2.1.9Equity & Fixed Income

Learn about debentures and convertible bonds

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WHAT is a debenture?

WHY does it exist? A company wants cash without diluting owners' control. Debt does exactly that: lenders get interest but no vote and no share of profits beyond the fixed coupon.

WHAT you're owed as a holder:

  • Periodic coupon payments (e.g. 8% of face value per year)
  • Face value (par) returned at maturity
  • A priority claim: if the company is liquidated, debt holders are paid before equity shareholders.

WHAT is a convertible bond?

Two key numbers:

WHY do convertibles exist?

  • For the company: it can borrow at a lower coupon than a plain bond, because it hands the investor a bonus — the upside option. Cheaper interest = attractive.
  • For the investor: downside protection of a bond (you still get coupons + principal if the stock stays flat) plus equity upside if the stock soars.

HOW to value a convertible — from first principles

A convertible is worth at least the greater of two things, because the holder chooses whichever is better:

Convertible valuemax(Bstraight bond value, Pconversion value)\text{Convertible value} \ge \max\big(\underbrace{B}_{\text{straight bond value}},\ \underbrace{P}_{\text{conversion value}}\big)

Deriving the conversion value PP. If I convert, I receive (conversion ratio) shares, each worth the current market price SS:

P=(Conversion ratio)×SP = (\text{Conversion ratio}) \times S

Why this step? Because conversion literally exchanges one bond for that many shares, and each share trades at SS. That's just counting what you'd hold after converting.

Deriving the straight bond value BB. Ignore the option; treat it as a normal bond. Discount every cash flow at the market yield yy:

B=t=1NC(1+y)t+F(1+y)NB = \sum_{t=1}^{N} \frac{C}{(1+y)^t} + \frac{F}{(1+y)^N}

Why this step? A rupee next year is worth less than a rupee today, so each future coupon CC and the final face value FF is divided by (1+y)t(1+y)^t — the time value of money. This is the pure "loan" worth, the floor the convertible can't fall below (assuming no default).

Why max\max and not sum? You can't both keep the bond AND own the shares — conversion is a swap. You pick the higher-value branch, so the guaranteed worth is the maximum. The market price sits a bit above this max because the option to wait and choose later has extra value.

Figure — Learn about debentures and convertible bonds

Worked examples


Debenture vs Convertible — at a glance

Feature Debenture (plain) Convertible bond
Cash flows Coupon + principal Coupon + principal or shares
Coupon rate Higher Lower
Equity upside None Yes (via conversion)
Best when Rates high, want income Expect stock to rise
Risk to holder Default/interest-rate Same + option can expire worthless

Recall Feynman: explain to a 12-year-old

Imagine you lend your friend ₹100 to open a lemonade stand. A debenture is a note that says "I'll pay you ₹8 every year and give your ₹100 back in 3 years" — a simple loan. A convertible bond is a special note: "same deal, BUT if the lemonade stand becomes super popular, you can swap your loan for a share of the stand instead of getting your ₹100 back." If the stand booms, you take the shares and get rich; if it stays small, you just take your money back. You choose the better outcome — that choice is why it's valuable, and why your friend pays you a bit less interest for it.


Active recall

What is a debenture?
A long-term, usually unsecured debt instrument paying a fixed coupon and returning face value at maturity; backed by issuer creditworthiness.
Why is a plain debenture usually higher-yielding than a secured bond?
It has no collateral, so more risk → investors demand a higher coupon to compensate.
What is a convertible bond in terms of components?
A straight bond PLUS an embedded call option on the issuer's stock (right to convert into shares).
Formula for conversion price
Conversion price = Face value ÷ Conversion ratio.
Formula for conversion value P
P = Conversion ratio × current share price S.
Why can a company issue convertibles at a lower coupon?
It gives investors the valuable upside conversion option, and investors accept less interest in exchange.
What is the floor value of a convertible bond?
Its straight-bond value B (PV of coupons + face value), assuming no default.
Value relationship for a convertible
V ≥ max(straight bond value B, conversion value P), and usually trades a bit above due to option time value.
Bond trades below par when?
When market yield > coupon rate (discount bond).
When should you NOT convert a convertible?
When conversion value P is less than the bond's redemption/face value — hold the bond for coupons and principal instead.
Who gets paid first in liquidation, debenture holders or shareholders?
Debenture (debt) holders — debt has priority claim over equity.

Connections

  • Bond Valuation and Yield to Maturity
  • Time Value of Money
  • Options and the Call Option Payoff
  • Equity Shares vs Debt Financing
  • Credit Risk and Ratings
  • Capital Structure of a Company

Concept Map

sell ownership

borrow

pure IOU

usually

higher risk means

pays

liquidation gives

plus call option

right to convert into

lets company borrow at

conversion value

worth at least

Company needs money

Equity / shares

Debt / bonds

Debenture

Unsecured

Higher coupon

Fixed coupon plus face value

Priority claim over equity

Convertible bond

Common shares

Lower coupon

P equals ratio times price S

max of bond value B and P

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, jab kisi company ko paisa chahiye, to do raaste hain: ya to apni ownership bech do (shares), ya phir udhaar lo (debt). Debenture ek simple udhaar ka kaagaz hai — company kehti hai "mujhe paisa do, main har saal fixed interest (coupon) dunga aur maturity pe tumhara principal wapas kar dunga." Zyadatar debentures unsecured hote hain, matlab koi asset gaadi nahi rakhi jaati, sirf company ki reputation pe bharosa hota hai. Isiliye risk thoda zyada hota hai aur coupon bhi thoda higher hota hai.

Convertible bond ek smart hybrid hai — yeh bhi ek bond hai, par isme ek bonus milta hai: agli baar stock upar chala gaya to tum apne bond ko shares me convert kar sakte ho. Yani agar company boom kar gayi, tum shares le lo aur profit kamao; agar stock flat raha, to tum simple bond ki tarah coupon aur principal le lo. Yeh choice hi iski asli value hai. Isiliye company convertible pe kam coupon deti hai — kyunki woh tumhe upside ka option de rahi hai, aur no free lunch, uske badle interest kam.

Value samajhna easy hai. Do numbers yaad rakho: conversion value P=ratio×SP = \text{ratio} \times S (kitne shares × unki price), aur bond floor BB (agar option ignore karo to normal bond ki value). Convertible ki keemat hamesha in dono me se bade wale ke aas-paas rehti hai — thodi upar, kyunki intezaar karne ka option bhi valuable hai. Jab stock high ho to convert karo, jab low ho to bond hold karke apna paisa safe rakho. Bas yahi core idea hai — bond ka floor tumhe girne se bachata hai, aur conversion tumhe upar ka fayda deta hai.

Test yourself — Equity & Fixed Income

Connections