About bond yield formula

[torajiro]

Hello, I have a question about the bond yield formula.
The calculation formula for this DLC is as follows.

CAPLAB.png (14.02 KiB) Viewed 1705 times

But I searched and found a formula like this:

2.png (16.1 KiB) Viewed 1705 times

https://taprun.com/calculators/yield-to-maturity
https://corporatefinanceinstitute.com/r ... urity-ytm/
https://ncalculators.com/investment/yie ... ulator.htm
https://studyfinance.com/yield-to-maturity/

In my country, there are the following formulas.

3.png (14.43 KiB) Viewed 1705 times

What I would like to ask is whether there is no problem with the formula that divides by the issue price alone.

The reason is that other formulas seem to divide by the Market price.
And I couldn't find a formula to divide it by the issue price alone.

As I wrote in my previous post, I am not a bank or financial institution expert.
I will publish the bond yield formula when introducing this DLC in my country.
And I want to make sure that there are no mistakes in the formulas currently used in the game.

[David]

Please see the tool-tips for the definitions of bond yield and coupon rate.

FYI, in the tool-tip for the bond coupon rate, "bond face value" means the same as the bond issue price.

[torajiro]

I'm trying to make a very simple sentence that describes this DLC in my native language.
When I explain the yield to others, I also try to explain the formula together.

For now, the yield can be explained by this formula.

CAPLAB.png (14.02 KiB) Viewed 1642 times

I feel that the yield of the image you uploaded is a little different...
If the formula changes, then I will recalculate again

[torajiro]

I will add a little more.

There are several patterns for calculating bond yields.
In my research, the formulas used in this DLC seemed to be a minority.
Isn't there a mistake in this DLC formula that uses the issue price (= bond face value) as the denominator? I asked.
David didn't deny it.
So, in this game, I understood that the denominator of the bond yield formula was issue price( = bond face value).
At least in version 6.5.14.

However, when I try to calculate the yield of your uploaded image, it seems to be different from the existing formula.
But even if it changes, I will follow the formula adopted by the programmer.

David, thank you for your reply.
You'll see why I asked later.

[David]

Isn't there a mistake in this DLC formula that uses the issue price (= bond face value) as the denominator? I asked.Z

Currently, the coupon rate uses the issue price, but the bond yield uses the market price.

FYI about their definitions:
the coupon rate: https://www.investopedia.com/terms/c/coupon-rate.asp
the bond yield: https://www.investopedia.com/terms/b/bond-yield.asp

Please let me know the details of the change you recommend and I will forward it to the dev team.

[torajiro]

I have no personal recommendation, because I don't have enough financial knowledge to persuade.

What I wanted to convey is simple.
”There are several patterns for calculating bond yields.
In my research, the formulas used in this DLC seemed to be a minority.
Perhaps the formula is mistake? I asked this topic."

I can't understand why we divide by face value or even use market price as the denominator.
Of course I can't explain.
But what I see is that there were few formulas with the denominator at the face value.

If you say this formula is correct, I will follow.
And in this game, using this formula will explain to people in my country.
You wrote to me "See the definition of coupon rate or yield", so
My interpretation is that the problem is my lack of understanding and the current formula is correct.

siki.png (57.36 KiB) Viewed 1592 times

Then there was a YTM formula in another article by the same writer in the link you showed me.
It seems that the denominator is the sum of the face value and the market price divided by 2.
https://www.investopedia.com/terms/y/yieldtoworst.asp

As I wrote earlier, I can't explain if this is correct.
You can choose whether or not to use the formula.
I will follow the formula you adopted.

[David]

Perhaps fellow members of this forum with the financial knowledge could comment on this.

[torajiro]

Probably even if explained in English, I don't think I can understand it because it is too advanced. (I am Japanese and English is not my native language)

What I want to know is "Is the current formula wrong?"
The answer comes out because you didn't say "I'll fix".
My purpose is not to have a deep discussion of formulas.
All right, thank you.

[beamthegreat]

I always assumed that the annualized yield shown in the game was the calculated YTM using discounted cashflows. All of OP's formula is an approximation of the yield. YTW is unrelated and only applies to callable bonds.