Contrast the Present Value of a Fixed Sum Concept with the Present

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The Answer is Fixed Sum
A dollar in hand today could be worth more than a dollar to be received next year. If an investor had it now, he or she could invest it, earn interest, and end up next year with more than one dollar. For instance, if $100 is invested at 5 percent for one year, the amount will grow to $105. Put differently, the present value of $105 expected to be received next year, discounted for one year at 5 percent, is $100. In general, the present value of a sum due n periods in the future is the amount which, if it were on hand today, would grow to equal the future sum. The present value of a fixed sum can be calculated by using the PV equation, or it could be calculated by using a financial calculator.
2. Present Value: Annuity
Perhaps the most important tool in the financial planner's kit is the present value of an annuity (PVA) concept. This is a valuable concept, since identification of an undervalued stock, evaluation of an income-producing limited partnership, or a lump sum versus a pension for life retirement settlement can be solved by using the PVA concept.
The PVA is calculated by using equation 3.5, or it could be calculated by using a financial calculator as demonstrated in Table 3.6.
Here are two examples to demonstrate when the present value of a fixed sum and the present value of an annuity are used. An investor expects to receive $10,000 from a limited partnership seven years from today. Using a discount rate of 10 percent, the present value of this fixed sum equals $5,131.58 (see Table 3.3). Next, we present an interesting problem which requires the use of the PVA concept. A client has just won a lottery. He is offered the following alternatives: (a) a four-year annuity with payments of $1,000 at the end of each year; or (b) a lump sum payment of $3,170 rounded off today. Which one should he choose if the market interest rate is 10 percent? At first blush, either the four-year payment or the lump sum may appear more attractive. However, if the money is expected to earn 10 percent a year, both alternatives are of equal value. The calculation of a present value of an annuity is presented in equation 3.7.

Contrast the Present Value of a Fixed Sum Concept with the Present

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