# Convertible Bond

A convertible bond is a bond that gives the bond-holder an option to convert the bond to a specified number of shares of the company’s common stock at a pre-determined conversion date. Convertible bonds give early-stage companies access to funding at lower rates while also reduce risk for the bond-holders.

The main advantage of convertible bonds is that they are useful both for early-stage high-risk companies and investors interested in lending to them. The investors demand high yield on straight bonds on start-ups and other small companies due to their high risk. But due to the conversion feature, the risk for investors is reduced and so does the yield which the companies must pay. If the company is successful, its stock price rises which makes the conversion option valuable and the bond-holders share the upside. However, if the company does not do well but is solvent, convertible debt bond-holders have the assurance of interest income. But, if the company defaults, convertible debt-holders are worse off than the straight debt-holders because they receive any money only after straight debt-holders are paid off.

## Conversion ratio

The number of shares of common stock to which a bond can be converted is called the bond’s conversion ratio.

### Formula

Conversion ratio can be calculated using the following formula:

 Conversion Ratio (CR) = No of Shares of Common Stock No. of Bonds

For example, if a \$1,000 par value bond can be converted to 20 shares of common stock, the conversion ratio is 20.

## Conversion price

The par value of convertible bond per share of common stock is called the conversion price, i.e. \$50 (=\$1,000/20).

### Formula

Conversion price is calculated by dividing the par value of bond by the conversion ratio:

 Conversion Price (CP) = Par Value of Bond Conversion Ratio

If the market price of the common stock rises, the convertible bonds behaves like equity, but if the market price is significantly lower than the par value of the bond, the bond behaves like a straight-bond i.e. as bond without any conversion feature.

## Conversion value

The product of conversion ratio and current market price of a share of common stock is called the conversion value.

### Formula

Conversion value can be calculated using the following formula:

Conversion Value = Conversion Ratio × Current Share Price

The excess of current market price of the bond over the higher of conversion value or the straight-bond value is called the conversion premium.

### Formula

Conversion Premium = Current Bond Price − MAX(CV, BV)

Where CV stands for conversion value and BV stands for bond value without the conversion feature i.e. the value of a straight bond.

## Example

A technology company issued \$100 million in convertible bonds on 1 January 20X1 with a maturity date of 31 December 20Y5. The last date of conversion is 31 December 20Y0. The bonds have \$1,000 par value and coupon rate of 6% compounded semiannually. 3 bonds can be converted to 50 shares of common stock. The current market interest rate is 5%.

It is 1 January 20X8 and the bonds currently trade at \$1,325 when the current share price of the stock is \$75.50 per share.

Find out the bond’s conversion ratio, conversion price, conversion value and conversion premium.

### Solution

 Conversion Ratio = 50 = 16.67 3
 Conversion Price = \$1,000 = 60 16.67

Conversion Value = 16.67 × 75.50 = \$1,258.58

The price of the bond as if it is a plain-vanilla bond can be worked out using Excel PRICE function which equals \$1,065.28.

The conversion value (\$1,258.58) is higher than the straight-bond value (\$1,065.28), so conversion premium equals \$66.42

Conversion Premium = \$1,325 – \$1,258.58 = \$66.42

The conversion premium reflects the potential of further stock price increase which before the conversion date.