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For your 50th birthday, your rich uncle has decided to make you an extremely gen

ID: 2649829 • Letter: F

Question


For your 50th birthday, your rich uncle has decided to make you an extremely generous gift. He is giving you $1 million! You have several options for receiving the money: Receive a $1 million lump sum payment Receive a 10-year annuity for $105,000 per year starting on your 51st birthday Receive a perpetuity of $50,000 per year for the rest of your life starting on your 50th birthday 3. In a 4- to 5-sentence discussion post, provide answers to the following questions: Which option would you choose? What are the pros and cons of each option?

Explanation / Answer

Assuming the 50th birthday to be today, (i.e 50th birthday is point 0 in calculating the time value of money) and assuming the rate of interest to be 10%:

Option 1: Receive a lumpsum of $ 1 million on the day of birthday. Its Present Value (PV) at point 0 will be $1 million.

Option 2: Receiving 10 year annuity of $105,000 for 10 years, starting from point 1. PV will be annuity/(1+interest rate)^time. Using this formula PV has been calculated:

Option 3: Value of perpetuity = amount/discount rate

= 50,000/0.10 = $500,000

So, the PV of all 3 options are:

As the PV of the 1st option is the maximum, you should opt for the $1 million lump sum payment.

The advantage of Option 1 is that you will receive the entire amount today. Economic value of money today is more than the economic value of money tomorrow.

The disadvantage of option 2 is that you are losing on the interest amount when compared to the option of receiving the lump sum payment.

Option 3 is the least desirable, as it is giving the least value.

Year Amount Discount factor PV 1 105,000.00 1.10 95,454.55 2 105,000.00 86,776.86 3 105,000.00 78,888.05 4 105,000.00 71,716.41 5 105,000.00 65,196.74 6 105,000.00 59,269.76 7 105,000.00 53,881.60 8 105,000.00 48,983.27 9 105,000.00 44,530.25 10 105,000.00 40,482.05 Total PV 645,179.55