This question was posted yesterday to my profile by Ifigeneia:
Hi Ifigeneia,
Can i ask the source, please?
(it is good but difficult question, IMO, but maybe a missed an easy route)?
The storage costs are not conveniently given as a constant %, or you could just use, what we'd like to use is F(0,2) = 1500*exp[(6% + u)*2.0 year].
So we need to retrieve the PV or FV of the storage, which is an annuity, so we can use Tuckman 3.5
(or see http://en.wikipedia.org/wiki/Present_value#Present_Value_of_an_Annuity)
... I think the question might be harder than the writer intended:
... because I don't know a continuous annuity formula (maybe there is a continuous annuity formula?) and without Excel it is tedious to discount 24 flows.
So I would need to convert the rate to monthly = [exp(6%/12)-1]*12 = 6.0150% is monthly equivalent to 6.0% continuous.
Then PV(annuity storage cost) annuity factor, A(T) = (1- [1/(1+6.0150%/12)]^24) * $6/6.0150% = $11.280, where $6 is the annual storage cost = 0.50*12;
btw, I myself need to lookup Tuckman 3.15, i do not have this annuity formula memorized.
And (yikes) this PV is in arrears (aka, annuity immediate), but since we pay beginning of month, it has PV (in advance; aka, due) = $11.280 *(1+6.0150%) = $11.3365
Then we can use F(0,2) = (1500+$11.3365)*exp(6%*2.0 year).
I *think* that's just my quick pass, it should be checked ... I would be very interested to see a solution? Thanks,
Hi Ifigeneia,
Can i ask the source, please?
(it is good but difficult question, IMO, but maybe a missed an easy route)?
The storage costs are not conveniently given as a constant %, or you could just use, what we'd like to use is F(0,2) = 1500*exp[(6% + u)*2.0 year].
So we need to retrieve the PV or FV of the storage, which is an annuity, so we can use Tuckman 3.5
(or see http://en.wikipedia.org/wiki/Present_value#Present_Value_of_an_Annuity)
... I think the question might be harder than the writer intended:
... because I don't know a continuous annuity formula (maybe there is a continuous annuity formula?) and without Excel it is tedious to discount 24 flows.
So I would need to convert the rate to monthly = [exp(6%/12)-1]*12 = 6.0150% is monthly equivalent to 6.0% continuous.
Then PV(annuity storage cost) annuity factor, A(T) = (1- [1/(1+6.0150%/12)]^24) * $6/6.0150% = $11.280, where $6 is the annual storage cost = 0.50*12;
btw, I myself need to lookup Tuckman 3.15, i do not have this annuity formula memorized.
And (yikes) this PV is in arrears (aka, annuity immediate), but since we pay beginning of month, it has PV (in advance; aka, due) = $11.280 *(1+6.0150%) = $11.3365
Then we can use F(0,2) = (1500+$11.3365)*exp(6%*2.0 year).
I *think* that's just my quick pass, it should be checked ... I would be very interested to see a solution? Thanks,
