# Allen

9.4 Find the following values assuming a regular, or ordinary, annuity:

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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

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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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