When using backward induction, you need to include the coupon while discounting (you discount VH + C indeed). So basically

Value at Node X = 0.5 ((VH+C)/(1+r)^x + (VL+C)/(1+r)^x) = X

But when you discount X back to get the value of the bond before Node X (lets say Node W), you will need to include the coupon at Node X when discounting to Node W.

This is yet another topic on this. I have done the readings through CFAI and Schweser plus EOC questions and never came across a scenario where the second model was used. Am I missing something (ie, thankfully not missing something)? Lol.

Yeah this is not clear; I dont get it either. I also rememberedpretty well last they did all the exercises using the first formula. I checked the book from last year and exercises and that’s true, they use to do it by including the coupon first and then discounting thr whole. Now they use the second fromula in the exercises althought the lectures gives you the first one. I dont get it. Magician can you help please?

EDIT: Actually the formula that you gave is wrong afilippi. Bond value at a node = 0.50 * [(VH) / (1 + i)] + [(VL) / (1 + i)] + C It should be 0.50 * [(VH +C ) / (1 + i)] + [(VL +C ) / (1 + i)] + C CHeck the last exercise in reading 43 of the CFAI. Exercise 10.

Ok, bumping this. Now that I’m going through this a little more in depth it seems the CFAI material is extremely confusing on this topic. In reading 43, example 3 they use:

It’s p***ing me off cause I had written this entire binomial section off as something I knew and did not have to really focus on any longer. Now I’ve spent hours trying to figure out this disconnect. D****t!

I think you all have it you are just getting slightly confused over one thing. When you use backward induction and a binomial tree you obviously take the par value and the coupon in the last period and discount to the second last period using the relevant interest rates and use the formula:

0.50 * [(VH + C) / (1 + i)] + [(VL + C) / (1 + i)]

So if the par value is 100 and the coupon is 5, with the two relevant interest rates being 6% and 4%, you get:

THESE VALUES are the values of the bond at time period 2!!! 99.0566 and 100.9615

Only when you want to find the value of the preceding node, i.e. time period 1, THEN you add the coupon of 5, and discount that back to the preceding node to find those values.

So to conclude – coupons are only added to the value of a bond at a particular node if you intend on discounting that back to the previous period.

Looking at the test questions on the site of the CFA institute, we see again as explanation the second formula… Frankly, its quite confusing. But I use the first formula as it is logical for me (I even draw a line with expected cash flows, look for the correct forward rates - because sometimes they give you an additional year to make you crazy..) and thats it. Tnx, Magician for all your priceless help you are giving to us!