After hearing a knock at your front door, you are surprised to see the Prize Pat

Question

After hearing a knock at your front door, you are surprised to see the Prize Patrol from a large, well-known magazine subscription company. It has arrived with the good news that you are the big winner, having won $30 million. You have three options.

Your financial adviser tells you that it is reasonable to expect to earn 13 percent on investments.   

Required:
1. Calculate the present value of each option. (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1.) (Use appropriate factor(s) from the tables provided. Enter your answers in dollars, not in millions.)

    

2. Determine which option you prefer.

(a) Receive $1.5 million per year for the next 20 years. (b) Have $10.5 million today. (c) Have $2.25 million today and receive $1,200,000 for each of the next 20 years.

Explanation / Answer

Solution:

Basically it is the problem of time value of money. We need to calculate the Present Value of ordinary annuity.

Part 1-a – PV of option a

Terms (n) = 20

Annual Receiving Amount = $1,500,000

Rate of Interest (R) = 13%

Present Value factor for ordinary annuity at 13% for 20 period = (1 + 1/(1+0.13)20) / 0.13 = 7.025

PV of Option 1 = Annual Receivable amount x pv factor for ordinary annuity = 1,500,000 x 7.025 = $10,537,500 or 10.5375 Million

Present Value of Option B = $10.5 million today is the present value.

Present Value of Option C

Present Value of Option C = $2.25 Million today + PV of ordinary annuity

= $2.25 Million + ($1.2 million x PV factor as calculated in part a 7.025)

= $2.25 + 8.43 Million

= $10.63 million

Part 2 – Determined which option is better

The Option C has highest Present Value. Hence Option C is better

Hope the above calculations, working and explanations are clear to you and help you in understanding the concept of question.... please rate my answer...in case any doubt, post a comment and I will try to resolve the doubt ASAP…thank you

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