Question

# You win the lottery and have a choice of receiving annual payments (beginning one year from...

 You win the lottery and have a choice of receiving annual payments (beginning one year from today) of \$50,000 for 25 years - or a lump sum of \$875,000. If the discount rate is 2.8%, how much do you gain by making the correct financial choice? \$50,000.00 \$875,000.00 2.8% 25 PV of Pmts: Gain: A share of stock has most recently paid am annual dividend of \$4.50. The next dividend will be paid one year from today. If you assume the dividend will grow in perpetuity at an annual rate of 2% as it has in the past, and the Required Rate of Return is 8.2%, what is the value of a share of this stock, \$4.50 8.2% 2.0% Answer: What would be the value of the stock described in the above question if the annual dividend was not expected to grow. Assume the same Required Rate of Return. Answer: You decide to buy a new car, a new BMW 325, because you think you'll look hip driving it. The car cost \$70,000, but you'll only need to finance \$62,500. You can finance it at 4.1% APR for 6 years. What will your monthly payments be? \$70,000.00 \$62,500.00 4.1% 6 12 Answer:

To compare both the options, we need to calculate the PV value of both.

PV of Option 1:

PV of Annuity = Amount * (1 - (1+R)^(-n))/R

Where, R is the discount rate (2.8%) and n is number of years (25 years). Putting the values in the formula:

= \$50,000 * (1 - (1.028^(-25))/0.028

= \$890,382

PV of option 2:

The other option is to get \$875,000 in lumpsum today.

Clearly, we should choose option 1 as it has greater PV.

The gain we make by choosing option 1 is:

\$890,382 - \$875,000 = \$15,382.

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