Transcript Chapter 12 (PPTX)

Principles of Investing
FIN 330
CHAPTER 12
Bond Valuation
Dr. David P. Echevarria
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Slide 1
BOND VALUATION
Special Section on BA II Plus
Purchasing Power
Dr. David P. Echevarria
Risk Management
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Slide 2
FIVE BOND PRICING THEOREMS
1. Bond prices move inversely to changes in
interest rates
2. The longer the maturity of a bond, the more
price sensitive the bond
3. The price sensitivity of bonds to changes in
interest rates increases as maturity increases, but
at a decreasing rate
4. Bonds with lower coupon rates are more price
sensitive
5. Yield decreases have a greater impact on bond
prices than similar yield increases
Dr. David P. Echevarria
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Slide 3
TYPES OF YIELD
• Coupon Yield
– The rate the bond promises to pay
• Current Yield
– The [annual] coupon divided by the current
price
• Yield to Maturity
– The rate returned if held to maturity
• Yield To First Call
– The adjusted YTM if bonds are called early
Dr. David P. Echevarria
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Slide 4
start here 3/20
FINANCIAL CALCULATORS &
BOND PRICES
• The value of a bond (VB) is a combination
of a present value of an annuity (the present
value of the coupons to be received) and the
present value of the face value of the bond.
• VB = $Coupon * PVIFA + $Face * PVIF
N
CFn
VB  
n
n 1 (1  k b )
Dr. David P. Echevarria
for n  1, 2, 3, ..., N
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Slide 5
FINANCIAL CALCULATORS &
BOND PRICES [BA II Plus]
• For example, suppose we have a bond paying a
12% coupon rate ($120), paid semi-annually. The
bond matures in 20 years and has a face value of
$1,000. If the current market rate (YTM) is 9%,
how much should this bond sell for (value)?
• In this type of problem we will use all five TVM
keys; [ N ] [ I/Y ] [ PV ] [ PMT ] [ FV ]
Dr. David P. Echevarria
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Slide 6
FINANCIAL CALCULATORS &
BOND PRICES [BA II Plus]
• The bond pays coupons (interest) twice a
year (semi-annual): We set the periods per
year (P/Y) and (C/Y) to 2.
• The 12% coupon rate ( $120 per year) is
paid in two [PMT=] $60 installments.
• The bond will have a maturity value [FV] of
$1000.00.
• The current market rate is [I/Y] 9% (the
required YTM for bonds in this risk class).
Dr. David P. Echevarria
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Slide 7
FINANCIAL CALCULATORS &
BOND PRICES [BA II Plus]
A. BA II PLUS Solution
1. ENTER 20 [2nd] [N], [N]
2. ENTER 9 [I/Y]
3. ENTER 60 [PMT]
4. ENTER 1000 [FV]
5. PRESS [CPT] [PV]
N = 40.00
I/Y = 9.00
PMT = 60.00
FV = 1,000.00
PV =
-1,276.02
We would have to pay $1,276.02 to buy
this bond today.
Dr. David P. Echevarria
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Slide 8
FINANCIAL CALCULATORS &
BOND PRICES [BA II Plus]
B. Playing "what if" with Several Different
YTM Values.
– For example, suppose the YTM is 11 percent;
"I/Y" = 11. Enter 11, press [I/Y], then [CPT] ,
then [PV]; -1,080.23
– If the YTM is 12%; enter 12, press [I/Y], then
[CPT], [PV]; 1,000.00 or $1,000.00 *
* If YTM = Coupon Rate, then PV = - FV
– If the YTM is 15%, the price is $811.08
Dr. David P. Echevarria
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Slide 9
Yield to First Call
• Callable Bonds Pay Premiums
– The premium results in a Yield-to-First-Call
different from the Coupon Rate.
– Calling a 30-year bond 5% coupon bond four
years after issuance @ 107.50.
–N=4
– PV = -1000
– PMT = 50
– FV = 1075.00
– CPT I/Y = 6.70%
Dr. David P. Echevarria
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Slide 10
Final Observations on Bonds
• When bonds sell at prices greater than their
maturity or Face values, the are said to be
selling at a premium.
• When bonds sell at prices less than their
maturity or Face values, the are said to be
selling at a discount.
• When bonds sell at prices equal to their
maturity or Face values, the are said to be
selling at a par.
Dr. David P. Echevarria
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Slide 11
HOMEWORK
• Questions: 1, 3, 6, 7
• Problems:10, 11, 12
Dr. David P. Echevarria
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Slide 12