Confused with IRR and YTM of a bond

Hi guys,
I have a very simple question that has been confusing me a bit recently. The best way to describe it is to give a simple example. Let's imagine a very simple 5 year %10 Annual Coupon Bond trading at 100. The current interest rate on similar securities on the market is also %10, that is YTM is %10.

We know that YTM of this bond is %10. However, assuming no reinvestment of coupons, we will be ending up with 1500$ at the end of 5th year. When I am trying to calculate IRR of PV=1000 and FV= 1500 and n=5 , I get an IRR of approximately %8,447 which is not equivalent to %10 YTM. However if we reinvest coupons we end up with approximately 1610,50 which gives us the %10 IRR which is equal %10 YTM based on the same step above(FV=1610,50, PV=1000 n=5) . So if we dont reinvest coupons, what yield will we get? Is it %10 YTM or %8,447 IRR?

Thank you very much

 

If you don't reinvest your coupons, your IRR will naturally be less, since you are not getting interest on the coupons that have been paid. IRR implicitly assumes that you reinvest any cash flows you get.

 

Buddy, you are confused. Your numbers are off. In your example, if principal is $1000, 10% coupon p.a. for 5 years cash flows should be

yr 0 1 2 3 4 5 -1000, 100, 100, 100, 100, 100+1000

IRR = 10% (IRR is the rate where if you discount the cashflows above with it, you get 0)

YTM is essentially the discount rate that will discount the coupons and principal back to a present value equivalent to the bond principal of $1000.

i.e 100/(1+r)^1 + 100/ (1+r)^2 + ....+ 1100/(1+r)^5 = 1000 (Solve for r) which r should be = 10%

 
super m:
Buddy, you are confused. Your numbers are off. In your example, if principal is $1000, 10% coupon p.a. for 5 years cash flows should be

yr 0 1 2 3 4 5 -1000, 100, 100, 100, 100, 100+1000

IRR = 10% (IRR is the rate where if you discount the cashflows above with it, you get 0)

YTM is essentially the discount rate that will discount the coupons and principal back to a present value equivalent to the bond principal of $1000.

i.e 100/(1+r)^1 + 100/ (1+r)^2 + ....+ 1100/(1+r)^5 = 1000 (Solve for r) which r should be = 10%

'super m' is right. I would just add that the yield to worst is always the same as the IRR. YTM will be the same as the IRR unless the bond is callable. Rule of thumb, if the bond price is below the call price, you calculate YTW by calculating the YTM, if higher than the call price, use the yield to call.
Maternity is a matter of fact, paternity is a matter of opinion.
 

The yield to maturity equals the internal rate of return only if (1) the probability of default is zero and (2) the bond cannot be called. For bonds where there is some default risk, or where the bond may be called, there is some probability that the promised payments to maturity will not be received, in which case, the promised yield to maturity will be more than the internal return.

Also, don't forget that YTM assumes reinvestment of the coupon cash flows. If you assume no reinvestment, your IRR will not equal your YTM.

 
Nakaldun7913:
The yield to maturity equals the internal rate of return only if (1) the probability of default is zero
Really? So, you're saying the YTM or the IRR of a bond issued by Ford Motor Company can not be calculated?
Maternity is a matter of fact, paternity is a matter of opinion.
 
Martinghoul:
Nakaldun7913:
Also, don't forget that YTM assumes reinvestment of the coupon cash flows. If you assume no reinvestment, your IRR will not equal your YTM.
This is incorrect... YTM makes no assumptions about coupon reinvestment. There are numerous papers on this.

There are papers, this is true, and the one you posted earlier is a fantastic one. The debate comes in on whether or not the formula for YTM implicitly assumes reinvestment. I, personally, agree with you. However, in nearly all academic textbooks this assumption holds true. This includes Fabozzi books and the CFA. As I said earlier, I am assuming the OP was reagarding academics/ homework etc. and not a real world application.

 
Best Response

What is wrong with you guys. Assuming you reinvest coupons, IRR = YTM BY DEFINITION. Why are you unnecessarily complicating things by talking about default rates and callability. They're not even relevant when talking about yield TO MATURITY.

I feel like this happens on every second thread; everyone here wants to show off how much they think they know by giving an unnnecessary amount of confusing, and often wrong, detail.

 

It isnt unnecessary. If you are talking about YTM on its OWN, then yes there is no need to involve callability or default risk. However, when you are relating YTM to IRR, as was the question in the OP, they become relevant factors. The OP was questioning why, under different circumstances the YTM and IRR may be different. I simply answered that question. I am assuming the OP is asking for academic purposes, in which case, these are things he/she should know.

 
Nakaldun7913:
It isnt unnecessary. If you are talking about YTM on its OWN, then yes there is no need to involve callability or default risk. However, when you are relating YTM to IRR, as was the question in the OP, they become relevant factors. The OP was questioning why, under different circumstances the YTM and IRR may be different. I simply answered that question. I am assuming the OP is asking for academic purposes, in which case, these are things he/she should know.

You're just confusing him though if he's asking a question this basic. If someone asks me to add 2+3=5, I don't start by defining the set of natural numbers and the axioms for additions.

You're wrong anyways; if you want to invoke callability we would use YTC or YTW. YTM is a strictly mathematical formula that literally calculates to maturity. Lastly, the question was IRR and YTM; you can't assume no reinvestment for the latter.

 

Ipsa voluptates eum fuga sed inventore eos. Possimus itaque architecto omnis et voluptatem repellat dignissimos. Culpa aspernatur voluptas eaque. Et asperiores et sequi natus. Animi sapiente quo ratione placeat aut. Neque magnam a nihil repudiandae et earum.

Career Advancement Opportunities

March 2024 Investment Banking

  • Jefferies & Company 02 99.4%
  • Goldman Sachs 19 98.8%
  • Harris Williams & Co. (++) 98.3%
  • Lazard Freres 02 97.7%
  • JPMorgan Chase 03 97.1%

Overall Employee Satisfaction

March 2024 Investment Banking

  • Harris Williams & Co. 18 99.4%
  • JPMorgan Chase 10 98.8%
  • Lazard Freres 05 98.3%
  • Morgan Stanley 07 97.7%
  • William Blair 03 97.1%

Professional Growth Opportunities

March 2024 Investment Banking

  • Lazard Freres 01 99.4%
  • Jefferies & Company 02 98.8%
  • Goldman Sachs 17 98.3%
  • Moelis & Company 07 97.7%
  • JPMorgan Chase 05 97.1%

Total Avg Compensation

March 2024 Investment Banking

  • Director/MD (5) $648
  • Vice President (19) $385
  • Associates (86) $261
  • 3rd+ Year Analyst (13) $181
  • Intern/Summer Associate (33) $170
  • 2nd Year Analyst (66) $168
  • 1st Year Analyst (202) $159
  • Intern/Summer Analyst (144) $101
notes
16 IB Interviews Notes

“... there’s no excuse to not take advantage of the resources out there available to you. Best value for your $ are the...”

Leaderboard

1
redever's picture
redever
99.2
2
Secyh62's picture
Secyh62
99.0
3
Betsy Massar's picture
Betsy Massar
99.0
4
BankonBanking's picture
BankonBanking
99.0
5
dosk17's picture
dosk17
98.9
6
DrApeman's picture
DrApeman
98.9
7
kanon's picture
kanon
98.9
8
CompBanker's picture
CompBanker
98.9
9
GameTheory's picture
GameTheory
98.9
10
Jamoldo's picture
Jamoldo
98.8
success
From 10 rejections to 1 dream investment banking internship

“... I believe it was the single biggest reason why I ended up with an offer...”