Your grandfather has offered you a choice of one of the three following alternat

Question

Your grandfather has offered you a choice of one of the three following alternatives: $11,000 now; $4,500 a year for ten years; or $66,000 at the end of ten years. Use Appendix B and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. a-1. Assuming you could earn 8 percent annually, compute the present value of each alternative: (Do not round intermediate calculations. Round your final answers to 2 decimal places.) a-2. Which alternative should you choose? $66,000 received at end of ten years $4,500 received each year for ten years $11,000 received now b-1. If you could earn 9 percent annually, compute the present value of each alternative: (Do not round intermediate calculations. Round your final answers to 2 decimal places.) b-2. Which alternative should you choose? $66,000 received each year for ten years $4,500 received at end of ten years $11,000 received now

Explanation / Answer

a-1 Assuming you could earn 8 percent annually compute the present value of each alternative Present value today $11,000 Year Cash flow Discount factor @ 8% Present Value 1 $4,500 0.925926 $4,166.67 2 $4,500 0.857339 $3,858.02 3 $4,500 0.793832 $3,572.25 4 $4,500 0.73503 $3,307.63 5 $4,500 0.680583 $3,062.62 6 $4,500 0.63017 $2,835.76 7 $4,500 0.58349 $2,625.71 8 $4,500 0.540269 $2,431.21 9 $4,500 0.500249 $2,251.12 10 $4,500 0.463193 $2,084.37 $30,195.37 Present value if $ 4500 received for 10 years $30,195.37 $66000*0.4632 30571.20 a-2 Alternative 3 will be chosen since the present value today is $ 30571.20 b-1 Assuming you could earn 9 percent annually compute the present value of each alternative Present value today $11,000 Year Cash flow Discount factor @ 9% Present Value 1 $4,500 0.917431 $4,128.44 2 $4,500 0.84168 $3,787.56 3 $4,500 0.772183 $3,474.83 4 $4,500 0.708425 $3,187.91 5 $4,500 0.649931 $2,924.69 6 $4,500 0.596267 $2,683.20 7 $4,500 0.547034 $2,461.65 8 $4,500 0.501866 $2,258.40 9 $4,500 0.460428 $2,071.93 10 $4,500 0.422411 $1,900.85 $28,879.46 Present value if $ 4500 received for 10 years $28,879.46 $66000*0.4224 27878.40 b-2 Alternative 2 will be chosen since the present value today is $ 28879.46

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