I had glossed over it before because I thought I knew this but coming back to it, I have a question: We pay monthly payment at the beginning of every month. Then the first payment should have 0 interest component (as happens in case of capital leases) and the entire payment should go toward reducing the principal. But that doesn’t happen. We calculate as if we were paying at the end of every month. Any reason why this is so? If you calculate PV given monthly mortgage payment, i and number of years in the BEGIN mode, the PV comes out to be higher than given. Say, PMT = 742.50 i = 8.125/12 n = 360 (for 30 yrs) FV = 0 PV you get as 100,677.47 in BEGIN mode (not 100,000 as you would get in the end mode) See page 403 of curriculum. What am I missing?
anish, I’m not exactly sure what your question is…are you just trying to understand why the PV of a payment stream with payments in the beginning of the month is more than the same payment stream at the end? I’m not sure, byt maybe this will help - the difference between the “ending period” stream and “begin” is that all the payments essentially get made 30-days earlier in the “begin” stream. The only payments that are affected by “beg or end” are the 1st payment (which occurs at T0 for the “beg” stream instead of T1 for “end”) and the last payment (which occurs 30-days earlier for the “beg” stream). The timing of all the other payments are identical since the “end” of T1 is the same as the “beginning” of T2, “end of T3 = beg of T4”, etc. The difference between the PV of the two streams is $677. This is completely accounted for by the difference in PV between the T0 and T360 payments: The PV T0 payment is obviously $742.50. The PV T360 is: n = 360 i = 8.125/12 FV = 742.5 Calc PV = $65.41 $742 - 65 = $677 Again, not sure if I answered your question, but hopefully the explanation above helps. Just remember that the only things that are different about “beg” and “end” streams is the timing of first and last payments…all the other payments are basically the same. anish Wrote: ------------------------------------------------------- > I had glossed over it before because I thought I > knew this but coming back to it, I have a > question: > > We pay monthly payment at the beginning of every > month. Then the first payment should have 0 > interest component (as happens in case of capital > leases) and the entire payment should go toward > reducing the principal. But that doesn’t happen. > We calculate as if we were paying at the end of > every month. Any reason why this is so? > > If you calculate PV given monthly mortgage > payment, i and number of years in the BEGIN mode, > the PV comes out to be higher than given. > Say, > PMT = 742.50 > i = 8.125/12 > n = 360 (for 30 yrs) > FV = 0 > PV you get as 100,677.47 in BEGIN mode (not > 100,000 as you would get in the end mode) > See page 403 of curriculum. > > What am I missing?
thisisbrianly Wrote: ------------------------------------------------------- > anish, I’m not exactly sure what your question > is…are you just trying to understand why the PV > of a payment stream with payments in the beginning > of the month is more than the same payment stream > at the end? I’m not sure, byt maybe this will > help - the difference between the “ending period” > stream and “begin” is that all the payments > essentially get made 30-days earlier in the > “begin” stream. > > The only payments that are affected by “beg or > end” are the 1st payment (which occurs at T0 for > the “beg” stream instead of T1 for “end”) and the > last payment (which occurs 30-days earlier for the > “beg” stream). The timing of all the other > payments are identical since the “end” of T1 is > the same as the “beginning” of T2, “end of T3 = > beg of T4”, etc. > > The difference between the PV of the two streams > is $677. This is completely accounted for by the > difference in PV between the T0 and T360 > payments: > > The PV T0 payment is obviously $742.50. > The PV T360 is: > n = 360 > i = 8.125/12 > FV = 742.5 > Calc PV = $65.41 > > $742 - 65 = $677 > > Again, not sure if I answered your question, but > hopefully the explanation above helps. Just > remember that the only things that are different > about “beg” and “end” streams is the timing of > first and last payments…all the other payments > are basically the same. > Thanks for your response Brian. Actually my question is ‘We pay monthly mortgage payment at the beginning of every month. Then the first payment (month 1) should have 0 interest component (as happens in case of capital leases) and the entire payment should go toward reducing the principal. But that doesn’t happen. Why?’ I am sorry if I was unclear before.
anish Wrote: > Thanks for your response Brian. Actually my > question is ‘We pay monthly mortgage payment at > the beginning of every month. Then the first > payment (month 1) should have 0 interest component > (as happens in case of capital leases) and the > entire payment should go toward reducing the > principal. But that doesn’t happen. Why?’ > > I am sorry if I was unclear before. anish, I think you need to take a step back…you are correct, with a “beg” stream the entire 1st payment is to pay down principal. That means that the loan is in this case $742 lower at each payment date than a “end” stream would be. You should look at the PV’s of these streams from the investors perspective - in this case, it’d be the lender/bank. Say I am making the loan to someone and they are required to pay me $742 each month for 30 years. Through simple TVM knowledge, I know that a payment stream that pays me earlier rather than later will result in a greater return, which would result in a greater NPV. Therefore, the NPV on the stream that pays me earlier at the beginning of the month (Beg) will be greater than the stream that pays me at the end of the month (End). This is evident in your PV calculations (100,677 vs 100,000).
Anish, are you sure it’s paid at the start of the month?
I don’t have the curriculum on me right now but why would you make a mortgage payment at t=0? That’s like taking a loan today and repaying some immediately which sounds kinda silly to me…
Kiakaha Wrote: ------------------------------------------------------- > Anish, are you sure it’s paid at the start of the > month? That’s what I gathered from: CFA Curriculum, Vol 5, Page 402, first line What do you think? Brian: Let me review it again. May be it will make sense tomorrow. Thanks for your help.
Anish, Not sure if I understand your question correctly but here is my explanation. Lets say you take a mortgage out on 1st June. Your first payment is due on 1st July. If you consider the date June 1st as T=0 then your mortgage payment is due @T=1. Therefore your calculation will be based on “end” mode and interest will be paid for the 1st month and not as you indicated like a cap lease. Hope this helps.
C3Po Wrote: ------------------------------------------------------- > Anish, > > Not sure if I understand your question correctly > but here is my explanation. > Lets say you take a mortgage out on 1st June. Your > first payment is due on 1st July. If you > consider the date June 1st as T=0 then your > mortgage payment is due @T=1. Therefore your > calculation will be based on “end” mode and > interest will be paid for the 1st month and not as > you indicated like a cap lease. Hope this helps. Right. It makes sense. Thanks C3Po