Dr Nick
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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
0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â $0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 250Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.909Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 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?Â
                                                                               $1,715.55
9.7 Consider another uneven cash flow stream:
 9.7
Year Ca Year                                Cash Flow              PV Factor                   Present Value
0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â $2,000Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1.000Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2,000.00
1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2,000Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.909Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 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 10Â 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
0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â $2,000Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1.611Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 3,222.00
1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2,000Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1.464Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 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
                                                                                                           =========