Your brother-in-law has just won the lottery and is coming to you for free advic

Question

Your brother-in-law has just won the lottery and is coming to you for free advice. He has two options in which he may receive his payments. He can elect: 1) 10 annual beginning-of-year payments of $1 million or, 2) 30 annual beginning-of year payments of $400,000. If he expects to earn a 5% return on his investments, which option offers the highest present value? (indicate all inputs in your financial calculator)

So I think I am doing incorrectly. I am doing the caculations as:

N=10, I=5, PMT= $1,000,000 PV= 7,721,734.92

N= 30 i= 5 pmt= 400,000 pv= $6,148,980.41

What am I doing wrong?

Explanation / Answer

The most important thing to consider in this question is that the payments are received in the BEGINNING of the period, hence it is an annuity due. You need to set your calculator in the BGN mode.

1) Option 1:

N = 10

I/Y = 5

PMT = $1,000,000

Solving for PV = $8,107,821.68

2) Option 2:

N = 30

I/Y = 5

PMT = $400,000

Solving for PV = $6,456,429.43

Hence, we can conclude that the first option of receiving $1,000,000 for 10 years at the beginning of the year is a better option as it has higher PV.

I hope my solution solves your query.

Regards.

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