# How to use the YIELD function

**What is the YIELD function?**

The YIELD function calculates the yield for a security that pays interest. The YIELD function is designed to calculate the bond yield.

## 1. Introduction

**What is yield for a security that pays interest?**

Yield is the annual return earned on a security like a bond that makes periodic interest payments, calculated based on the security's annual coupon payments and current market price relative to face value.

**What is bond yield?**

Bond yield is the overall interest rate paid by a bond issuer that combines the bond's fixed coupon rate and the market-driven capital gains or losses based on whether the bond sells above or below par value prior to maturity.

**How is the YIELD function calculated?**

The YIELD is calculated through a hundred iterations if there is more than one coupon period until redemption. The resolution uses the Newton method based on the formula used for the PRICE function. The yield is changed until the estimated price given the yield is close to price.

The math formula behind the PRICE function if N>1 is :

PRICE = (redemption / ((1 + (yld / frequency))^(N - 1 + (DSC/E)) + (Î£(k=1 to N) (100 x (rate / frequency)) / ((1 + (yld / frequency))^(k - 1 + (DSC/E) - (100 x (rate / frequency) x A/E)

- redemption is the redemption value per $100 face value
- yld is the yield per period
- frequency is the number of payment periods per year
- N is the number of periods
- DSC = number of days from settlement to next coupon date.
- rate is the interest rate per period
- k is the summation counter
- A = number of days from beginning of coupon period to settlement date.
- E = number of days in coupon period in which the settlement date falls

The YIELD is calculated as follows if there is one coupon period or less until redemption:

YIELD = ((redemption / 100) + (rate / frequency)) - ((par / 100) + ((A / E) Ã— (rate / frequency))) / (par / 100) + ((A / E) Ã— (rate / frequency)) Ã— (frequency Ã— E / DSR)

redemption is the redemption value of the security per $100 face value

rate is the annual coupon rate

frequency is the number of coupon payments per year

par is the price of the security per $100 face value

A is the number of days from the settlement date to the next coupon date

E is the number of days in the coupon period

DSR is the day count convention used

## 2. Syntax

YIELD(*settlement, maturity, rate, pr, redemption, frequency, [basis]*)

settlement |
Required. The security's settlement date which is the date after the issue date. |

maturity |
Required. The date when the security expires. |

rate |
Required. The security's annual coupon rate. |

pr |
Required. The security's price per $100 face value (par amount). |

redemption |
Required. The security's redemption value per $100 face value. |

frequency |
Required. The number of coupon payments per year. Annual payments, frequency = 1; semiannual, frequency = 2; quarterly, frequency = 4. |

[basis] |
Required. The Treasury bill's price per $100 face value (par amount). |

Basis |
Day count |

0 (default) |
US (NASD) 30/360 |

1 |
Actual/actual |

2 |
Actual/360 |

3 |
Actual/365 |

4 |
European 30/360 |

**What is bond maturity?**

Bond maturity is the date when a bond's term ends, at which point the issuer must repay the bond's par value and any final interest due to bondholders. A 30-year bond issued today will have a maturity date 30 years from now.

**What is the bond's settlement date?**

A bond's settlement date is the date when the trade is finalized and the bond is delivered to the buyer in exchange for payment to the seller. Settlement for US treasury bonds is usually T+1 day.

**What is the security's annual coupon rate?**

The annual coupon rate is the fixed annual interest rate the security pays based on the face value, stated at the time of issue, such as a 5% coupon paid yearly on a $1,000 bond resulting in $50 of interest annually.

**What is the security's redemption value per $100 face value?**

The redemption value per $100 face value is the amount the issuer must repay the investor per each $100 of the initial principal when the bond matures, typically $100.

**What is the number of coupon payments per year?**

The number of coupon payments per year is how many times annually the bond issuer pays interest to the bondholder, with typical frequencies being annual, semiannual, and quarterly payments.

## 3. Example 1

**You have invested in a bond that pays an annual coupon rate of 6%, has a face value of $1,000, and matures in 5 years. The current market price of the bond is $950. What is the yield of this bond?**

Here are the arguments:

- settlement: 9/30/2024 The settlement date of the security
- maturity: 9/30/2029 The maturity date of the security
- rate: The annual coupon rate (6%)
- pr: 95 The price of the security per $100 face value (($950/$1,000)*100 = 95)
- redemption: 100 The redemption value per $100 face value (100)
- frequency: 1 The number of coupon payments per year (1 for annual)
- [basis]: 0 (zero) The day count convention (optional, defaults to 0)

Here is how I calculate the pr argument in cell C5:

Formula in cell C10:

The formula in cell C6 returns 7.23% which represents the yield of this bond.

## 4. Example 2

**You are considering investing in two bonds. Bond A pays a quarterly coupon rate of 5%, has a face value of $5,000, matures in 3 years, and is currently trading at $4,800. Bond B pays a semi-annual coupon rate of 6%, has a face value of $10,000, matures in 4 years, and is currently trading at $9,500. Which bond has a higher yield?**

Here are the arguments:

For Bond A:

- settlement : 1/1/2024
- maturity : 1/1/2028
- rate : 0.05 (5%)
- pr : ($4,800/$5,000)*100
- redemption : 100
- frequency : 4 (4 for quarterly)
- [basis] : 0 (zero)

For Bond B:

- settlement : 9/30/2024
- maturity : 9/30/2028
- rate : 0.06 (6%)
- pr :Â ($9,500/$10,000)*100
- redemption : 100
- frequency : 2 (2 for semi-annual)
- [basis] : 0 (zero)

Bond A calculation, formula in cell C11:

Bond B calculation, formula in cell F11:

Keep in mind to use theÂ DATE function if you enter dates in the function instead of using cell references. For example,

Date arguments are truncated to integers.

## 5. Why is the function not working?

The YIELD function returns:

- #VALUE! error ifÂ
*settlementÂ*or*Â maturityÂ*is not a valid data type. - #NUM! error if
*pr*Â <= 0 (zero)- redemption <= 0
- frequency <> 1, 2 or 4
- basis < 0 (zero)
- settlement >= maturity

### Functions in 'Financial' category

The YIELD function function is one of 27 functions in the 'Financial' category.

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