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Understanding and modelling convertible bonds

Think of a convertible bond ("CB") as a two-flavored neapolitan ice-cream. It's not plain vanilla (pun intended).

Modelling convertible debt in excel can be hairy. The debt portion takes into account the coupon payments as well as the loan principal being redeemed at maturity, while the equity reflects the swapping of the debt into shares of the company in the future.


Too technical?


Consider this:

A fast growing company is looking for additional funding to expand its business. There are a few options in the market but the founders prefer not to raise new equity - partly because the value of the shares at this juncture are lower and they do not want to dilute the company too early on.


One option is to borrow from the bank, which will likely charge them an interest rate of say 12%.

Plain vanilla bond @12% interest rate

Another option is to raise the $1 million as a convertible bond i.e. allowing the lenders to change that liability into equity at some point of time in the future.

This becomes interesting for the lenders because not only do they receive the fixed income payments, but also stand to benefit if the value of the company's shares increase significantly in the future. The downside risks are mitigated, but at the same time, they get the upside.


This creates a kind of valuation gap because, all costs being equal:

  • A lender would always prefer to issue a CB rather than a plain vanilla bond to enjoy the upside; and

  • A company will always choose to a plain vanilla bond since the fixed income payments in both scenarios are effectively the same

As a shareholder, why else would I want to dilute equity?


So, in order to balance the risk-reward, the lenders will typically offer the company a lower coupon rate in a CB issuance. Let's assume in this case, a coupon rate of 8%.

Convertible bond priced at 8% but with equity upside

To account for the value in the CB, we go back to our analogy of our two-flavoured neapolitan ice-cream - to value the liability and equity components separately.


The liability component

We treat the liability in a CB like a plain vanilla bond i.e. using the 12% as the interest rate (also the discount rate) and calculate the present value (PV) based on the fixed income payments of 8%. In this example, the bond matures in 5 years.

The value of the liability component in a convertible bond is calculated based on the present value of all fixed coupon payments from the CB, discounted by the interest rate of a plain vanilla debt.

There's no real way to value the future equity in the CB, hence, the value of equity here is the plug i.e. CB face value - value of the liability component. The proforma balance sheet at the onset looks like this:

Now, assuming there is no conversion during the term of the bond, the accounting treatment for the liability component in the CB would look like this. You can see that the outstanding liability is equivalent to the face value of the CB at the end of 5 years.

For every successive year that the CB is not converted, the value of the liability component increases, approaching the face value at maturity. This 'book value' is adjusted every year based on the difference between the actual coupon paid and the 12% interest rate i.e. what the company would have owed the lenders based on issuing a 12% plain vanilla bond.


Every year that the CB does not convert translates into sunk costs for the company

Also, for every year that the CB does not convert, the 12% interest rate also translates to "sunk costs", impacting the company's retained earnings as illustrated below:



What happens when the CB eventually converts?

Let's assume that the CB holder converts in year 3 before maturity. The liability component is extinguished and the company is free of debt. Next comes the treatment of equity on the books.

Firstly, the face value of the CB upon issuance is immediately recognized as the share capital i.e. a straight swap of debt into equity.


The valuation of the CB in the year of conversation reflects the sum of the equity and debt components. In this case it is calculated as:

Value of CB = equity component + liability component

The difference between the value of the CB and its face value of $1,000,000 is accounted for as the "share premium".


Note that the straight bond interest component remains recognized as a sunk cost.


And that's all there is to it. To better understand how the math works, refer to the editable worksheet below:


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