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Gill, Madura. Personal Finance, 4th Canadian Edition 2019. p. 56.

  1. True or False? It is always better to choose a lump sum than periodic payments over time.

p. 519

  1. T

Doesn't the answer depend on the amount of lump sum vs. periodic payments and inflation?

Or are the authors assuming that if lump sum = P, then you get n periodic payments of $\frac{P}{n}$ (for a total of $n × \frac{P}{n}$)? Then inflation will cause each P/n to be worth less.

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    $\begingroup$ If the question did not provide more information, then you are correct in your doubts. For example, it is not better to choose a single lump sum of \$1 than monthly payments of \$100, so that the given statement is false. $\endgroup$ – Kenny LJ Jul 30 at 6:13
  • $\begingroup$ +1 for @KennyLJ. My guess is that the author is assuming, as you said, the sum of periodic payment is equal to lump sum payment. $\endgroup$ – Art Jul 30 at 8:43
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    $\begingroup$ The author probably also ignored the possibility of negative interest rates. Tssk. $\endgroup$ – Brian Romanchuk Jul 30 at 11:00
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The answer depends on the assumed interest rate of the periodic payments, compared to the expected return of alternative investments.

To be viable as a 'good' choice, the period payments must total to an amount that is equal to or greater than what could be achieved by taking the lump sum and doing something with it. In practice, this means that a period payment must total to a larger amount than the lump sum payment, with the difference increasing as the total amount of time of payments does.

For instance, the very large lotteries in the United States offer a lump sum amount that is somewhere on the order of 60% of the 'advertised' amount, which is what would be earned over 30 years of periodic payments. This figure is calculated assuming a 5% year-over-year increase of the payment amount.

Whether one is better than the other depends on what would be done with the lump sum money in the meantime. If one could invest the money or start a business with an expected rate of return greater than the one used to generate the periodic payment amount, then it is a bad idea to take the periodic payment; conversely, if the rate used in the periodic payment calculation is greater than what one would expect to earn themselves, then it would be a bad idea to take the lump sum.

In the real world, since the periodic payment calculation is usually made with a conservative, guaranteed rate, the lump sum would be better. If the periodic payment calculation is made with an assumed rate of 0% (ie, the total of all payments is equal to the lump sum amount), the lump sum will always be superior, assuming it can be used to earn any money at all. It sounds like the author is implicitly assuming one of these two scenarios.

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