September – December 2023 Allen

Business & Finance

9.4 Find the following values assuming a regular, or ordinary, annuity:a The present value of $400 per year for ten years at 10 percent= $400 x 6.145= $2,458.00b The future value of $400 per year for ten years at 10 percent= $400 x 15.937= $6,374.80c The present value of $200 per year for five years at 5 percent= $200 x 4.329= $865.80d The future value of $200 per year for five years at 5= $200 x 5.526= $1,105.209.6 Consider the following uneven cash flow stream:Year Cash Flow PV Factor Present Value0 $01 250 0.909 227.252 400 0.826 330.403 500 0.751 375.504 600 0.683 409.805 600 0.621 372.60Total 1,715.55=======a What is the present (Year 0) value if the opportunity cost (discount) rate is 10 percent?$1,715.559.7 Consider another uneven cash flow stream:9.7Year Ca Year Cash Flow PV Factor Present Value0 $2,000 1.000 2,000.001 2,000 0.909 1,818.002 0 0.826 0.003 1,500 0.751 1,126.504 2,500 0.683 1,707.505 4,000 0.621 2,484.00Total 9,136.00=======a. What is the present (Year 0) value of the cash flow stream if the opportunity cost rate is 10 percent?$9,136.00b What is the value of the cash flow stream at the end of Year 5 if the cash flows are invested in an account that pays 10 percent annuallyYear Cash Flow FV Factor Future Value0 $2,000 1.611 3,222.001 2,000 1.464 2,928.002 0 1.331 0.003 1,500 1.210 1,815.004 2,500 1.100 2,750.005 4,000 1.000 4,000.00Total 14,715.00=======9.9 Assume that you just won $35 million in the Florida lottery, and hence the state will pay you 20 annual payments of $1.75 million each beginning immediately. If the rate of return on securities of similar risk to the lottery earnings (e.g., the rate on 20-year U.S. Treasury bonds) is 6 percent, what is the present value of your winnings?Present Value of Annuity of Annuity of $1,750,000 for 20 yearsImmediate Payment $ 1,750,000Annuity for 19 years at 6% (1,750,000 x 11.158) $19,526,500Total $21,276,500=========

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