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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
=======
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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