# allen 4

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

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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

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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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