# 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.