CONVERTIBLE BOND CALCULATOR

Input/Output Data Definitions


Recommended books on convertible bonds
  1. Brief description of the calculator
  2. Input definitions
  3. Output definitions

CALCULATOR DESCRIPTION

This is an on-line calculator that analyses convertible bonds. It analyses: There are 7 inputs that are required for the calculator. There are a further 4 optional inputs, for the more involved analytical calculations.

Note: For ease of immediate use, the calculator starts with default values for all inputs. When using the more advanced analytical calculations, make sure that all inputs are valid.


CB CALCULATOR INPUT DEFINITIONS

CB TERM INPUTS

Maturity
Number of years to maturity of the bond.
For example: If the current year is 1996 and the bond matures in 2011, then 15 is input.

Coupon Rate
The coupon rate of the bond, expressed as a percentage.
For example: If the bond's coupon is described as 8.75%, then 8.75 is input.

Coupon Rate Frequency
The frequency of the coupon payments (whether annual or semi-annual) can be input using the radio buttons to the right of the Coupon Rate input field.

Conversion Ratio
Describes the number of shares received when converting one bond.
For example: Sometimes the value may have to be adjusted before input. If the conv-ratio is described as "15.876 ordinary shares per 100 convertibles", then the figure is adjusted to a per-bond input value of 0.15876.

Par Value
The par value, or maturity value, of the bond. This will usually be a round figure such as $1,000. The units here should be the same units as those for share and CB prices.
For example: If the par is described as Yen100,000, then 100,000 is input.

[ top ]

MARKET VALUE INPUTS

CB Price
The market price of the bond. The units used here must be the same as those for the par value and the share price.
For example: If the bond is quoted as "96% of a par value (of $1,000)", then 960 is input.

Share Price
Share price of the underlying company. The units used here must be the same as those for the par value and the CB price.

Dividend Yield
The annual dividend yield on the underlying shares.
For example: If the current div-yld is 4.5%, then this is input as 4.5.

[The remaining input values are optional...]

Straight Bnd Yield
This is the yield on a non-convertible bond, but one with comparable quality rating and investment features (i.e. similar maturity, coupon). Unfortunately, there is no immediately easy way to determine such a bond. At the moment we are not aware of any internet source for this. So, now, the best method of determining an equivalent straight bond yield, may be from a market prices table in a newspaper.
For example: If comparable straight bonds are currently yielding 12.75%, then 12.75 is input.

Share Volatility
Here we want the estimated volatility of the shares over the period to maturity of the bond. This figure is used for the option theory analysis of the bond. This will be the most difficult value to determine for input (we have a brief discussion of volatility in the context of option models).
For example: If share price volatility is estimated at 24.8%, then 24.8 is input.

Risk-Free Rate
This is the risk-free rate (commonly taken as a government bond yield) for the period to maturity of the bond. If the CB has 15 years to maturity then the 15-year risk-free rate is required. This figure is used for the option theory analysis of the bond, and for discounting the cash flows in the dividend growth table.
For example: If the risk-free rate is 11.8%, then 11.8 is input.

Dividend Growth
This is the estimated annual growth in dividends to maturity of the bond. The figure is used for calculation of the dividend growth table.
For example: If it is thought that dividends will grow at 10% over the period to expiry of the bond, then 10 is input.

[ top ]

CB CALCULATOR OUTPUT DEFINITIONS

1.STOCK CONVERSION

market conversion price
The effective price that would be paid for each share, by buying the CB and converting immediately into the shares.

market conversion premium
The market conversion price is usually at a premium to the actual share price, reflecting the lesser downside risk of the CB and the superior yield over share dividends. This premium is expressed here as the straight difference between the market conversion price and the current share price. As such, the units will be the same as those of the share price.

market conversion prem(percent)
This is a more useful way of expressing the market conversion premium, in which it is expressed as a percentage of the share price.

[ top ]

2.INCOME COMPARISON (SHARES v CB)

simple yield(CB)
The annual coupon amount expressed as a percentage of the current CB market price.

ytm(CB)
The yield to maturity of the bond (i.e the interest rate that will make the present value of the cash flows - both coupon payments and final maturity value - equal to the bond market price). For semi-annual pay bonds, the bond-equivalent yield is computed by doubling the periodic interest rate.

Premium payback period (Break-even time)
The income from the CB is usually greater than that on the share (from dividends). As mentioned above, this is one of the reasons for the market conversion premium. The Premium payback period describes the numbers of years it would take for the income differential (CB over shares) to recover the initial market conversion premium paid when buying the bond.
Note: the Premium payback period does not take into account the time value of money. [For a more detailed analysis of the income differential, see the Dividend Growth Table].

[ top ]

[Most of the rest of the calculations depend on the "optional inputs"...]

3.VALUE OF STRAIGHT BOND

straight value
It can be useful to compare the CB market price, with the value of an equivalent bond (i.e. similar terms: coupon, maturity, quality rating), but one that is non-convertible (i.e. a straight bond). This value can then be used in the analysis of downside risk and further in an options analysis approach to CB's.
[Note: requires input of straight bond yield].

straight value(per share)
The value above, expressed on a per share basis.
[Note: requires input of straight bond yield].

prem over straight val(percent)
From the above we can now calculate the premium of the share price over the straight value(per share).
[Note: requires input of straight bond yield].

[ top ]

4.DOWNSIDE RISK

The downside risk of a CB (i.e. the minimum price of the CB) can be regarded as the maximum of either,
  1. the conversion value - the value of the bond if converted immediately into shares, and those shares sold in the market at the current market price, or
  2. the straight value - the value of the bond purely on the basis of it's future cash payments (coupon and maturity value) and disregarding the conversion option into shares.

conversion value
The value of the bond if converted immediately into shares, and those shares sold in the market at the current market price (i.e. simply the conversion ratio multiplied by the share price). The figure in square brackets, represents the downside risk, as the percentage fall from the current CB price to it's conversion value.

straight value
[As defined above.] The figure in square brackets, represents the downside risk, as the percentage fall from the current CB price to it's straight value.
[Note: requires input of straight bond yield].

[ top ]

5.THEORETICAL OPTION EVALUATION

It is possible to regard convertible bonds as a composite of straight bond and option (an option to buy shares). This can lead to two further stages of analysis:

  1. Analysis of the embedded option - to measure the "expensiveness" of this option as determined by the current CB market price.

  2. Theoretical value of the CB - by determining the theoretical component values of straight bond and share option.
embedded option price(per share)
If we accept that a CB has the two components: straight bond and share option, the latter's component of the CB price is simply the difference between the CB market price and the straight bond value (which we have respectively input and calculated above).
[Note: requires input of straight bond yield].

implied volatility
Given the option price (that component of the CB price), we can use an option model to determine the implied volatility of the option. This implied volatility is a very good measure of the "expensiveness" of the share option embedded in the convertible bond.
Note: the option model used is Black-Scholes adjusted for a continuous dividend yield, and where the interest rate used is the input risk-free rate.
[Note: requires input of straight bond yield].

option value per share
From the input of share price volatility, it is possible to calculate the value of an option similar to that embedded in the CB (i.e. an option with the same maturity, strike etc.) The option model used is that as described above (for the calculation of implied volatility).
[Note: requires input of share volatility].

option value
The above value expressed equivalent to the CB price (i.e. option value per share multiplied by the conversion ratio).

cb value
The theoretical CB value is the sum of the straight value and the option value (both calculated above).
[Note: requires input of straight bond yield and share volatility].

[ top ]

6.DIVIDEND GROWTH TABLE

This table analyses in detail the income differential between the CB and underlying shares, and allows for the effect of different dividend growth rates to be analysed. (The forecast div. growth rate is indicated each time in the title to the table).
year
The income for each year to maturity of the CB is calculated.

coupon
The fixed coupon amount received each year from the CB.

dividend
This shows the absolute annual dividends received each year from the shares. The first payment derives from the input of the dividend yield and share price, while subsequent years' amounts are based on the input forecast dividend growth rate.

npv-cpn
The net present value of the cash flows (resulting from coupon payments) accumulated up to that year. Account is taken of whether the coupon payments are annual or semi-annual.

npv-div
The net present value of the cash flows (resulting from dividend payments) accumulated up to that year. It is assumed that the dividends are paid on a semi-annual basis.

[ top ]

[ NumaWeb Home ]
Copyright © 1995 Numa Financial Systems Ltd. All rights reserved.