# Allen

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=========