This is on today right? So we will use BGN Mode also butterfly perpetuity comes at t – 1 and we use n =4??
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In perpetuity there is no beginning mode or end mode. Pv of perpetuity is cashflow/r%. Here the pv will be at t-1. But here r is given as compounding semi annually. First we need find EAR and rest of the sum is simple. First payment to be made exactly four years from today. So it is at beginning of 5th year which is same as end of 4th year. So our pv of annuity will come at beginning of 4th year which is same as end of 3rd year. So to find pv today we have to discount the cashflow by 3 years. In these kind of sums if you find any difficulty please use january 1 as today then you will understand easily.
First we will calculate EAR
PV=1
N=1*2
I=4/2
CPT FV
(1.0404-1)*100
=4.04
Then we will calculate value of perpetuity
25000/.0404
=618811,88
Now we will calculate PV of perpetuity
FV=-618811.88
N=3
I=4.04
CPT PV
549487.2415
While calculating perpetuity we don’t require BGN mode, the value computed here comes for 1 year back. While doing such questions always refer to a time line