Bonds
Definition and valuation
Lecture plan:
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Foreword
Definitions & concepts
Valuation and YTM calculation
More bond-related concepts
Concept definition
Bonds = corporate debt
…corporate bonds, that is
Bond: The concept
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debt instrument
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the issuer of the bond borrows money
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interest, aka coupon is paid periodically
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principal aka face value is repaid at maturity
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Bonds: what they mean to the firm
• do not represent ownership interest in the firm
• payment of interest is tax-deductible
• unpaid debt is a liability of the firm
More definitions
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coupon: fixed amount of annual or semi-annual interest
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face value (par): usually $100, $1,000, or $10,000
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coupon rate: coupon/face value
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yield-to-maturity (YTM) the rate that makes the PV of bond’s
cash flows equal its current price.
Yield-to-maturity - Exemplification
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Case 1: Xcorp's 11%, 20 yr. bond,currently sells for $859.5. The
present value of the cash flows from this bond is:
– PV = 110/(1+r) + 110/(1+r)2 + .....+ 110/(1+r)20 +1,000/(1+r)20
– $895.5 = 110/(1+r) + 110/(1+r)2 + .....+ 110/(1+r)20 +1,000/(1+r)20
– r = 13%
How to solve for r aka YTM
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use a financial calculator, or
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use an approximation formula:
– ytm ~ [coupon + (face value - price)/t] / [(price + face value)/2]
– ytm ~ [110 + (1,000 - 859.5)/20] / [(859.5 + 1,000)/2]
Yield-to-maturity - Exemplification (con’t)‫‏‬
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Case 2: Xcorp's 11%, 20 yr. bond,currently sells for $1.182.6
The present value of the cash flows from this bond is:
– PV = 110/(1+r) + 110/(1+r)2 + .....+ 110/(1+r)20 +1,000/(1+r)20
– $1,182.6 = 110/(1+r) + 110/(1+r)2 + .....+ 110/(1+r)20 +1,000/(1+r)20
– r = 9%
Yield-to-maturity - Exemplification (con’t)‫‏‬
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Case 3: Xcorp's 11%, 20 yr. bond,currently sells for $1.000. The
present value of the cash flows from this bond is:
– PV = 110/(1+r) + 110/(1+r)2 + .....+ 110/(1+r)20 +1,000/(1+r)20
– $1.000 = 110/(1+r) + 110/(1+r)2 + .....+ 110/(1+r)20 +1,000/(1+r)20
– r = 11%
Yield-to-maturity - Exemplification (con’t)‫‏‬
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Case 4: Tcorp. 14%, semi-annual coupon, 7-yr. bond, currently
sells for $917.56:
– Set $ 917.56 = 70PVA(r, t=14) + 1,000PV(r, t=14)
– r ~ 8%
– Hence, YTM = 2(8%) = 16% (remember to annualize)
A pattern emerges:
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YTM (interest rates) and bond prices move inversely:
– when YTM < CR, then P > $1,000 (premium bond)‫‏‬
– when YTM > CR, then P < $1,000 (discount bond)‫‏‬
– when YTM = CR, then P = $1,000 (at par bond)‫‏‬
Attention!
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These are set from the
beginning:
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These change as a result of
market forces:
– coupon rate
– YTM
– face value
– bond price
– maturity
The Economic Meaning of the Yield-to-Maturity
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the YTM is the annual rate of return one will earn if:
– one holds the bond until maturity, and
– one reinvests all coupon at the YTM rate
Other bond-related concepts
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Indenture: written agreement between the corporation and the
lender detailing the terms of the debt issue
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Protective covenant: part of the indenture limiting certain
transactions that can be taken by the company, in order to
protect the bondholders
– Positive covenants
– Negative covenants
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Bond trustee: makes sure that the terms of the indenture are
obeyed
Exemplification - Covenants
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As a covenant under the new credit facility, Cambior must comply with a
Mandatory Hedging Program. This program includes an undertaking to
ensure that Cambior's commitments to deliver gold will not, at anytime,
exceed 90% of its total proven and probable recoverable reserves. It
further requires that,after March 31, Cambior will be required to have
hedges in place on a minimum of 70% of the forecasted loan life
production in order to establish an average minimum gold price of US
$495/oz on all production, including the impact of the prepaid gold forward
sale agreement. As part of the Mandatory Hedging Program, Cambior will
have the right to roll forward its contracts up to the final maturity date of
the loan. In addition, the hedging facility will not be subject to margin calls.
Cambior will issue to the banking syndicate 1.3 million warrants to
purchase common shares of Cambior at Cdn $0.56 per share, a 25%
premium over the closing price of Cambior's shares on the Toronto Stock
Exchange on November 29. Cambior currently has 75,562,871 common
shares outstanding.The warrants are exercisable at any time on or before
December 31, 200x. The issue of warrants remains subject to regulatory
approval.
Other bond-related concepts (con’t)‫‏‬
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Sinking fund: account managed by the bond trustee for early
bond redemption
Bond rating
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reflects the perceived probability of default
is done by well established financial institutions:
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Dominion Bond Rating Service
Canadian Bond Rating Service
Standard & Poor
Moody’s
Bond rating (con’t)‫‏‬
Rating
AAA
AA
What it means
highest quality bond
A
BBB
BB
mildly speculative
B
CCC
highly speculative
CC
C
stay away!
Types of bonds
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Stripped bonds (aka deep discount or zero coupon bonds)‫‏‬
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Floating rate bonds
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Callable bonds
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Retractable bonds (putable bond)
Types of bonds (con’t)‫‏‬
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Convertible bonds: callable bonds that can be
exchanged for stock
Convertible bonds: Glossary of terms
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conversion ratio: # of shares to be exchanged for one bond
conversion value: (conversion ratio)(current share price)‫‏‬
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conversion price: (face value of bond)/ (conversion ratio)
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voluntary conversion: conversion initiated by bondholders
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call price: price at which the firm issuing the convertible can call
(redeem) the bond.
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call protection: time period during which bonds cannot be
called
call premium: (call price) - (face value)‫‏‬
Convertible bonds: Exemplification
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Case: A firm issues convertible debt at a call price of $105/bond
and a conversion ratio of 1 bond for 2 shares. The stock
currently sells at $30/share.
– conversion value is $60.
– conversion price is $50
– call premium is $5
Convertible bonds: Exemplification (con’t)‫‏‬
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After three years, the market price of the bond is $90 and the
share price is $45.
– conversion ratio is $90.
– The bondholder is indifferent between holding a bond worth $90 or
two shares worth $ 90
Convertible bonds: Exemplification (con’t)‫‏‬
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After another year, the market price of the bond is still $90, and
stock price is $55.
– conversion value is $110. The firm should call the bonds before the
stock price increases even more.
Canada Newswire release:
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VANCOUVER, July 7 /CNW/ - Imperial Ginseng Products Ltd.
NASDAQ
Trading Symbol: IGPFF , is pleased to announce that subject to regulatory
approval, it has received subscriptions for a private placement of $495,000 of
Series I Participating Convertible Bonds at 12%, pursuant to a $3.0 million
Offering Memorandum dated March 30. The conversion prices of the Bonds are
at $1.60 per share until January 31, and increase by $0.25 per share each
January until January 31, 2011. Total proceeds from this Offering, less the 8%
commission and applicable finance fees payable on the funds raised, will be
used by Imperial to finance ongoing farm operations.