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on Tuesday, June 16th, 2009 at 6:43 pm and is filed under Lottery.
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2 Responses to “If the market interest rates are currently 12%, how much does the lottery have to invest today?”
or the easier way is to use the new present value of an annuity function in a spreadsheet with 12000 as the payment, .12 as the interest rate, and 10 as the term.
If they’re paying the first $12000 up front, then 9 more payments over the next 9 years, do the same calculation as above using 9 as the “n”, which gives $63939.00, plus the initial $12,000 for a total of $75939.00
You just have to discount future value to net present value (NPV) using that interest rate. Assuming Joe already get paid today, the lottery have to invest another $63939 now to ensure Joe get paid $12000 every year (12% interest) for another nine years.
NPV=P/(1+i)^n
e.g.
- Yr 0 $12000 = $12000 NPV @ 12% interest
- Yr 1 $12000 = $10714 NPV @ 12% interest
- Yr 2 $12000 = $9566 NPV @ 12% interest
.
- Yr 9 $12000 = $4327 NPV @ 12% interest
so, the lottery need a total of $63939 investment to match $12000 yearly payment. I used this to calculate my stock intrinsic value anyway.
June 19th, 2009 at 10:04 am
If the payments are made at the end of each year, then that’s a basic net present value of an annuity calculation:
PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]
= 12000 * [(1 - (1 / (1 + .12)^10)) / .12]
= 12000 * [(1 - (1 / 3.10584820834421)) / .12]
= 12000 * [(1 - 0.321973236590696) / .12)]
= 12000 * 5.65022302841087
= 67802.68
or the easier way is to use the new present value of an annuity function in a spreadsheet with 12000 as the payment, .12 as the interest rate, and 10 as the term.
If they’re paying the first $12000 up front, then 9 more payments over the next 9 years, do the same calculation as above using 9 as the “n”, which gives $63939.00, plus the initial $12,000 for a total of $75939.00
June 22nd, 2009 at 4:59 am
You just have to discount future value to net present value (NPV) using that interest rate. Assuming Joe already get paid today, the lottery have to invest another $63939 now to ensure Joe get paid $12000 every year (12% interest) for another nine years.
NPV=P/(1+i)^n
e.g.
- Yr 0 $12000 = $12000 NPV @ 12% interest
- Yr 1 $12000 = $10714 NPV @ 12% interest
- Yr 2 $12000 = $9566 NPV @ 12% interest
.
- Yr 9 $12000 = $4327 NPV @ 12% interest
so, the lottery need a total of $63939 investment to match $12000 yearly payment. I used this to calculate my stock intrinsic value anyway.