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 = $2,458.00 b The future value of $400 per year for ten years at 10 percent = $400 x 15.937 = $6,374.80 c The present value of $200 per year for five years at 5 percent = $200 x 4.329 = $865.80 d The future value of $200 per year for five years at 5 = $200 x 5.526 = $1,105.20 9.6 Consider the following uneven cash flow stream: Year Cash Flow PV Factor Present Value 0 $0 1 250 0.909 227.25 2 400 0.826 330.40 3 500 0.751 375.50 4 600 0.683 409.80 5 600 0.621 372.60 Total 1,715.55 ======= a What is the present (Year 0) value if the opportunity cost (discount) rate is 10 percent? $1,715.55 9.7 Consider another uneven cash flow stream: 9.7 Year Ca Year Cash Flow PV Factor Present Value 0 $2,000 1.000 2,000.00 1 2,000 0.909 1,818.00 2 0 0.826 0.00 3 1,500 0.751 1,126.50 4 2,500 0.683 1,707.50 5 4,000 0.621 2,484.00 Total 9,136.00 ======= a. What is the present (Year 0) value of the cash flow stream if the opportunity cost rate is 10 percent? $9,136.00 b 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 annually Year Cash Flow FV Factor Future Value 0 $2,000 1.611 3,222.00 1 2,000 1.464 2,928.00 2 0 1.331 0.00 3 1,500 1.210 1,815.00 4 2,500 1.100 2,750.00 5 4,000 1.000 4,000.00 Total 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 years Immediate Payment $ 1,750,000 Annuity for 19 years at 6% (1,750,000 x 11.158) $19,526,500 Total $21,276,500 =========
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