L&T Finance Bond Yield Calculation

by on October 19, 2010

I got a comment about how the yield for the L&T Finance Bonds have been calculated and though I have a slightly longer post scheduled on the topic later; I thought Iâ€™d do a quick one for now.

There are 4 series of L&T Finance Bonds, and two of them offer cumulative returns while two others offer annual returns.

L&T Finance Bonds: Cumulative Option

Letâ€™s first look at the cumulative ones first, which is series 2 & 4. Cumulative series mean that you donâ€™t get a payment every year, but get a lump-sum at the end of the bond buyback period.

In L&T Finance Bondâ€™s case â€“ Series 2 is 7.75% for 7 years, and Series 4 is 7.50% for 5 years, so using compound interest â€“ you can calculate the amount after 5 and 7 years as follows:

 Cumulative Option Series 2 Series 4 Principal 1000 1000 Interest Rate 7.75% 7.50% Time in years 7 5 Amount atÂ  buyback period 1686.25 1435.63

From the above table you see the amount at the end of the buyback period in both the series. Now keep in mind that these are tax saving infrastructure bonds, so your effective purchase price is lesser than the face value of the bond. If you fall in the 30.6% tax bracket, then your taxable income reduces by the amount of L&T bonds you buy (up to a cap of 20,000).

So based on your tax rate, you need to calculate your effective price, and find out at what rate you need to invest that amount, and reinvest the interest earned on it to come at the final buyback amount (1,686.25 and 1435.63) calculated above. You can use the CAGR calculator on this site to help you arrive at the yield of these two series. That page has details on how this is calculated as well.

 Cumulative Option Series 2 Series 4 Principal 1000 1000 Tax Rate 30.90% 30.90% Effective Purchase Price 691.00 691.00 Amount atÂ  buyback period 1686.25 1435.63 CAGR 13.59% 15.75%

The last row in the table above contains the CAGR or yield on both these series, and what this shows you is that if you had invested Rs. 691 in Series 2 for 7 years at 13.59% compounded annually, you would’ve gotten 1,686.25 at the end of 7 years, which is what the yield of this series is.
L&T Finance Bonds: Annual Interest Option

In this case you get interest paid out to you every year, so you use a concept called Yield To Maturity (YTM). This formula takes into account the discounted cash flow, effectively seeing how much money you will get in total, and what itâ€™s worth today. It also assumes that whatever money you get will be reinvested with the coupon rate or 7.75% in Series 1 or 7.50% in Series 4.

You can calculate the YTM using an online calculator or Excel. Plug in the Face Value, Market Price, Coupon Rate and Time in the calculator, and it will show you the YTM.

Here is how that table will look like.

 Cumulative Option Series 1 Series 3 Principal 1000 1000 Tax Rate 30.90% 30.90% Market Price / Effective Purchase Price 691.00 691.00 Coupon Rate 7.75% 7.50% Time 7 years 5 years Yield to Maturity 15.23% 17.20%

The 17.20% number that you see in Series 3 basically means that the cash flows from this bond discounted at 17.20% will equal the present value of future cash flows at the same rate.

To come up with the 17.20% number you need to use Excel or an online calculator or something, but then after that you can take the cash flows for each period, discount it with the 17.20% and see what the present value of each amount in each period is, and the sum of those cash flows at 17.20% should be 0. This is just for those of you interested in diving further into the calculation.

Here is how the Series 3 table of what I am talking about look like.

 Series 3 Cashflows Yield 1 + Yield Time Multiplier (Yield ^ Time) Present Value (Cashflows / Multiplier) Time 0 -691 17.2 1.172 – – -691 Time 1 75 17.2 1.172 1 1.172 63.993174 Time 2 75 17.2 1.172 2 1.37358 54.601684 Time 3 75 17.2 1.172 3 1.60984 46.588468 Time 4 75 17.2 1.172 4 1.88673 39.751252 Time 5 1075 17.2 1.172 5 2.21125 486.15013 Sum 0.08

If you look at the last column of the above table â€“ Present Value (Cashflows / Multiplier) thatâ€™s the column that shows you the present value of each of these payments at the discount rate.

So, 63.99 invested at 17.2% for 1 year becomes 75; 39.75 invested for 4 years at 17.20 will be 75 and so on.

So, this is basically how the yield for this L&T Finance bond is being calculated, and also the IDFC Infrastructure bond and you can read more about NPV, IRR and YTM at Wiki to get a better understanding of this calculation.

I hope this helped those of you who were trying to figure out the calculation, and if I’ve made any mistakes or if you have any other questions or comments please let me know.

And one last thing, these calculations don’t take into account taxes paid on interest payments; that’s just the way yields are calculated – pretax.

B. Viswanath October 20, 2010 at 1:22 am

One thing that I am not able to understand. Maybe you can clarify it for me.
The tax benefit (on initial investment) is only for the first year. Therefore, the amount that has been invested is equal to 1000 from the 2nd year and not 691, isnt it? Therefore, is it right to consider 691 to calculate yield? If not, what happens to yield if the amount is changed to 1000 from the 2nd year onwards?
Thanks

Manshu October 20, 2010 at 12:50 pm

Tax will be saved from this year’s income, not 2011 that you’ll pay in 2012, so that’s the reason it’s included at the beginning.

mjason October 20, 2010 at 2:44 am

Very good info, i was trying to figure out how the YTM was being quote. Thanks.

Manshu October 20, 2010 at 12:46 pm

Supriya October 20, 2010 at 4:41 am

Hi
I wanted to know how the figures are arrived at. As the returns on annual payout are higher than cumulative returns and returns on buy back of bonds after 5 years is higher than returns on holding the bond for 7 years?
So does it mean that if you hold the bond for a longer period then the rate of return diminishes?

Manshu October 20, 2010 at 12:28 pm

The rate of return in the case of a tax saving bond includes the component of tax that you saved also. Since the interest rate is the same in both cases, the tax saved gets distributed between 5 years in one case, and 7 years in another, so effectively the benefit you get because of the tax saving is spread out longer over the 7 year period and that declines the return.

The rate of interest itself remains the same.

Supriya October 20, 2010 at 9:40 pm

Thanks a Ton Manshu. :). great help really. 🙂

Manshu October 21, 2010 at 6:46 am

You are welcome Supriya 🙂 and I appreciate the fact that you took time out to leave the second comment.

Confused October 20, 2010 at 7:48 am

how does the presence of a buy-back option change the rate of return in case of IDFC and these bonds?

Manshu October 20, 2010 at 11:34 am

That’s because the yield is then calculated using the shorter time period, and the tax benefit is spread out for say 5 years instead of 10.

Nirav Doshi October 20, 2010 at 11:55 pm

Hi,
Do you think there would be more such issues of Infra Bonds ?
If yes, it would make sense to wait for some time as interest rates are climbing. Next issue may offer a little higher interest rate.

Thanks,
Nirav.

Manshu October 21, 2010 at 3:14 am

There could be Nirav, but I haven’t heard of them so far; that might just be because they’ve not been announced yet, or I just missed the announcement.

Sreekar Yaddanapudi October 22, 2010 at 12:22 am

Hello Manshu,

I have gone through the calculations in your article and also the answers to the comments posted. I got the answers to all my questions … fantastic stuff !

regards
Sreekar

Manshu October 22, 2010 at 2:51 am

Thanks for your comment Sreekar! Hope to see you around here now!

Ramesh October 22, 2010 at 4:51 am

Hello Manshu,

I am new to this infra bonds and want to know some details, although i gone trough all your posts still confused. 🙂
following.
1) If i invest 20ooo now in L&T infra bonds, Can i show this 20k as 80ccf for this year(2010-2011) ?
2) If i want to buy 5 bonds each i.e. series1 5 bonds,series2 5 bonds,series3 5 bonds ,series4 5 bonds . is it possible?
3) what is my final returns if i invest 20k now on this infra bonds, after excluding all the taxes and charges.

Thanks,
Ramesh

Manshu October 22, 2010 at 7:06 am

Hi Ramesh,

1. Yes.
2. Yes.
3. You can check out the different yields on this page http://www.onemint.com/2010/10/18/lt-infrastructure-bonds-review/

I guess you could do a simple average to see what the overall return is. I’m not sure what the expenses charge would be in your case, so it’s better to check from whoever is selling you these bonds.

As per tax, you can deduct tax on the interest based on your tax rate, however as the cumulative series will be sold during the DTC period, I’m not sure how that is handled. So, I am unable to comment on that.

I hope this helped you a little bit.

Ritesh Shah October 29, 2010 at 6:28 am

Hello Manshu,
thanks for details on how the yield is calculated in case of interest payment done annually (YTM method). i was confused when i saw the table given by the issuer, specifically when yield for 5 years option is more than for 7 years option. but now its very much clear. so it means that the best option in terms of yield or return on investment is option 3 if someone is planning to buyback the bonds before maturity and option 1 if someone wants to wait till maturity, isn’t it? so, if investor dont read or go through the table and just go by basic understanding that cumulative option will give more return than simple one, then he will end up to have less return on investment.
one thing which i want to ask is that as the L&T’s bond has less rating compared to IDFC’s, is there any real disadvantage (in terms of security of investment) in investing in L&T’s compared to IDFC’s.

Manshu October 29, 2010 at 1:04 pm

Well Ritesh, it’s hard for me or anyone else to say how L&T Finance will be 7 years down the line or whether the credit rating means much or not…I guess you just need to keep the fact that this is slightly riskier than IDFC or SBI in mind if you’re investing. Also, I think you will find this post about limitations in the way bond yields are calculated useful:
http://www.onemint.com/2010/10/26/limitations-of-the-way-yields-are-calculated-for-tax-saving-bonds/

Ritesh Shah October 29, 2010 at 10:04 pm

Thanks Manshu. this link gave me good informations about yields. so, it seems that actual yield calculations are really complicated.

Manish November 12, 2010 at 11:51 pm

Great Job. Thanks

Manshu November 13, 2010 at 3:58 am

Thanks Manish!

Pavan January 11, 2011 at 7:16 am

Excellent info Manshu! I got exactly the information I was looking for. I get results from your site very often on google and read them. But today I spent more time on your website and found that it has a wealth of information. Thanks for it all!

Manshu January 11, 2011 at 8:55 am

Your comment and thoughts are much appreciated Pavan. I love it when someone takes the time to leave a comment even when they’re not seeking any info. Than you – you made my day!

Raghavendra Kumar February 1, 2011 at 7:22 pm

Hi Manish,

Thanks for the write-up, very useful and very informative, helped clarify the concepts 🙂 But I have a question, see if you can give me a direction;
1. Can CAGR be compared against YTM?? The Cashflows from Cumulative Option is definitely going to be higher than annual payout option(considering other factors remaining same) and one is not able to invest the interest payment at the same rate of interest. which implies that inspite of YTM showing a higher percentage the cash flow from annual payout option is less than cumulative option for any time period.

Manshu February 2, 2011 at 7:31 pm

No, it won’t be higher, since for a fresh issue the par value will be 5k, purchase price 5k and so the YTM will come out at the same percentage as the annual interest rate.

Kumar March 8, 2011 at 9:55 pm

Hi

Why don’t you expose companies (like Sriram Transport Finance) and banks who mislead the inncent public with a hotch-potch boosted so called “effective yield” calculation on cumulative FD that has nothing to do with bond yield calculation ?

Manshu March 10, 2011 at 5:48 pm

I actually do have a post about limitations on bond yields here:

http://www.onemint.com/2010/10/26/limitations-of-the-way-yields-are-calculated-for-tax-saving-bonds/

I don’t know if its exposing anyone or anything since all of this info is easily available publicly, and no one is hiding it.

M.Radhakrishnan July 31, 2012 at 6:27 pm

Can you show the calculations of WACC for past 5 years for Larsen & Toubro?