You just won the lottery! You have two choices for payout of your winnings. You

Question

You just won the lottery! You have two choices for payout of your winnings. You can either choose a payment of $6 million in five years’ time, or a lump sum of $3.8 million right now.                                                                     (13 marks total)

a. Assuming that you can reinvest any cash you receive at an annual rate of return of 10%—simple interest—which option would you prefer?          (2 marks)

b. Assuming that you can reinvest any cash you receive at an annual rate of return of 10%—compound interest—which option would you prefer?         (2 marks)

c. At what simple interest rate would you be indifferent between the two options? To solve this problem, you may use the equation manipulation method, the trial and error method, or the Goal Seek function in MS Excel (under Data—What-if-Analysis). If you choose to use trial and error method, try the rates between 11% and 12%, with 0.1% increments. If you choose to use Excel, ensure that you show your Excel formulas when presenting your answer. Marks will be deducted for incomplete or unclear answers.                                             (3 marks)

d. At what compound interest rate would you be indifferent between the two options? To solve this problem, you may use either the equation manipulation method, the trial and error method or the Goal Seek function in MS Excel (under Data—What-if-Analysis). If you choose to use trial and error method, try the rates between 9% and 10%, with 0.1% increments. If you choose to use Excel, ensure that you show your Excel formulas when presenting your answer. Marks will be deducted for incomplete or unclear answers.                         (3 marks)

e. How far into the future can the $6 million be deferred before we become indifferent between receiving the money now and receiving it in the future, assuming a compound rate of return of 10%?                              (3 marks)

Explanation / Answer

Option 1 Option 2 Prize now Prize after five years Principal                        3.80           6.00 =3.8*10%*5 Simple intrest after 5 years                        1.90 Total After five Years                        5.70           6.00 If Simple rate of interest, I will prefer option 2 Compound Interest Principal                        3.80           6.00 =3.8*(1+10%)^5 Simple intrest after 5 years                        6.12 Total After five Years                        6.12           6.00 If Compound rate of interest, I will prefer option 1 If simple rate of interest, total investment equivalent to 6 million at the end of five year Principal                        3.80           6.00 =3.8*11.6%*5 Simple intrest after 5 years                        2.20 Total After five Years                        6.00           6.00 If Simple rate of interest, 11.6% is the point of indifferent If Compound rate of interest, total investment equivalent to 6 million at the end of five year Principal                        3.80           6.00 =3.8*(1+9.55%)^5 Simple intrest after 5 years                        6.00 Total After five Years                        6.00           6.00 If Compound rate of interest, 9.55% is the point of indifferent If Compound rate of interest 10%, period of indifferent Principal                        3.80           6.00 =3.8*(1+10%)^(4.8) Simple intrest after 5 years                        6.00 Total After five Years                        6.00           6.00 If Compound rate of interest 10%, period of indifferent is 4.8 years

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