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# Making investment decissions based on present values

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1. Your Uncle Joe has just died and left \$10,000 payable to you when you turn 30 years old. You are now 20. Currently, the annual rate of interest on can obtain by buying 10-year bonds is 6.5 percent. Your brother offers you \$6,000 cash right now to sign over your inheritance. Should you do it? No he should not do it be because if he waits 10 more years, he will get more money.

2. Calculate the present value of the income streams A to E in Table 1 at an 8 percent interest rate and again at 10 percent rate.

Suppose that the investment behind the flow of income in E is a machine that cost\$1,235 at the beginning of the year 1. Would you buy the machine if the interest rate were 8 percent? If the interest rate were 10 percent?

TABLE 1

End of Year A B C D E
1 \$80 \$80 \$100 \$100 \$500
2 80 80 100 100 300
3 80 80 1,100 100 400
4 80 80 0 100 300
5 1,080 80 0 100 0
6 0 80 0 1,100 0
7 0 1,080 0 0 0

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#### Solution Preview

Please refer attached file for better clarity of tables.

Solution 1.

PV=FV/(1+r)^n
FV=Future Value
PV=Present Value
r = rate of interest
n=number of periods
Present Value of \$10,000 payable after 10 years=10000/(1+0.065)^10=\$5327.2604

Since PV of amount receivable is less than \$6000, it should accept \$6000.

Solution 2.

For calculating PV of any cash flow, we can use formula used in problem 1. You can also use "PV of \$1 received at the end of n periods" to find PV factor.

Refer tables and get PV factor at 8%. PV of any cash flow will be equal to cash flow multiplied by PV factor.

Summation of all PV's for 7 years will give you Total PV of cash flows in each case.

Present Value of cash flows
Year ...

#### Solution Summary

There are two problems. Solution to each problem describes the steps to determine present value of cash flows associated with various alternatives.

\$2.49