Hi all, Got a question on a mock and I couldn’t figure out why N=3 instead of N=4. Jist of question is as follows: - - - - - - - - - Scholarship fund wants to pay out a $25,000 scholarship annually indefintely. The fund will begin paying the scholarship at the end of 4 years and will be able to return 4% compounded semi-annually. What is the current amount that must be deposited today to ensure this can continue indefinitely? - - - - - - - - - So I solved it as follows: 4% EAR = ((1+(.04/2))^2 = 4.04% FV = (25,000 / .0404) = $618,811.11 Discount that back to the PV that must be deposited to ensure $25,000 is available every year. This is where I go wrong. The payment is an annuity, NOT an annuity due, so why is the answer N=3 and not N=4? I discount back to N=4 for a PV of $528,149.98. However, the answer is N=3, PV = $549,487.24. - - - - - - - - - Simple question then. If the PMT isn’t required until the end of the 4th year, why are we only discounting it 3 years? Are all PV perpetuities solved for a PV of (N - 1)?
You use that formula A/r for a perpetuity that gives first payment at the end of next year. So 618811 is the amount at the end of 3 yrs (so that the first payment is at the end of 4 yrs)
So $618,811 is the amount that needs to be in the account at the *BEGINNING* of the 4th year to ensure indefinite payments of $25,000 and as such, is discounted at N=3? So PV’s for perps. will always be (N-1) then? If so, makes sense.
johnnyBuz Wrote: ------------------------------------------------------- > So $618,811 is the amount that needs to be in the > account at the *BEGINNING* of the 4th year to > ensure indefinite payments of $25,000 and as such, > is discounted at N=3? > > So PV’s for perps. will always be (N-1) then? If > so, makes sense. Yes. PV for perpetuity will be (n-1). If it is perpetuity “due”, its value will be the value of perpetuity plus the payment you get right now.
I know I am way behind this post but I had a hard time wrapping my head around this rule as well. If you are using your calculator would you leave it in END mode? I worked it with n=4 in begin mode originally.
I know I am way behind this post but I had a hard time wrapping my head around this rule as well. If you are using your calculator would you leave it in END mode? I worked it with n=4 in begin mode originally. thanks!
Yeah, you will first calculate the perpetuity value and then use n = 3 to discount it in END mode…
I think this is wrong, you shouldn’t be using EAR but stated rate. So the answer I’m getting is PV3=$625k and discounted to PV0 = $554,498.11 Refer to solution to Q12 in reading 5.
>>>>>>>>>>>>>The thing I don’t understand is why? i.e. why do we use stated rate and not EAR?<<<<<<<<<<<<<<
To me, logically, since we’re compounding more than once a year, so the perpetuity should be worth more than one that has a compound rate of just yearly.
They go with the annual compounding to match the payment frequency: the PV expression becomes simpler. There is an expression using the semi-annual rate, but it’s a little more complicated; however will produce the SAME numerical answer. It’s not part of the CBOK, so I won’t bore you with it.
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When using the PV of a perpetuity formula, it assumes a one-period offset between the first payment and the value. So, in the first calculation, you get the value of the perpetuity as of t=3.
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You use the EAR when discounting (both in calculating the t=3 perpetuity value and in discounting it back to time zero) because the discount rate is the percentage change in $1 over the periodicity of the perpetuity. Since the perpetuity has annual payments, use the EAR of 8.16%.