Question

1. Congratulations!  You won the sweepstakes.  The sweepstakes rules entitle you to a choice of one of the following prizes.  Using the concept of present value, which choice is the most valuable to you if your opportunity rate is 8%?

Choice A:  $50,000 per year for the next 20 years

Choice B:  $35,000 today, plus $45,000 per year for the next 25 years

Choice C:  $210,000 today, plus $13,000 per year for the next 40 years

Answer 1

Choice A:

Present Value of Annuity = Periodic Payment*[{1-(1+i)^(-n)} / i]

= 50,000*[{1-(1+8%)^(-20)} /8%]

= 490,907.3704

Choice B:

Present Value of Annuity = Periodic Payment*[{1-(1+i)^(-n)} / i]

= 45,000*[{1-(1+8%)^(-25)} /8%]

= $ 480,364.9285

Present Value = Amount today +Present Value of Annuity

= 35000+480364.9285

= $ 515,364.93

Choice C:

Present Value of Annuity = Periodic Payment*[{1-(1+i)^(-n)} / i]

= 13000*[{1-(1+8%)^(-40)} /8%]

= 155019.9733

Present Value = Amount today +Present Value of Annuity

= 210000+155019.9733

= $ 365,019.97

Answer = Choice B would be  the most valuable as it has the highest present value.