Ch,7,
Valuation
and
Characteristics
of
? 2002,Prentice Hall,Inc,
Characteristics of Bonds
? Bonds pay fixed coupon (interest)
payments at fixed intervals (usually
every 6 months) and pay the par
value at maturity,
Characteristics of Bonds
? Bonds pay fixed coupon (interest)
payments at fixed intervals (usually
every 6 months) and pay the par
value at maturity,
0 1 2,,, n
$I $I $I $I $I $I+$M
example,ATT 6 1/2 29
? par value = $1000
? coupon = 6.5% of par value per year,
= $65 per year ($32.50 every 6 months),
? maturity = 28 years (matures in 2029),
? issued by AT&T,
example,ATT 6 1/2 29
? par value = $1000
? coupon = 6.5% of par value per year,
= $65 per year ($32.50 every 6 months),
? maturity = 28 years (matures in 2029),
? issued by AT&T,
0 1 2 … 28
$32.50 $32.50 $32.50 $32.50 $32.50 $32.50+$1000
Types of Bonds
? Debentures - unsecured bonds,
? Subordinated debentures - unsecured
“junior” debt,
? Mortgage bonds - secured bonds,
? Zeros - bonds that pay only par value at
maturity; no coupons,
? Junk bonds - speculative or below-
investment grade bonds; rated BB and
below,High-yield bonds,
Types of Bonds
? Eurobonds - bonds denominated in
one currency and sold in another
country,(Borrowing overseas),
? example - suppose Disney decides to sell
$1,000 bonds in France,These are U.S,
denominated bonds trading in a foreign
country,Why do this?
Types of Bonds
? Eurobonds - bonds denominated in
one currency and sold in another
country,(Borrowing overseas),
? example - suppose Disney decides to sell
$1,000 bonds in France,These are U.S,
denominated bonds trading in a foreign
country,Why do this?
– If borrowing rates are lower in France,
Types of Bonds
? Eurobonds - bonds denominated in
one currency and sold in another
country,(Borrowing overseas),
? example - suppose Disney decides to sell
$1,000 bonds in France,These are U.S,
denominated bonds trading in a foreign
country,Why do this?
– If borrowing rates are lower in France,
– To avoid SEC regulations,
The Bond Indenture
? The bond contract between the firm
and the trustee representing the
bondholders,
? Lists all of the bond’s features,
coupon,par value,maturity,etc,
? Lists restrictive provisions which are
designed to protect bondholders,
? Describes repayment provisions,
Value
? Book Value,value of an asset as shown on
a firm’s balance sheet; historical cost,
? Liquidation value,amount that could be
received if an asset were sold individually,
? Market value,observed value of an asset
in the marketplace; determined by supply
and demand,
? Intrinsic value,economic or fair value of
an asset; the present value of the asset’s
expected future cash flows,
Security Valuation
? In general,the intrinsic value of an
asset = the present value of the stream
of expected cash flows discounted at
an appropriate required rate of
return,
? Can the intrinsic value of an asset
differ from its market value?
Valuation
? Ct = cash flow to be received at time t,
? k = the investor’s required rate of return,
? V = the intrinsic value of the asset,
V =
t = 1
n S $C
t
(1 + k)t
Bond Valuation
? Discount the bond’s cash flows at
the investor’s required rate of
return,
Bond Valuation
? Discount the bond’s cash flows at
the investor’s required rate of
return,
– the coupon payment stream (an
annuity),
Bond Valuation
? Discount the bond’s cash flows at
the investor’s required rate of
return,
– the coupon payment stream (an
annuity),
– the par value payment (a single
sum),
Bond Valuation
Vb = $It (PVIFA kb,n) + $M (PVIF kb,n)
$It $M
(1 + kb)t (1 + kb)n Vb = +
n
t = 1
S
Bond Example
? Suppose our firm decides to issue 20-year
bonds with a par value of $1,000 and
annual coupon payments,The return on
other corporate bonds of similar risk is
currently 12%,so we decide to offer a 12%
coupon interest rate,
? What would be a fair price for these
bonds?
0 1 2 3,,, 20
1000
120 120 120,,, 120
P/YR = 1
N = 20
I%YR = 12
FV = 1,000
PMT = 120
Solve PV = -$1,000
Note,If the coupon rate = discount
rate,the bond will sell for par value,
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,12,20 ) + 1000 (PVIF,12,20 )
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,12,20 ) + 1000 (PVIF,12,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,12,20 ) + 1000 (PVIF,12,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
PV = 120 1 - (1.12 )20 + 1000/ (1.12) 20 = $1000
,12
? Suppose interest rates fall
immediately after we issue the
bonds,The required return on
bonds of similar risk drops to 10%,
? What would happen to the bond’s
intrinsic value?
P/YR = 1
Mode = end
N = 20
I%YR = 10
PMT = 120
FV = 1000
Solve PV = -$1,170.27
P/YR = 1
Mode = end
N = 20
I%YR = 10
PMT = 120
FV = 1000
Solve PV = -$1,170.27
Note,If the coupon rate > discount rate,the bond will sell for a premium,
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,10,20 ) + 1000 (PVIF,10,20 )
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,10,20 ) + 1000 (PVIF,10,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,10,20 ) + 1000 (PVIF,10,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
PV = 120 1 - (1.10 )20 + 1000/ (1.10) 20 = $1,170.27
,10
? Suppose interest rates rise
immediately after we issue the
bonds,The required return on
bonds of similar risk rises to 14%,
? What would happen to the bond’s
intrinsic value?
P/YR = 1
Mode = end
N = 20
I%YR = 14
PMT = 120
FV = 1000
Solve PV = -$867.54
P/YR = 1
Mode = end
N = 20
I%YR = 14
PMT = 120
FV = 1000
Solve PV = -$867.54
Note,If the coupon rate < discount rate,
the bond will sell for a discount,
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,14,20 ) + 1000 (PVIF,14,20 )
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,14,20 ) + 1000 (PVIF,14,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,14,20 ) + 1000 (PVIF,14,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
PV = 120 1 - (1.14 )20 + 1000/ (1.14) 20 = $867.54
,14
Suppose coupons are semi-annual
P/YR = 2
Mode = end
N = 40
I%YR = 14
PMT = 60
FV = 1000
Solve PV = -$866.68
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 60 (PVIFA,14,20 ) + 1000 (PVIF,14,20 )
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 60 (PVIFA,14,20 ) + 1000 (PVIF,14,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 60 (PVIFA,14,20 ) + 1000 (PVIF,14,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
PV = 60 1 - (1.07 )40 + 1000 / (1.07) 40 = $866.68
,07
Yield To Maturity
? The expected rate of return on a
bond,
? The rate of return investors earn on
a bond if they hold it to maturity,
Yield To Maturity
? The expected rate of return on a
bond,
? The rate of return investors earn on
a bond if they hold it to maturity,
$It $M
(1 + kb)t (1 + kb)n P0 = +
n
t = 1
S
YTM Example
? Suppose we paid $898.90 for a
$1,000 par 10% coupon bond
with 8 years to maturity and
semi-annual coupon payments,
? What is our yield to maturity?
P/YR = 2
Mode = end
N = 16
PV = -898.90
PMT = 50
FV = 1000
Solve I%YR = 12%
YTM Example
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
898.90 = 50 (PVIFA k,16 ) + 1000 (PVIF k,16 )
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
898.90 = 50 (PVIFA k,16 ) + 1000 (PVIF k,16 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
898.90 = 50 (PVIFA k,16 ) + 1000 (PVIF k,16 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
898.90 = 50 1 - (1 + i )16 + 1000 / (1 + i) 16
i
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
898.90 = 50 (PVIFA k,16 ) + 1000 (PVIF k,16 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
898.90 = 50 1 - (1 + i )16 + 1000 / (1 + i) 16
i solve using trial and error
Zero Coupon Bonds
? No coupon interest payments,
? The bond holder’s return is
determined entirely by the
price discount,
Zero Example
? Suppose you pay $508 for a zero
coupon bond that has 10 years
left to maturity,
? What is your yield to maturity?
Zero Example
? Suppose you pay $508 for a zero
coupon bond that has 10 years
left to maturity,
? What is your yield to maturity?
0 10
-$508 $1000
Zero Example
P/YR = 1
Mode = End
N = 10
PV = -508
FV = 1000
Solve,I%YR = 7%
Mathematical Solution,
PV = FV (PVIF i,n )
508 = 1000 (PVIF i,10 )
,508 = (PVIF i,10 ) [use PVIF table]
PV = FV /(1 + i) 10
508 = 1000 /(1 + i)10
1.9685 = (1 + i)10
i = 7%
Zero Example
0 10
PV = -508 FV = 1000
The Financial Pages,Corporate Bonds
Cur Net
Yld Vol Close Chg
Polaroid 11 1/2 06 19.3 395 59 3/4,.,
? What is the yield to maturity for this bond?
P/YR = 2,N = 10,FV = 1000,
PV = $-597.50,
PMT = 57.50
? Solve,I/YR = 26.48%
The Financial Pages,Corporate Bonds
Cur Net
Yld Vol Close Chg
HewlPkd zr 17,.,20 51 1/2 +1
? What is the yield to maturity for this bond?
P/YR = 1,N = 16,FV = 1000,
PV = $-515,
PMT = 0
? Solve,I/YR = 4.24%
The Financial Pages,Treasury Bonds
Maturity Ask
Rate Mo/Yr Bid Asked Chg Yld
9 Nov 18 139:14 139:20 -34 5.46
? What is the yield to maturity for this
Treasury bond? (assume 35 half years)
P/YR = 2,N = 35,FV = 1000,
PMT = 45,
PV = - 1,396.25 (139.625% of par)
? Solve,I/YR = 5.457%
Valuation
and
Characteristics
of
? 2002,Prentice Hall,Inc,
Characteristics of Bonds
? Bonds pay fixed coupon (interest)
payments at fixed intervals (usually
every 6 months) and pay the par
value at maturity,
Characteristics of Bonds
? Bonds pay fixed coupon (interest)
payments at fixed intervals (usually
every 6 months) and pay the par
value at maturity,
0 1 2,,, n
$I $I $I $I $I $I+$M
example,ATT 6 1/2 29
? par value = $1000
? coupon = 6.5% of par value per year,
= $65 per year ($32.50 every 6 months),
? maturity = 28 years (matures in 2029),
? issued by AT&T,
example,ATT 6 1/2 29
? par value = $1000
? coupon = 6.5% of par value per year,
= $65 per year ($32.50 every 6 months),
? maturity = 28 years (matures in 2029),
? issued by AT&T,
0 1 2 … 28
$32.50 $32.50 $32.50 $32.50 $32.50 $32.50+$1000
Types of Bonds
? Debentures - unsecured bonds,
? Subordinated debentures - unsecured
“junior” debt,
? Mortgage bonds - secured bonds,
? Zeros - bonds that pay only par value at
maturity; no coupons,
? Junk bonds - speculative or below-
investment grade bonds; rated BB and
below,High-yield bonds,
Types of Bonds
? Eurobonds - bonds denominated in
one currency and sold in another
country,(Borrowing overseas),
? example - suppose Disney decides to sell
$1,000 bonds in France,These are U.S,
denominated bonds trading in a foreign
country,Why do this?
Types of Bonds
? Eurobonds - bonds denominated in
one currency and sold in another
country,(Borrowing overseas),
? example - suppose Disney decides to sell
$1,000 bonds in France,These are U.S,
denominated bonds trading in a foreign
country,Why do this?
– If borrowing rates are lower in France,
Types of Bonds
? Eurobonds - bonds denominated in
one currency and sold in another
country,(Borrowing overseas),
? example - suppose Disney decides to sell
$1,000 bonds in France,These are U.S,
denominated bonds trading in a foreign
country,Why do this?
– If borrowing rates are lower in France,
– To avoid SEC regulations,
The Bond Indenture
? The bond contract between the firm
and the trustee representing the
bondholders,
? Lists all of the bond’s features,
coupon,par value,maturity,etc,
? Lists restrictive provisions which are
designed to protect bondholders,
? Describes repayment provisions,
Value
? Book Value,value of an asset as shown on
a firm’s balance sheet; historical cost,
? Liquidation value,amount that could be
received if an asset were sold individually,
? Market value,observed value of an asset
in the marketplace; determined by supply
and demand,
? Intrinsic value,economic or fair value of
an asset; the present value of the asset’s
expected future cash flows,
Security Valuation
? In general,the intrinsic value of an
asset = the present value of the stream
of expected cash flows discounted at
an appropriate required rate of
return,
? Can the intrinsic value of an asset
differ from its market value?
Valuation
? Ct = cash flow to be received at time t,
? k = the investor’s required rate of return,
? V = the intrinsic value of the asset,
V =
t = 1
n S $C
t
(1 + k)t
Bond Valuation
? Discount the bond’s cash flows at
the investor’s required rate of
return,
Bond Valuation
? Discount the bond’s cash flows at
the investor’s required rate of
return,
– the coupon payment stream (an
annuity),
Bond Valuation
? Discount the bond’s cash flows at
the investor’s required rate of
return,
– the coupon payment stream (an
annuity),
– the par value payment (a single
sum),
Bond Valuation
Vb = $It (PVIFA kb,n) + $M (PVIF kb,n)
$It $M
(1 + kb)t (1 + kb)n Vb = +
n
t = 1
S
Bond Example
? Suppose our firm decides to issue 20-year
bonds with a par value of $1,000 and
annual coupon payments,The return on
other corporate bonds of similar risk is
currently 12%,so we decide to offer a 12%
coupon interest rate,
? What would be a fair price for these
bonds?
0 1 2 3,,, 20
1000
120 120 120,,, 120
P/YR = 1
N = 20
I%YR = 12
FV = 1,000
PMT = 120
Solve PV = -$1,000
Note,If the coupon rate = discount
rate,the bond will sell for par value,
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,12,20 ) + 1000 (PVIF,12,20 )
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,12,20 ) + 1000 (PVIF,12,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,12,20 ) + 1000 (PVIF,12,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
PV = 120 1 - (1.12 )20 + 1000/ (1.12) 20 = $1000
,12
? Suppose interest rates fall
immediately after we issue the
bonds,The required return on
bonds of similar risk drops to 10%,
? What would happen to the bond’s
intrinsic value?
P/YR = 1
Mode = end
N = 20
I%YR = 10
PMT = 120
FV = 1000
Solve PV = -$1,170.27
P/YR = 1
Mode = end
N = 20
I%YR = 10
PMT = 120
FV = 1000
Solve PV = -$1,170.27
Note,If the coupon rate > discount rate,the bond will sell for a premium,
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,10,20 ) + 1000 (PVIF,10,20 )
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,10,20 ) + 1000 (PVIF,10,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,10,20 ) + 1000 (PVIF,10,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
PV = 120 1 - (1.10 )20 + 1000/ (1.10) 20 = $1,170.27
,10
? Suppose interest rates rise
immediately after we issue the
bonds,The required return on
bonds of similar risk rises to 14%,
? What would happen to the bond’s
intrinsic value?
P/YR = 1
Mode = end
N = 20
I%YR = 14
PMT = 120
FV = 1000
Solve PV = -$867.54
P/YR = 1
Mode = end
N = 20
I%YR = 14
PMT = 120
FV = 1000
Solve PV = -$867.54
Note,If the coupon rate < discount rate,
the bond will sell for a discount,
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,14,20 ) + 1000 (PVIF,14,20 )
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,14,20 ) + 1000 (PVIF,14,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 120 (PVIFA,14,20 ) + 1000 (PVIF,14,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
PV = 120 1 - (1.14 )20 + 1000/ (1.14) 20 = $867.54
,14
Suppose coupons are semi-annual
P/YR = 2
Mode = end
N = 40
I%YR = 14
PMT = 60
FV = 1000
Solve PV = -$866.68
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 60 (PVIFA,14,20 ) + 1000 (PVIF,14,20 )
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 60 (PVIFA,14,20 ) + 1000 (PVIF,14,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
PV = 60 (PVIFA,14,20 ) + 1000 (PVIF,14,20 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
PV = 60 1 - (1.07 )40 + 1000 / (1.07) 40 = $866.68
,07
Yield To Maturity
? The expected rate of return on a
bond,
? The rate of return investors earn on
a bond if they hold it to maturity,
Yield To Maturity
? The expected rate of return on a
bond,
? The rate of return investors earn on
a bond if they hold it to maturity,
$It $M
(1 + kb)t (1 + kb)n P0 = +
n
t = 1
S
YTM Example
? Suppose we paid $898.90 for a
$1,000 par 10% coupon bond
with 8 years to maturity and
semi-annual coupon payments,
? What is our yield to maturity?
P/YR = 2
Mode = end
N = 16
PV = -898.90
PMT = 50
FV = 1000
Solve I%YR = 12%
YTM Example
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
898.90 = 50 (PVIFA k,16 ) + 1000 (PVIF k,16 )
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
898.90 = 50 (PVIFA k,16 ) + 1000 (PVIF k,16 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
898.90 = 50 (PVIFA k,16 ) + 1000 (PVIF k,16 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
898.90 = 50 1 - (1 + i )16 + 1000 / (1 + i) 16
i
Bond Example
Mathematical Solution,
PV = PMT (PVIFA k,n ) + FV (PVIF k,n )
898.90 = 50 (PVIFA k,16 ) + 1000 (PVIF k,16 )
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
898.90 = 50 1 - (1 + i )16 + 1000 / (1 + i) 16
i solve using trial and error
Zero Coupon Bonds
? No coupon interest payments,
? The bond holder’s return is
determined entirely by the
price discount,
Zero Example
? Suppose you pay $508 for a zero
coupon bond that has 10 years
left to maturity,
? What is your yield to maturity?
Zero Example
? Suppose you pay $508 for a zero
coupon bond that has 10 years
left to maturity,
? What is your yield to maturity?
0 10
-$508 $1000
Zero Example
P/YR = 1
Mode = End
N = 10
PV = -508
FV = 1000
Solve,I%YR = 7%
Mathematical Solution,
PV = FV (PVIF i,n )
508 = 1000 (PVIF i,10 )
,508 = (PVIF i,10 ) [use PVIF table]
PV = FV /(1 + i) 10
508 = 1000 /(1 + i)10
1.9685 = (1 + i)10
i = 7%
Zero Example
0 10
PV = -508 FV = 1000
The Financial Pages,Corporate Bonds
Cur Net
Yld Vol Close Chg
Polaroid 11 1/2 06 19.3 395 59 3/4,.,
? What is the yield to maturity for this bond?
P/YR = 2,N = 10,FV = 1000,
PV = $-597.50,
PMT = 57.50
? Solve,I/YR = 26.48%
The Financial Pages,Corporate Bonds
Cur Net
Yld Vol Close Chg
HewlPkd zr 17,.,20 51 1/2 +1
? What is the yield to maturity for this bond?
P/YR = 1,N = 16,FV = 1000,
PV = $-515,
PMT = 0
? Solve,I/YR = 4.24%
The Financial Pages,Treasury Bonds
Maturity Ask
Rate Mo/Yr Bid Asked Chg Yld
9 Nov 18 139:14 139:20 -34 5.46
? What is the yield to maturity for this
Treasury bond? (assume 35 half years)
P/YR = 2,N = 35,FV = 1000,
PMT = 45,
PV = - 1,396.25 (139.625% of par)
? Solve,I/YR = 5.457%
