How to Price a Convertible Bond in an Interview: Conversion Ratio, Parity and Bond Floor Step by Step

"We're pricing a five-year convertible for a mid-cap tech company. Reference price is EUR 40, thirty percent premium, one and a half percent coupon, and their straight paper trades at six. Walk me through what the bond is worth." That is a real interview question, and it is answerable in about four minutes with nothing more than mental arithmetic and a clear sequence. This walkthrough gives you that sequence: seven steps, in order, with the numbers worked out, plus the traps that catch candidates who know the theory but have never actually run the calculation.

The Setup

Every convertible bond pricing question gives you some subset of the following inputs. If one is missing, ask for it — asking is a better signal than guessing.

The full version of this task, with the model answer laid out step by step, is the convertible bond pricing case study. Work through it out loud before reading the solution — the point of these questions is fluency under time pressure, not recognition.

Step 1: Conversion Price

Conversion Price = Reference Share Price × (1 + Conversion Premium)

EUR 40.00 × 1.300 = EUR 52.00

This is the effective price at which the company sells stock if the bonds convert. State explicitly that the option is issued out of the money — the shares must rise 30% before conversion makes economic sense. Candidates who skip that sentence often go on to make the mistake described later of computing dilution off the current share price.

Step 2: Conversion Ratio

Conversion Ratio = Par per Bond / Conversion Price

EUR 100,000 / EUR 52.00 = 1,923.08 shares per bond

The ratio is fixed at pricing and does not float with the share price. It is adjusted only for defined dilutive events — stock splits, rights issues, dividends above a stated threshold — which is why convertible term sheets carry long anti-dilution schedules. If you want to see how a rights issue mechanically forces such an adjustment, the theoretical ex-rights price calculation is the relevant tool.

Step 3: Parity (Conversion Value)

Conversion Value = Conversion Ratio × Current Share Price

1,923.08 × EUR 40.00 = EUR 76,923, or 76.9% of par

Parity is what the bond is worth if converted right now and the shares sold immediately. At issue it must sit below par — that is what a positive conversion premium means. Quote it as a percentage of par as well as in euros; convertible desks talk in points, and doing the same signals familiarity with the market rather than the textbook.

A useful cross-check: parity divided by par should equal 1 / (1 + premium). Here, 1 / 1.30 = 76.9%. If your parity percentage does not match that, you have made an arithmetic error somewhere in steps 1 to 3.

Step 4: The Bond Floor

This is the step that separates candidates. The bond floor is the present value of the convertible's own cash flows discounted at the issuer's straight-debt yield, not at the convertible's coupon.

Bond Floor = Coupon × [1 − (1 + y)^−n] / y + Par × (1 + y)^−n

Where y = 6.00% and n = 5. The coupon is 1.50% × EUR 100,000 = EUR 1,500 per year.

So the floor is 81.0% of par.

If you cannot compute 1.06^5 in your head, say so and approximate: 6% over five years compounds to roughly 1.34, so the discount factor is roughly 0.75, and the principal alone is worth about EUR 75,000. Add EUR 6,000 or so of discounted coupons and you land at EUR 81,000. Interviewers reward a transparent approximation far more than a silent pause. The underlying discounting mechanics are the same ones covered in the walkthrough on calculating bond duration and price sensitivity, and if the bond maths itself is shaky, the bond basics case on duration, yield and price is the prerequisite.

Step 5: The Implied Option Value

Embedded Option Value = Issue Price − Bond Floor

EUR 100,000 − EUR 81,044 = EUR 18,956, or 19.0% of par

This residual is what investors are implicitly paying for the call option on the issuer's shares. It is a market-implied figure, not a model output — you have backed it out of the issue price rather than valued it directly.

The natural follow-up is how a desk would value it independently. The answer is a binomial tree or a Black-Scholes variant using the stock's implied volatility, dividend yield, the risk-free rate and the issuer's credit spread. A convertible arbitrage fund compares that model value with the 19.0% the market is charging: if the bond looks cheap to model, they buy it and short the delta-equivalent share count, isolating volatility and credit while hedging out direction. You do not need to build the model in an interview, but you should be able to name the inputs and explain who trades on the difference.

Scaled to the whole issue, 19.0% of EUR 200.0m is roughly EUR 37.9m of value transferred to investors at pricing. Keeping that number in view is what makes the next step honest.

Step 6: The Interest Saving

Pre-Tax Interest Saving = (Straight Debt Yield − Convertible Coupon) × Issue Size

(6.00% − 1.50%) × EUR 200.0m = 4.50% × EUR 200.0m = EUR 9.0m per year

After-Tax Interest Saving = EUR 9.0m × (1 − 0.250) = EUR 6.75m per year

Two points to make out loud. First, use the after-tax number when discussing cash flow and coverage, because interest is deductible. Second, resist the framing that this is free money: EUR 45.0m of cumulative pre-tax saving over five years sits against roughly EUR 37.9m of option value handed over up front. The convertible is cheap on cash and expensive on equity. Candidates who present only the coupon saving get asked, immediately, what it cost — and the ones who have not thought about it visibly stall.

The coverage angle is worth a sentence too: a 1.50% coupon rather than a 6.00% one transforms interest coverage, which is exactly the metric a lender stress-tests when sizing a facility. The logic is the same as in the debt capacity case on leverage, covenants and cash flow serviceability.

Step 7: Dilution on Full Conversion

New Shares = Issue Size / Conversion Price

EUR 200,000,000 / EUR 52.00 = 3,846,154 shares

Dilution = 3,846,154 / (100,000,000 + 3,846,154) = 3.70% of the enlarged share count

Note the denominator. Dilution is conventionally quoted against the enlarged count, not the existing one; 3.85% against 100.0m is the pre-issue figure and is not what a term sheet would print. Getting this right is a small detail that reads as precision.

The comparison that lands is against a straight equity raise: EUR 200.0m at EUR 40.00, before any placement discount, creates 5.0m shares and dilutes holders by roughly 4.8% immediately, unconditionally. The convertible dilutes less, and only if the stock rises 30% first. That contrast is the issuer's entire rationale in one sentence.

Where the Shares Show Up Before Conversion

The most common follow-up to this whole exercise is accounting: when do those 3.85m shares actually hit the numbers? The answer is the if-converted method, not the treasury stock method. Add the after-tax coupon — EUR 2.25m here — back to net income, add the full 3.85m shares to the denominator, and if the combination raises earnings per share the instrument is anti-dilutive and is excluded entirely.

The distinction from options and warrants matters, and candidates blur it constantly. Options go through the treasury stock method, where you assume the exercise proceeds buy back shares at the market price; convertibles go through if-converted, where you assume the debt disappears and the coupon comes back. Our guides to diluted EPS under both methods and to basic versus diluted share count cover the mechanics, and the dilution deep dive case works through options, restricted stock units and convertibles together.

Where the Bond Shows Up in the Valuation Bridge

Unconverted, the convertible is debt: add the EUR 200.0m to net debt when bridging equity value to enterprise value. Comfortably in the money, most practitioners flip the treatment — remove the debt, add the 3.85m shares — because that is what the market is already pricing.

Never do both. Carrying the debt and the shares simultaneously double-counts the instrument and overstates enterprise value by roughly the issue size, which is a genuinely disqualifying error in a modelling test. If the bridge needs revision, the full EV-to-equity bridge case covers minorities, associates, pension deficits and leases alongside conventional debt.

Five Traps to Avoid

• Using the current share price as the conversion price. A 30% premium on EUR 40.00 means conversion at EUR 52.00. Using EUR 40.00 overstates both the conversion ratio and the dilution by roughly 30%.
• Discounting at the convertible's own coupon. Discounting 1.50% cash flows at 1.50% simply returns par and makes the option look worthless. The floor must use the straight-debt yield of 6.00%.
• Confusing parity with the bond floor. Parity (76.9%) is the equity value of the conversion right; the floor (81.0%) is the debt value with no conversion right at all. They answer opposite questions.
• Calling the low coupon a free lunch. The saving is paid for with roughly 19.0% of par in option value. Say so before you are asked.
• Ignoring dilution until conversion happens. Under if-converted, the shares hit diluted EPS as soon as the instrument is dilutive, potentially years before a single bond converts.

The Follow-Ups You Should Expect

"What if the credit spread widens to 9.00%?" Rediscount: the annuity factor drops to 3.8897 and the principal factor to 0.6499, giving a floor of EUR 70,828, or 70.8% of par — more than ten points lower. Then make the analytical point: the floor is weakest exactly when it is needed, because spreads widen when the equity story is breaking down. Option value and debt value fall together rather than offsetting.

"Why not just issue equity?" Price (EUR 52.00 versus EUR 40.00 or less), cost (EUR 6.75m after tax annually), and signalling (a convertible says management expects the stock higher; a placement says the opposite). Then give the trade-offs: option value given away, refinancing risk if the shares never reach the strike, and an investor base of arbitrage funds who will short the stock as a hedge on day one.

"What is a busted convertible?" One where the shares have fallen so far that the option is worthless and the bond trades purely on credit. At EUR 20.00 per share, parity collapses to about EUR 38,462, or 38.5% of par. Arbitrage funds exit, high yield and distressed investors buy in, and the issuer faces a cash refinancing at a coupon several times the original 1.50%.

"How does this compare with other ways to raise capital?" This is an invitation to show breadth. A convertible sits alongside accelerated bookbuilds, rights issues, straight bonds and IPOs, and the choice depends on the issuer's rating, volatility, shareholder base and urgency. Being able to move from here into the IPO process end to end or into how ratings and covenants drive high yield versus investment grade pricing shows the product set as a menu rather than a list of definitions.

Practise the Sequence, Not the Answer

The seven steps — conversion price, conversion ratio, parity, bond floor, option value, interest saving, dilution — work on any set of inputs. Change the premium to 25%, the coupon to 2%, or the straight-debt yield to 7%, and the sequence is unchanged. That is what makes it worth drilling: you are learning a procedure, not a result.

Run it end to end on the convertible bonds case study, then vary the inputs yourself and check that the cross-checks still hold: parity as a percentage of par should equal 1 / (1 + premium), and the floor plus the option value should always sum to the issue price. For the conceptual background behind each term, the companion piece on what a convertible bond is and why issuers use them covers the same ground from the other direction.