuming 30 day months (360 day years)
Current yield
6.189% <-- =B5*100/B6
page 5
Why is the YTM of Pagenet = 9.6460% >> 6.6181%? • GE’s bond is for 11 years, Pagenet’s is for 8.5 years. Downsloping term structure? This is unlikely, as the following graph shows (Pagenet is rate B; the B-yield curve is not reported on Bloomberg).
Chapter 11, Some bond basics
page 6
• Risk premium? GE’s bond is rated AAA, Pagenet is rated B. This is surely the primary reason for the difference in the yields. NOTE: The YTM is not an expected return, it is an IRR based on the promised payments. This is unlike any other return we calculate in finance! All costs of capital are based on expected returns. NOTE: In second set of slides we show that: • Expected Pagenet bond yield = 7.392% << 9.457% = YTM
Chapter 11, Some bond basics
page 7
TWO PROBLEMS 1. Calculate the COST OF DEBT in order to calculate the WACC—for this you need the EXPECTED BOND RETURN. NOTE: It may not matter that much: E D WACC = E (rE ) + E (rD ) * (1 − t C ) . E+D E+D D If = 20%, t C = 40% . Then whether Pagenet’s E+D E (rD ) = 95% . or 7.4% will change the WACC by ∆WACC = [ 9.5% − 7.4%] * (1 − t C ) = 21% . * 0.6 * 0.2 = 0.25%
D E + D.
This is well within the usual bounds of error for most WACCs! Chapter 11, Some bond basics
page 8
2. Value a bond. Here there are two approaches: • Standard finance approach: Discount expected bond payments at expected (risk-adjusted) bond return. This gets us back to the problem of YTM versus expected bond return. • Standard industry approach: Discount promised bond payments at rating-adjusted YTM
Chapter 11, Some bond basics
page 9
Chapter 11, Some bond basics
page 1
PAGENET BOND
Chapter 11, Some bond basics
page 2
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
B
C
D
E
F
G
H
I
PAGENET BOND Settlement date (current date) Bond coupon Price Maturity Date of last interest payment Date of next interest payment Days from last interest to settlement Days from last interest to next interest Invoice price calculation Price Accrued interest Invoice price
96.7779 0.0724 <-- Should be (8.875%/2 * 3 days / 184)*100 96.8503 Note: Bloomber calculates accrued interest based on 30 day months: =3/180*8.875/2. This gives 0.073958333
Yield calculation
Chapter 11, Some bond basics
4-Aug-97 8.875% <-- Interest paid semiannually 96.777949 1-Feb-06 1-Aug-97 1-Feb-98 3 184
Date 4-Aug-97 1-Feb-98 1-Aug-98 1-Feb-99 1-Aug-99 1-Feb-00 1-Aug-00 1-Feb-01 1-Aug-01 1-Feb-02 1-Aug-02 1-Feb-03 1-Aug-03 1-Feb-04 1-Aug-04 1-Feb-05 1-Aug-05 1-Feb-06
Payment -96.8503 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 4.4375 104.4375
Yield to maturity XIRR YIELD
9.6460% <-- =XIRR(B22:B39,A22:A39) 9.4347% <-- =YIELD(B4,B7,B5,B6,100,2)
Notes XIRR is the actual IRR of the payments, taking into account the actual bond payment dates YIELD is the standardized yield assuming 30 day months (360 day years)
Current yield
9.170% <-- =B5*100/B6
page 3
GENERAL ELECTRIC CAPITAL CORP. BOND
Chapter 11, Some bond basics
page 4
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
B
C
D
E
F
G
H
I
GE BOND Settlement date (current date) Bond coupon Price Maturity Date of last interest payment Date of next interest payment Days from last interest to settlement Days from last interest to next interest
4-Aug-97 5.880% <-- Interest paid semiannually 95.0117 15-Sep-08 15-Mar-97 15-Sep-97 142 184
Invoice price calculation Price Accrued interest Invoice price
95.0117 2.2689 <-- Should be 5.880%/2 * 142 days / 184 97.2806 Note: Bloomberg calculates accrued interest based on 30 day months: =139/180*5.88/2. This gives 2.270333333
Yield calculation Date
Chapter 11, Some bond basics
Payment 4-Aug-97 15-Sep-97 15-Mar-98 15-Sep-98 15-Mar-99 15-Sep-99 15-Mar-00 15-Sep-00 15-Mar-01 15-Sep-01 15-Mar-02 15-Sep-02 15-Mar-03 15-Sep-03 15-Mar-04 15-Sep-04 15-Mar-05 15-Sep-05 15-Mar-06 15-Sep-06 15-Mar-07 15-Sep-07 15-Mar-08 15-Sep-08
-97.2806 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 2.94 102.94
Yield to maturity XIRR YIELD
6.6181% <-- =XIRR(B22:B45,A22:A45) 6.5167% <-- =YIELD(B4,B7,B5,B6,100,2)
Notes XIRR is the actual IRR of the payments, taking into account the actual bond payment dates YIELD is the standardized yield assuming 30 day months (360 day years)
Current yield
6.189% <-- =B5*100/B6
page 5
Why is the YTM of Pagenet = 9.6460% >> 6.6181%? • GE’s bond is for 11 years, Pagenet’s is for 8.5 years. Downsloping term structure? This is unlikely, as the following graph shows (Pagenet is rate B; the B-yield curve is not reported on Bloomberg).
Chapter 11, Some bond basics
page 6
• Risk premium? GE’s bond is rated AAA, Pagenet is rated B. This is surely the primary reason for the difference in the yields. NOTE: The YTM is not an expected return, it is an IRR based on the promised payments. This is unlike any other return we calculate in finance! All costs of capital are based on expected returns. NOTE: In second set of slides we show that: • Expected Pagenet bond yield = 7.392% << 9.457% = YTM
Chapter 11, Some bond basics
page 7
TWO PROBLEMS 1. Calculate the COST OF DEBT in order to calculate the WACC—for this you need the EXPECTED BOND RETURN. NOTE: It may not matter that much: E D WACC = E (rE ) + E (rD ) * (1 − t C ) . E+D E+D D If = 20%, t C = 40% . Then whether Pagenet’s E+D E (rD ) = 95% . or 7.4% will change the WACC by ∆WACC = [ 9.5% − 7.4%] * (1 − t C ) = 21% . * 0.6 * 0.2 = 0.25%
D E + D.
This is well within the usual bounds of error for most WACCs! Chapter 11, Some bond basics
page 8
2. Value a bond. Here there are two approaches: • Standard finance approach: Discount expected bond payments at expected (risk-adjusted) bond return. This gets us back to the problem of YTM versus expected bond return. • Standard industry approach: Discount promised bond payments at rating-adjusted YTM
Chapter 11, Some bond basics
page 9
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