Bonds

Definition and valuation

Lecture plan:

Foreword Definitions & concepts Valuation and YTM calculation More bond-related concepts

Concept definition

Bonds = corporate debt

…corporate bonds, that is

Bond: The concept

debt instrument

the issuer of the bond borrows money

interest, aka coupon is paid periodically

principal aka face value is repaid at maturity.

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

coupon: fixed amount of annual or semi-annual interest

face value (par): usually $100, $1,000, or $10,000

coupon rate: coupon/face value

yield-to-maturity (YTM) the rate that makes the PV of bond’s

cash flows equal its current price.

Yield-to-maturity - Exemplification

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

use a financial calculator, or

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)

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)

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)

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:

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!

These are set from the beginning:

– coupon rate

– face value

– maturity

These change as a result of market forces:

– YTM

– bond price

The Economic Meaning of the Yield-to-Maturity

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

Indenture: written agreement between the corporation and the lender detailing the terms of the debt issue

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

Bond trustee: makes sure that the terms of the indenture are obeyed

Exemplification - Covenants

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)

Sinking fund: account managed by the bond trustee for early

bond redemption

Bond rating

reflects the perceived probability of default

is done by well established financial institutions:

– Dominion Bond Rating Service– Canadian Bond Rating Service– Standard & Poor– Moody’s

Bond rating (con’t)

Rating What it means

AAA highest quality bond

AA

A

BBB

BB mildly speculative

BCCC highly speculative

CC

C stay away!

Types of bonds

Stripped bonds (aka deep discount or zero coupon bonds)

Floating rate bonds

Callable bonds

Retractable bonds (putable bond)

Types of bonds (con’t)

Convertible bonds: callable bonds that can be

exchanged for stock 

Convertible bonds: Glossary of terms

conversion ratio: # of shares to be exchanged for one bond conversion value: (conversion ratio)(current share price)

conversion price: (face value of bond)/ (conversion ratio) voluntary conversion: conversion initiated by bondholders  call price: price at which the firm issuing the convertible can call

(redeem) the bond.  call protection: time period during which bonds cannot be

called call premium: (call price) - (face value)

Convertible bonds: Exemplification

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)

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)

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:

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.