BUSM4160: Time Value of Money and Lottery Winnings Optimization

This report analyzes three lottery payout options for Mr. Elliot Lee, using the time value of money concept to determine the most financially advantageous choice. Option 1 offers a lump sum of $200,000, while Option 2 provides $25,000 upfront plus nine annual payments of $25,000, discounted at a 2.5% inflation rate, resulting in a present value of $224,272. Option 3 consists of $20,000 upfront and nine inflation-adjusted annual payments of $20,000, totaling a present value of $200,000. The analysis concludes that Option 2 is the most beneficial, as it yields the highest present value. Therefore, the report recommends that Mr. Lee select Option 2 to maximize his lottery winnings in present terms.

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Introduction and problem of statement
A key tool in financial decision making is the concept of time value of money. The main
argument as per this concept is that the money in the present is more valuable than the same
money expected in the future (Petty et. al., 2016). Based on the given scenario, Mr. Elliot Lee
was sent a lottery ticket by his aunt on the occasion of his 30th birthday. This lottery ticket
proved to be the winning ticket. The lottery has provided three options of payment for the
lottery winnings. The key objective of this report is to present an analysis of these three
options for determining the best option for Mr. Lee whereby the present value of his receipts
are maximized.
Discussion
It is noteworthy that money has opportunity cost since the money in the present can be
deployed for earning interest or elsewhere. As a result, if money is received in the future,
then there is loss of these earnings which needs to be compensated through higher future
payments. Further, it is also known that purchasing power of money decreases in the future
owing to inflation (Damodaran, 2015).
The three options available to Mr. Lee for claiming his lottery winnings would be critically
discussed in the wake of the above discussion.
Option 1: $ 200,000 on April 1, 2019. In this case, all the money is being received in the
present. As a result, the present value of receipts is $ 200,000 only.
Option 2: Money received in the present (i.e. April 1, 2019) = $ 25,000. Also, 9 annual
payments of $ 25,000 each would be received starting from April 1, 2020. The discounting
rate for these payments is considered to be 2.5% p.a. which is expected average inflation rate
(RBA, n.d.).
Present Value (as on April 1, 2019) = 25000 + 25000/(1.025) + 25000/(1.025)2 +
25000/(1.025)3 + 25000/(1.025)4 + 25000/(1.025)5 + 25000/(1.025)6 + 25000/(1.025)7 +
25000/(1.025)8 + 25000/(1.025)9 = $ 224,272
Hence, this option amounts to receiving $ 224,272 in present terms i.e. on April 1, 2019.
Option 3: Money received in the present (i.e. April 1, 2019) = $ 20,000. Also, 9 annual
payments of $ 20,000 each adjusted for inflation would be received starting from April 1,

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2020. Considering that the future payments would be adjusted for inflation, hence there
would be no erosion of purchasing power of money for future payments (Parrino and
Kidwell, 2014).
Hence, Present Value (as on April 1, 2019) = 20000 + 20000*9 = $200,000
Conclusion
From the above analysis, it is evident that the present value of option 1 and option 3 is the
same at $200,000. However, the present value for option 2 is higher at $224,272. Considering
that Mr. Lee would aim for highest receipts in present terms, hence the most preferred option
for him would be option 2 (Petty et. Al., 2016). Therefore, Mr. Lee would accept $ 25,000 in
cash on April 1, 2019 along with nine annual payments of $ 25,000 each from April 1, 2020.

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References
Damodaran, A. (2015), Applied corporate finance: A user’s manual, 3rd ed., New
York:Wiley, John & Sons, pp. 65-66
Parrino, R. and Kidwell, D. (2014) ,Fundamentals of Corporate Finance,4th ed., London:
Wiley Publications, pp. 76
Petty, JW, Titman, S, Keown, A, Martin, JD, Martin, P, Burrow, M & Nguyen, H (2016),
Financial Management, Principles and Applications, 3rd ed., Sydney: Pearson Education &
French Forest Australia, pp. 88-89
RBA (n.d.) Inflation Target, [Online] Available at https://www.rba.gov.au/inflation/inflation-
target.html [Accessed March 25, 2019]