## What is Valuation?

It is the process to determine the value or worth of an asset, liability, debt of the company. It can be determined by many processes or techniques. Many factors can impact the valuation of an asset, liability, or the company, like:

- Earning of the company
- Economic factors
- Market value
- Technological upgradations

## Types of Valuation Models

**Absolute Valuation Models**

These models attempt to derive the value of an asset, liability, or the company based on the factors that are impacted by the company itself such as earning of the company, dividend paid by the company, cash flows of the company, growth of the company, etc. These models have no relations with the other companies.Â

**Relative Valuation ModelsÂ **

Under this model, the value of an asset is derived by comparing the company with other companies.Â

### What is Bond Valuation?

It is a written promise to pay the debt on the agreed terms and conditions. It allows the public listed company to borrow money from the market. It is issued under a contract having specified details such as principal amount, date of issuance, interest rate, amount of payment, underlying collateral, etc. It is a balance sheet item and treated as a current asset if the amount is due to be received in one year. If the amount is not due till one year, then it is to be to be treated as non â€“current assets in the balance sheet.

### Valuation of note

Before considering its valuation, we will summarize its features:

- Principal amount - It is the amount that is taken from the borrower and needs to be returned on a future date to the investor.
- Coupon rate/ Interest rate - It is the rate at which it is issued. Interest/coupon is paid monthly, quarterly, or annually to the holders/investor at the specific coupon/interest rate.
- Maturity can range to few years.
- It can also be called bonds having a maturity of 7 to 10 years.

In the case of a general debt, it is done by discounting the present value of future cash flows using an appropriate discount rate. But in the case of valuation of note, the value of the collateral underlying it will also impact it. Notes having the backing of collateral generally provide a lower yield as the default risk is lower and these are more secured than notes without collateral.

### Valuation of the Convertible Note

Convertible Note is a type of a note which has features of both debt and equity instrument. In this instrument, the investor has the option to convert the debt into equity. The main benefit of a convertible note is the payment of dividends to the investor and repayment of principal on maturity.

It also provides the investor the option to convert the interest and the principal amount to equity at a specified rate at a specific time which is known as conversion price which is usually fixed while issuing the convertible note itself, in the very beginning.

So, while selling a convertible note, the seller is also selling a call option on equity having a strike rate equivalent to the conversion price. In the same way, the investor is buying a call option.

Generally, the interest is paid annually, semi-annually, or monthly rather than to be paid in cash. To find the valuation of the convertible instrument, the relationship between the interest rate and the amount of the note.

Generally, the amount of the note has a vice versa relationship with the market interest rate. As the market interest rate goes up, the price comes down as the new investment will offer more yield and people starts investing in new investments.

Following the same pattern, when the market interest rate goes down, the price goes up as the new securities/investment will generate a lower yield.

**Yield to Maturity > Coupon/Interest rate---------------------------Note sells at discount.****Yield to Maturity = Coupon/Interest rate---------------------------Note sells at par value.****Yield to Maturity < Coupon/Interest rate---------------------------Note sells at a premium.**

**In the above sequence, we conclude that :**

- If the market rate/ yield to maturity is more than the coupon rate, then it is selling at discount.
- If the market rate/ yield to maturity is equal to the coupon rate, then it is selling at par/ face value.
- If the market rate/ yield to maturity is less than the coupon rate, then it is selling at a premium.

**Formula**

$\begin{array}{l}Amount:\text{}\xe2\u02c6\u2018\text{}C/\text{}{\left(1+r\right)}^{t\text{}+}F/{\left(1+r\right)}^{t}\hfill \\ C=\text{}Coupon/\text{}interest\text{}amount\hfill \\ F=\text{}Face\text{}value\hfill \\ r=\text{}Rate\text{}of\text{}interest\hfill \\ t=\text{}time\text{}to\text{}maturity\hfill \end{array}$

**Example**

An Investor naming X buys a note from the ABC company with the following characteristics:

- Face value of $ 2,000
- The coupon rate of 10%
- Maturity period - 4 years.

The future cash flows of the company are

- Year 1- $200
- Year 2- $200
- Year 3- $200
- Year 4- $ 2200

We can create three different scenarios based on the market interest rate or discount rate of 8%, 10%, and 12%.

| Cash Flows ( a) | PVF at 8% (b) | Amount ( a*b) |

Year 1 | $ 200.00 | $ 0.93 | $ 185.19 |

Year 2 | $ 200.00 | $ 0.86 | $ 171.47 |

Year 3 | $ 200.00 | $ 0.79 | $ 158.77 |

Year 4 | $ 2,200.00 | $ 0.74 | $ 1,617.07 |

$ 2,132.49 |

| Cash Flows ( a) | PVF at 10% (b) | Amount ( a*b) |

Year 1 | $ 200.00 | $ 0.91 | $ 181.82 |

Year 2 | $ 200.00 | $ 0.83 | $ 165.29 |

Year 3 | $ 200.00 | $ 0.75 | $ 150.26 |

Year 4 | $ 2,200.00 | $ 0.68 | $ 1,502.63 |

$ 2,000.00 |

| Cash Flows ( a) | PVF at 12% (b) | Amount ( a*b) |

Year 1 | $ 200.00 | $ 0.89 | $ 178.57 |

Year 2 | $ 200.00 | $ 0.80 | $ 159.44 |

Year 3 | $ 200.00 | $ 0.71 | $ 142.36 |

Year 4 | $ 2,200.00 | $ 0.64 | $ 1,398.14 |

$ 1,878.51 |

It shows the relationship between the market interest rate and the market value of the note.

- When the market value (8%) is lower than the coupon rate (10%), the value exceeds the par value or it is at a premium.
- When the market value (10%) is equal to the coupon rate (10%), the value is at par value.
- When the market value (12%) is more than the coupon rate (10%), the value less than the par value or it is a discount.

** **Adjustment for semi-annual coupon rate

When a convertible note makes semi-annual interest payments, then certain adjustments need to be made to the amount calculation:

- The rate of coupon/ interest is halved
- The number of years is doubled
- Yield to maturity is halved

**Example:** If a convertible note having face value of $ 1000, having a coupon rate of 10%, and maturity of 4 years, and yield to maturity or market interest rate or discount rate of 8% makes semi-annual payments. Then for calculation of price, coupon rate is considered as 5% and yield to maturity is considered as 4 %, and no of years till maturity is considered as 8 years. Price is calculated as below:

| Cash Flows ( a) | PVF 4% (b) | Amount ( a*b) |

Year 1 | $ 50.00 | $ 0.96 | $ 48.08 |

Year 2 | $ 50.00 | $ 0.92 | $ 46.23 |

Year 3 | $ 50.00 | $ 0.89 | $ 44.45 |

Year 4 | $ 50.00 | $ 0.85 | $ 42.74 |

Year 5 | $ 50.00 | $ 0.82 | $ 41.10 |

Year 6 | $ 50.00 | $ 0.79 | $ 39.52 |

Year 7 | $ 50.00 | $ 0.76 | $ 38.00 |

Year 8 | $ 1,050.00 | $ 0.73 | $ 767.22 |

$ 1,067.33 |

**Formula is termed as:**

$\begin{array}{l}Amount:\text{}\xe2\u02c6\u2018\text{}C/\text{}{\left(1+r/2\right)}^{t*2\text{}+}F/{\left(1+r/2\right)}^{t*2}\hfill \\ C=\text{}Coupon/\text{}interest\text{}amount\hfill \\ r=\text{}Rate\text{}of\text{}interest\hfill \\ t=\text{}time\text{}to\text{}maturity\hfill \\ F=\text{}Face\text{}value\hfill \end{array}$

On similar terms, if the coupon payments are made monthly or quarterly, adjustments are made to the amount of coupon, rate of interest, and time to maturity.

Formula for monthly coupon payment is:

$Amount:\text{}\xe2\u02c6\u2018\text{}C/\text{}{\left(\text{}1+r/12\right)}^{t*12}+\text{}F/{\left(\text{}1+r/12\right)}^{t*12}$

Formula for quarterly coupon payment is:

$Amount:\text{}\xe2\u02c6\u2018\text{}C/\text{}{\left(\text{}1+r/4\right)}^{t*4}+\text{}F/{\left(\text{}1+r/4\right)}^{t*4}$

One concept that is the basis of convertible notes is the concept of a Valuation cap.

## Valuation Cap

This entitles investors to convert their convertible notes into equity at the price of

- Valuation cap ( V.Cap)
- Qualified financing share price.

Qualified financing is termed as the conversion of the note into equity when the sale of equity excesses a certain threshold.

Under this, the maximum rate is fixed on which convertible notes will be converted into equity. To convert it into a share price, the V.Cap is divided by series A value.

**Example:** Mr. Z invested in an ABC company using a note with $ 1 million V.Cap. It is decided by series A investors that the value of the company is $ 2 million and pay $ 1/ share. So, by dividing $ 1 million by $ 2 million, we get an effective rate of $ 0.50 per share. Now you will receive double the shares at the same rate.

## Conclusion

Notes have been used in day to day working of the company which makes valuation a prime task. In the case of either general or convertible notes, we need to use specific formulas to derive the proper valuation.

## Context and Application

This topic is important in the examination of undergraduate and graduate courses such as:

- B.Com
- M.Com

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