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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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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