Contingent immunization

hi, just a quick question for you guys. on p32 of the session 8 of Schweser (book 3) about the contingent immunization example, i am confused about the different ways the book uses to calculate the minimum level of assets needed today to achieved the terminal value. in step 2, the author simply assumes PMT = 0 when calculating the PV; however, in step 3, it instead takes into account the PMT to arrive the PV today. i think we should be consistent for these two scenarios in that the only difference is the immunized rate assumed. and i believe we should always consider the reinvestment of the coupon patments. what do you guys think?

I was just looking at that as well. I can’t figure out the logic of sometimes including the PMT and then sometimes not…

In step 2, they are tricking the calculator, as actually you do have payments: you buy (pv) 19.432.662 notional of the 9% coupon bond you get 4.5% every 6 months = 874.470 each coupon is assumed to be reinvested at 4.5% every 6 months this means + first coupon, after reinvestment 5 periods, accouts for 1.089.748 + second coupon, after reinvestment 4 periods, accouts for 1.042.821 + third coupon, after reinvestment 3 periods, accouts for 997.915 + fourth coupon, after reinvestment 2 periods, accouts for 954.943 + fifth coupon, after reinvestment 1 period, accouts for 913.821 + sixth coupon + notional back = 20.307.131 So at maturity you get the sum of all = 25.306.380 = exactly your required terminal value WITH THE CALCULATOR, YOU CAN ONLY DO THIS WITH PMT = 0 IF YOU ASSUME THAT EVERY COUPON CAN BE REINVESTED AT THE SAME RATE (9% p.a., 4.5% s.a.) If then the rate moves from 9% p.a. to 12% p.a., YOU ALREADY HAVE THE 9% p.a. BOND, so you must use pmt = whatever, instead of zero, and use the new I/Y If this is in the exam, for “step 2”, I would not complicate my life, and do the calculation as required / (1+rate)^period, instead of using pmt, i/y, pv, etc. I would only use that in “step 3” hope this helps

the reason why it sets the PMT = 0 is because in step 1 it did not take into account the reinvestment of these coupon payments either. so just to be consistent, in step 2, it sets the PMT = o in this case. to sum up, if you see step 1 and step 2 altogether, then it makes sense to use PMT = 0 since when calculating the terminal value it did not take account the coupon reinvestment either in setp one. this actually arises another question. why didnt the book take into account the coupon reinvestment when calculating the terminal value in step 1?? the logic schweser apllies is not consistent…confused…

they do in step one, as they compound the (1+4%). If coupons were not reinvested, the calculation would just be 20 mio x(1 + 6 x 4%)