Speech codes and expressive harm

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

                                                                                                            =========