Conversion Thresholds And Forced Conversion

Why Conversion Thresholds Matter

A convertible bond gives its holder a choice between the bond’s contractual claim and shares of the issuing company, subject to the security’s terms. The share price helps determine the value of that choice, but a single share-price threshold does not answer every conversion question. At maturity, the relevant comparison is usually between the conversion value and the amount payable on redemption. Before maturity, the holder must also consider the value of keeping the bond and its conversion right. If the issuer calls the bond, the comparison is generally between conversion value and the amount due under the call terms.

Keeping these comparisons separate is important. A call provision may specify a stock-price trigger that permits the issuer to call the bond; that trigger is not necessarily the share price at which conversion is financially preferable to redemption. A call can prompt conversion by limiting the holder’s alternative to converting or accepting the call payment. If holders convert, the issuer’s debt claim is extinguished and shares are issued, changing the claims on the company.

Definition: The conversion ratio, denoted $n$, is the number of shares a holder receives for each bond converted. At share price $S$, the conversion value per bond is $nS$. A conversion threshold is the share price at which conversion value equals a specified alternative value, such as the maturity redemption amount or the call payment. The threshold is meaningful only when that alternative and the relevant contract terms are specified.

The Maturity Threshold

Suppose one bond can be redeemed at maturity for $F$, or converted into $n$ shares. Assume the bond is physically settled in shares if converted, the holder can choose either alternative at maturity, and there are no additional payments, accrued coupons, transaction costs, or other terms affecting the choice. The holder compares $F$ with $nS_T$, where $S_T$ is the share price at maturity.

\text{Conversion is preferred at maturity if } nS_T > F, \qquad S_T^*=\frac{F}{n}.

The threshold $S_T^*$ follows by setting the two alternatives equal: $nS_T=F$. Dividing both sides by the positive conversion ratio $n$ gives $S_T=F/n$. Above that price, the shares are worth more than redemption; below it, redemption pays more. At exact equality, the two alternatives have equal value before considering any non-financial preferences or contract details.

This is a maturity comparison, not a universal rule for converting early. Before maturity, the holder gives up the bond’s remaining payments and the right to convert later. The relevant alternative is the value of continuing to hold the convertible, not automatically its face value. A spot-price threshold based only on face value and conversion ratio can therefore be misleading before maturity.

Worked Example: Choosing at Maturity

A hypothetical bond has a face amount of $1,200 and matures today. Its holder may receive $1,200 in cash or convert it into 30 shares. There are no other payments or conversion costs. Find the threshold and determine the better choice if the share price is (a) $44 and (b) $38.

Method. Calculate conversion value as $nS_T$, then compare it with the $1,200 redemption amount. The threshold is:

S_T^*=\frac{F}{n}=\frac{\$1{,}200}{30}=\$40.00 \text{ per share}.

At $S_T=\$44$, conversion value is $30\times \$44=\$1{,}320$. Since $1,320 exceeds $1,200, conversion is worth $120 more than redemption.

At $S_T=\$38$, conversion value is $30\times \$38=\$1{,}140$. Since $1,140 is $60 below the redemption amount, the holder should take the $1,200 redemption payment.

Check. At the $40 threshold, $30\times \$40=\$1{,}200$, so the two choices are equal. The calculation avoids the common mistake of comparing the share price itself with the bond’s face amount; the comparison must use the value of all shares received.

Before Maturity: Compare Conversion with Continued Ownership

Before maturity, a holder considering voluntary conversion gives up the bond and its remaining contractual benefits. Define $H(S,t)$ as the market value at time $t$ of continuing to hold the convertible, given the relevant market conditions and contract terms. In a simplified immediate-choice comparison, conversion is attractive when $nS>H(S,t)$; holding is preferable when $nS<H(S,t)$. If the two values are equal, the immediate alternatives tie.

This comparison does not provide a general closed-form threshold from $F$ and $n$ alone. The value $H(S,t)$ may itself depend on the share price, time remaining, interest rates, credit risk, and the bond’s conversion and call terms. If a problem supplies a market value for the continuing convertible, it can be compared directly with $nS$. If it does not supply enough information to value the continued claim, face value alone is not a substitute.

Important distinction: $F/n$ is the equality threshold between conversion value and face-value redemption at maturity under the stated simplified terms. Before maturity, conversion must be assessed against the value of continuing to hold the convertible. When a call is made, assess conversion against the contractual call payment. These alternatives need not be equal.

A conversion price is sometimes quoted as the face amount divided by the conversion ratio. It is a useful way to express the maturity break-even share price when face value is the applicable redemption alternative. It should not be mistaken for a guarantee that a holder will convert as soon as the share price exceeds that figure. A holder may prefer to retain the convertible before maturity because the bond still has value beyond its immediate conversion value.

Calls, Call Triggers, and Forced Conversion

A callable convertible gives the issuer the right to redeem the bond under specified conditions. If the issuer exercises that right, the holder commonly has a choice, subject to the contract and applicable procedures, between accepting the call payment and converting. For this immediate comparison, let $C$ be the total call payment per bond, including any accrued interest if the terms require it. The equality threshold is then:

nS=C \qquad\Longrightarrow\qquad S_{\text{call}}^*=\frac{C}{n}.

If the share price is above $C/n$, conversion value exceeds the call payment. If it is below $C/n$, accepting the call payment is worth more on this comparison. At equality, the alternatives have the same value. This conclusion assumes the holder can act within the stated notice period and that no other payment or restriction changes the comparison.

Some callable convertibles also specify a call trigger, such as requiring the share price to exceed a stated level for a specified number of trading days before the issuer may call. That condition determines whether the issuer is permitted to call; it does not by itself determine whether conversion beats the call payment. A trigger can be above or below the call-payment conversion threshold. The contract may also include call-protection periods, notice requirements, or other conditions that affect whether a call is available.

Check whether the call is permitted.
Apply the call date, stock-price trigger, observation period, and any other specified conditions. A high share price alone may not satisfy all of them.

Find the amount payable on a call.
Use the contractual call price and include accrued interest or other amounts only as the problem or contract specifies.

Compare the holder’s alternatives.
Calculate $nS$ and compare it with the total call payment. Do not confuse the call trigger with this economic comparison.

Trace the issuer’s claims after the election.
If the holder converts, the bond liability is retired and the specified shares are issued. If the holder takes the call payment, the issuer pays cash and retires the bond.

Worked Example: A Call Trigger Is Not the Conversion Threshold

A hypothetical company has bonds with a $1,000 face amount and a conversion ratio of 20 shares per bond. The terms allow a call only after a protected period and only if the share price is at least 130% of the $50 conversion price on 20 of 30 consecutive trading days. The call payment is $1,040 per bond, with no additional accrued interest. The protected period has ended and the trigger has been satisfied. Compare the holder’s choices when the share price is (a) $55 and (b) $50.

Method. First separate the permission to call from the holder’s election. The conversion price used in the trigger condition is $ \$1{,}000/20=\$50$. Therefore, the trigger level is $1.30\times \$50=\$65$, and it must be met on the specified 20 of 30 trading days. The problem states that this condition has been satisfied, so the call is permitted.

The holder’s conversion threshold against the $1,040 call payment is:

S_{\text{call}}^*=\frac{\$1{,}040}{20}=\$52.00.

At $S=\$55$, conversion value is $20\times \$55=\$1{,}100$. This exceeds the call payment by $\$1{,}100-\$1{,}040=\$60$, so converting is preferable on the stated comparison.

At $S=\$50$, conversion value is $20\times \$50=\$1{,}000$. This is $40 less than the $1,040 call payment, so accepting the call payment is preferable.

Check. The $65 trigger level answers whether the issuer may call; the $52 threshold answers whether conversion value exceeds the call payment. Confusing these figures would lead to an incorrect election analysis.

What Conversion Changes for the Issuer

When a holder converts, the issuer does not pay the bond’s call amount to that holder. Instead, under the assumed physical-settlement terms, the issuer removes the bond liability and issues the conversion shares. That reduces outstanding debt and increases the number of shares outstanding. Existing shareholders consequently own a smaller fraction of the total shares, although the exact effect on their wealth depends on the company’s value and the terms of the transaction.

If holders accept a call payment instead, the issuer pays cash and retires the debt. Thus a call can prompt a change in the form of the issuer’s claims: some or all of the debt may be replaced by equity if holders convert, or by a cash outflow if they redeem. A call does not guarantee conversion. The holder’s choice, the call terms, and the share price all matter.

Worked Example: Debt Retired and Shares Issued

A hypothetical issuer has 3,000 callable bonds outstanding. Each bond has a $1,000 face amount, a conversion ratio of 24 shares, and a call payment of $1,030. The call has been validly exercised, and the share price during the election period is $45. Assume every holder makes the same value-maximizing election, with no transaction costs, accrued interest, or other payments. Before conversion, the issuer has 1,500,000 common shares outstanding. Calculate the election, the debt removed, the shares issued, and the ownership fraction represented by the original shares after conversion.

Method. Compare the conversion value per bond with the call payment:

nS=24\times \$45=\$1{,}080, \qquad \$1{,}080-\$1{,}030=\$50.

Conversion is worth $50 more per bond than taking the call payment, so all 3,000 holders convert under the assumptions.

The face amount of debt retired is $3{,}000\times \$1{,}000=\$3{,}000{,}000$. The number of shares issued is $3{,}000\times 24=72{,}000$. Total shares after conversion are $1{,}500{,}000+72{,}000=1{,}572{,}000$.

The original shares therefore represent:

\frac{1{,}500{,}000}{1{,}572{,}000} =0.954198\ldots \approx 95.42\%.

The original shareholders’ fraction falls from 100% to approximately 95.42%; the converted holders own the remaining approximately 4.58%. Check. The two fractions sum to 100% (to the displayed precision), and the issuer retires $3,000,000 of face debt while issuing 72,000 shares. This calculation avoids the mistake of treating conversion as a cash redemption: under the assumed terms, conversion retires the bond by issuing equity instead.

Common Mistakes and Practical Checks

Using the wrong alternative. At maturity, compare with the maturity redemption amount; after a call, compare with the call payment; before maturity, consider the value of continuing to hold the convertible.
Forgetting the conversion ratio. Compare $nS$ with the bond payment, not $S$ with the entire bond amount.
Treating the call trigger as the holder’s conversion threshold. The trigger governs the issuer’s permission to call. The conversion threshold against a call payment is $C/n$.
Calling an early conversion automatic. A share price above face value divided by the conversion ratio does not by itself show that early conversion is best; the holder may give up valuable remaining bond and conversion rights.
Overstating what a call does. A call can induce conversion, but the holder may instead take the call payment if it is the better contractual alternative.

For any conversion problem, identify the decision date and the holder’s available alternatives before calculating. State whether the problem concerns maturity, voluntary conversion before maturity, or a valid issuer call. Then calculate the conversion value, use the correct alternative value, and only after determining the election trace the resulting debt and share changes. That method is aligned with the SOA VEE Accounting and Finance syllabus.

Check Your Understanding

For each problem, identify the relevant comparison before calculating.

A bond can be redeemed at maturity for $1,500 or converted into 30 shares. There are no other payments. Find the threshold and the preferred choice if the maturity share price is $48. (Answer: Threshold $50 per share; redeem for $1,500.)
A callable bond has 16 shares per bond and a total call payment of $832. The call has been validly made. Find the conversion threshold and the preferred choice at a share price of $54. (Answer: Threshold $52 per share; convert, since the shares are worth $864.)
A bond has face value $1,000 and a ratio of 25 shares. Before maturity, the share price is $46 and a supplied market value for continuing to hold the convertible is $1,180. Ignoring other effects, should the holder convert immediately? (Answer: No; conversion is worth $1,150, which is $30 less than continued ownership.)
A callable bond has 18 shares per bond, a $900 call payment, and a trigger requiring the share price to be at least $60 on 15 of 20 trading days. The trigger has been met. At a current share price of $52, compare conversion with accepting the call payment. (Answer: Conversion value is $936, exceeding the call payment by $36; conversion is preferable.)
An issuer calls 2,500 bonds, each convertible into 32 shares, and all holders convert. The issuer previously had 800,000 shares outstanding. Find the shares issued, total shares after conversion, and the fraction of the total represented by the original shares. (Answer: 80,000 shares issued; 880,000 total shares; original shares represent $800{,}000/880{,}000=90.91\%$.)

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