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Delayed Perpetuity

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Delayed Perpetuity


1. Let's explain the problem: You have a series of payments (a perpetuity) that start not immediately, but after some delay—in this case, the first payment is two years from today. 2. Normally, a perpetuity's present value formula assumes the first payment happens at the end of the first period (year 1). If payments start later, we cannot just apply this formula directly from today. 3. Instead, we think from the time just before the payments begin. Here, at year 1, you want enough money to fund all the future parties starting year 2. From year 1 onward, the payments look exactly like a regular perpetuity. 4. The present value of these perpetuity payments at year 1 is given. For example, if you need $375,000 at year 1 to fund the parties, your goal is to find how much money you need today (year 0) to have $375,000 one year from now. 5. So, you calculate the present value of $375,000 discounted back one year at the interest rate. This tells you how much to invest today. 6. A common mistake is to discount the $375,000 twice—once to year 1 and again to today—because the payments start two years from now. But the perpetuity formula already discounts back one period before the first payment. 7. The key idea is that these formulas always give the value one period before the first payment, regardless of how far away that is. 8. So, for delayed perpetuities or annuities, first find the value at one period before the first payment and then discount back to today. This explanation helps avoid the error of 'discounting twice' and shows how to correctly handle delayed perpetuities.