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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
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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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