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In this week's Powerball lottery, the lucky winner walked away with a $294 million prize, to be...

Question:

In this week's Powerball lottery, the lucky winner walked away with a {eq}\$294 {/eq} million prize, to be paid in {eq}26 {/eq} yearly installments of {eq}\$11.3 {/eq} million. The first installment will be paid immediately, of course. She was given the alternative of taking a lump sum of {eq}\$168 {/eq} million.

(a) What discount rate was used to calculate the lump sum?

(b) If the relevant discount rate (market rate) had been {eq}9.5\% {/eq} instead, what would the lump sum have been?

Finding the Internal Rate of Return:

The internal rate of return (IRR) measures the annual profitability of an investment. In most cases, there is no formula that can be used to express the IRR. Instead, we have to use a trial and error approach to "guess" the rate that results in a net present value (NPV) of zero. A financial calculator employs the same guessing approach.

Answer and Explanation: 1

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(a)

Let,

  • PV = present value = $168 million
  • PMT = periodic payment = $11.3 million
  • n = number of years = 26
  • r = internal rate of return

The internal...

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How to Calculate the Present Value of an Annuity

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Chapter 8 / Lesson 3
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Learn how to find present value of annuity using the formula and see its derivation. Study its examples and see a difference between Ordinary Annuity and Annuity Due.


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