Build a working spreadsheet to answer this question:

Xenia wins the lottery! She has a choice between

Option A: $21,000,000.00 received today.

Option B: 24 payments of $1,737,119.56 at the start of every year for 24 years, with the first payment today.

The nominal annual interest rate is i⁽²⁶⁾ = 9.000%. Xenia wants you to advise them which option to choose.

a) Build a spreadsheet (see the posted example) to compare the present value of the 2 options. Which would you recommend?

b) Suppose instead you assumed they would never spend any of the money, instead saving it all until the time of the last payment of Option B. Find the future value of both options at this time. Would this calculation change your recommendation?

c) If the interest rate were i⁽²⁶⁾ = 4.000% instead, would that change which option you recommend?

d) Obviously there is some interest rate i⁽²⁶⁾ at which the present value of the two options is the same. Find that value (accurate to 3 decimal places, e.g. 3.456%) using either trial and error or goal seek. (Warning: if you are using trial and error using only 3 decimal places for the interest rate, the present values you compute might not match exactly!)

The spreadsheet should look similar to the sample Template below:

1 2 3 4 5 6 7 8 9 10 II 12 23 24 25 26 27 28 29 A 34 35 0 1 13 14 15 16 17 Year Payment Amount 18 19 20 21 22 2 3 4 5 6 7 8 9 10 30 11 31 12 32 13 3.3 14 B 15 16 Nominal Rate r(m) Compounding m Effective Ann. Rate i Option A (lump sum) amount Option B (annual) amount Number of years n $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000,00 $1,125.000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000,00 Total PV(Payments) PV factor 1.00000 0.97066 0.94218 0.91454 0.88771 0.86167 0.83639 0.81185 0.78803 0.76491 0,74247 0.72069 0.69954 0.67902 0.65910 0.63976 0.62099 D 3.000% 2 3.02% i (1+i(m)/m)^m-1 $15,000,000.00 $1,125,000.00 25 PV(Payment) $17,207,224.85 Total FV(Payments) $1,125,000.00 $1,091,994.47 $1,059,957.26 $1,028,859.97 $998,675.01 $969,375.64 $940,935.85 $913,330.44 E S886,534.92 $860,525.53 $835,279,22 $810,773.59 $786,986.91 $763,898.09 $741,486.66 $719,732.73 $698,617.03 FV factor 2.04348 1.98353 1.92533 1.86885 1.81402 1.76080 1.70914 1.65900 1.61032 1.56308 1.51722 1.47271 1.42950 1.38756 1.34686 F $38,854,052.23 FV(Payment) $2,298,913.08 $2,231,466.99 $2,165,999.65 $2,102,453.00 $2,040,770.71 $1,980,898.07 $1,922,781.98 $1,866,370.92 $1,811,614.86 $1,758,465.25 $1,706,874.95 $1,656,798.23 $1,608,190.66 $1,561,009.16 $1,515,211.88 G PV(t=0) FV(t=n-1) 1.30734 $1,470,758.22 $1,427,608.74. 1.26899 H I Option A: $15,000,000.00 $30,652,174.34 Option B: J $17,207,224.85 $38,854,052.23 a) Which option is better? b) New rate, now which option is better? c) New rate, now which option is better? d) Ifr(m) 4.697% the two options are worth the same. K Diff: A-B -$2,207,224.85 -$8,201,877.89 L 35 36 37 38 39 40 41 42 43 44 45 46 A 16 17 18 19 20 21 22 23 24 25 B $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $0.00 C 0.62099 0.60277 0.58509 0.56792 0.55126 0.53509 0.51939 0.50415 0.48936 0.47500 D $698,617.03 $678,120.83 $658,225.95 $638,914.75 $620,170.11 $601,975.41 $584,314.50 $567,171.73 $550,531.91 $0.00 E 1.26899 1.23176 1.19562 1.16054 1.12649 1.09344 1.06136 1.03023 1.00000 0.97066 F $1,427,608.74 $1,385,725.20 $1,345,070.44 $1,305,608.43 $1,267,304.16 $1,230,123.67 $1,194,033.99 $1,159,003.13 $1,125,000.00 $0.00 G H I J K L 1 2 3 4 5 6 7 8 9 10 II 12 23 24 25 26 27 28 29 A 34 35 0 1 13 14 15 16 17 Year Payment Amount 18 19 20 21 22 2 3 4 5 6 7 8 9 10 30 11 31 12 32 13 3.3 14 B 15 16 Nominal Rate r(m) Compounding m Effective Ann. Rate i Option A (lump sum) amount Option B (annual) amount Number of years n $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000,00 $1,125.000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000,00 Total PV(Payments) PV factor 1.00000 0.97066 0.94218 0.91454 0.88771 0.86167 0.83639 0.81185 0.78803 0.76491 0,74247 0.72069 0.69954 0.67902 0.65910 0.63976 0.62099 D 3.000% 2 3.02% i (1+i(m)/m)^m-1 $15,000,000.00 $1,125,000.00 25 PV(Payment) $17,207,224.85 Total FV(Payments) $1,125,000.00 $1,091,994.47 $1,059,957.26 $1,028,859.97 $998,675.01 $969,375.64 $940,935.85 $913,330.44 E S886,534.92 $860,525.53 $835,279,22 $810,773.59 $786,986.91 $763,898.09 $741,486.66 $719,732.73 $698,617.03 FV factor 2.04348 1.98353 1.92533 1.86885 1.81402 1.76080 1.70914 1.65900 1.61032 1.56308 1.51722 1.47271 1.42950 1.38756 1.34686 F $38,854,052.23 FV(Payment) $2,298,913.08 $2,231,466.99 $2,165,999.65 $2,102,453.00 $2,040,770.71 $1,980,898.07 $1,922,781.98 $1,866,370.92 $1,811,614.86 $1,758,465.25 $1,706,874.95 $1,656,798.23 $1,608,190.66 $1,561,009.16 $1,515,211.88 G PV(t=0) FV(t=n-1) 1.30734 $1,470,758.22 $1,427,608.74. 1.26899 H I Option A: $15,000,000.00 $30,652,174.34 Option B: J $17,207,224.85 $38,854,052.23 a) Which option is better? b) New rate, now which option is better? c) New rate, now which option is better? d) Ifr(m) 4.697% the two options are worth the same. K Diff: A-B -$2,207,224.85 -$8,201,877.89 L 35 36 37 38 39 40 41 42 43 44 45 46 A 16 17 18 19 20 21 22 23 24 25 B $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $1,125,000.00 $0.00 C 0.62099 0.60277 0.58509 0.56792 0.55126 0.53509 0.51939 0.50415 0.48936 0.47500 D $698,617.03 $678,120.83 $658,225.95 $638,914.75 $620,170.11 $601,975.41 $584,314.50 $567,171.73 $550,531.91 $0.00 E 1.26899 1.23176 1.19562 1.16054 1.12649 1.09344 1.06136 1.03023 1.00000 0.97066 F $1,427,608.74 $1,385,725.20 $1,345,070.44 $1,305,608.43 $1,267,304.16 $1,230,123.67 $1,194,033.99 $1,159,003.13 $1,125,000.00 $0.00 G H I J K L