Question

Please Show all work and formulas!

Problem 4

You have just won a lottery of $1 million and you can choose among the following three payout options.  The effective annual interest rate (EAR) is 5%.

Option A: $200,000 right now and $100,000 every two years, starting 2 years from now and ending 16 years from now.

Option B: $100,000 a year at the end of the next 10 years, with the first payment one year from today.

Option C: Twenty annual payments of $40,000 and a 21^st payment of $200,000.  The first payment is made right now. The 21^st payment is due 20 years from now.

Please calculate the present values of all three options. Which option should you choose?

Problem 5

Today is January 1, 2019, and your friend Arnold Armstrong signs a 4-year contract to play for a minor league football team.  He will receive $300,000 for 2019, $500,000 for 2020, $700,000 for 2021, and $900,000 for 2022. All payments are made at the end of year.  Assume 10% annual interest rate (EAR).

a.   What is the present value of his contract?

b.   If instead of annual payments he wants equal dollar amount month-end cheques over his contract period, starting January 31, 2019, how large is his monthly pay?

Answer 1

Option A: YEAR cash flows $200,000 $0 $100,000 $0 $100,000 2 3 $100,000 $0 so $100,000 pv @ 5% 1.0000 0.9524 0.9070 0.8638 0.8227 0.7835 0.7462 0.7107 0.6768 0.6446 0.6139 0.5847 0.5568 0.5303 0.5051 0.4810 0.4581 8 discounted cash flows $200,000.00 $0.00 $90,702.95 $0.00 $82,270.25 $0.00 $74,621.54 $0.00 $67,683.94 $0.00 $61,391.33 $0.00 $55,683.74 $0.00 $50,506.80 $0.00 $45,811.15 $728,671.69 11 $100,000 $0 $100,000 14 $100,000 $0 $100,000 Present value 16

Option B: YEAR 0 1 2 3 4 5 pv @ 5% 1.0000 0.9524 0.9070 cash flows $100,000 $100,000 $100,000 $100,000 $100,000 $100,000 $100,000 $100,000 $100,000 $100,000 Present value 0.8638 0.8227 0.7835 0.7462 discounted cash flows $100,000.00 $95,238.10 $90,702.95 $86.383.76 $82,270.25 $78,352.62 $74,621.54 $71,068.13 $67,683.94 $64,460.89 $810,782.17 8 0.7107 0.6768 0.6446

Option C: YEAR 0 i 2 3 4 5 pv @ 5% 1.0000 0.9524 0.9070 0.8638 0.8227 0.7835 0.7462 0.7107 10 111 12 13 14 15 16 17 18 19 20 cash flows $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $200,000 Present value 0.6768 0.6446 0.6139 0.5847 0.5568 0.5303 0.5051 0.4810 0.4581 0.4363 0.4155 0.3957 0.3769 discounted cash flows $40,000.00 $38,095.24 $36,281.18 $34,553.50 $32,908.10 $31,341.05 $29,848.62 $28,427.25 $27,073.57 $25,784.36 $24,556.53 $23,387.17 $22,273.50 $21,212.85 $20,202.72 $19,240.68 $18,324.46 $17,451.87 $16,620.83 $15,829.36 $75,377.90 $598,790.73

Choose option B as having high present value