![]() After all, if there are no more valuable choices to make, you lose little by giving up liquidity. Liquidity is valuable because it allows you to make choices. When opportunity costs are low, you have nothing better to do with your liquidity, but when opportunity costs are higher, you may sacrifice more by having no liquidity. When opportunity cost or risk is low, waiting for liquidity doesn’t matter as much as when opportunity costs or risks are higher. On the other hand, if your discount rate is higher than 4 percent, or if you feel that your use of that liquidity would earn you more than 4 percent, then you have more lucrative things to do with that money and you want it now: the annuity is worth less to you than the payout.įor an annuity, as when relating one cash flow’s present and future value, the greater the rate at which time affects value, the greater the effect on the present value. You can afford to wait for that liquidity and collect it over twenty years because you have no better choice. In other words, if your discount rate is about 4 percent or less-if you don’t have more lucrative choices than earning 4 percent with that liquidity-then the annuity is worth more to you than the immediate payout. The annuity would be worth the same to you as the lump-sum payout if your discount rate were 4.16 percent. Your discount rate or opportunity cost will determine the annuity’s value to you, as Figure 4.8 "Lottery Present Value with Different Discount Rates" shows.įigure 4.8 Lottery Present Value with Different Discount RatesĪs expected, the present value of the annuity is less if your discount rate-or opportunity cost or next best choice-is more. So the question is, What is the annuity worth to you? The value of the annuity is not simply $10 million, or $500,000 × 20, because those $500,000 payments are received over time and time affects liquidity and thus value. The present value of the lump-sum payout is $6,700,000. You would choose the alternative with the greatest value. The lottery agency offers you a choice: take $500,000 per year over 20 years or take a one-time lump-sum payout of $6,700,000. The discount rate, which determines that present value, is chosen at the discretion of the lottery agency. To make the annual payment more attractive for you-it isn’t, because you would want to have more liquidity sooner-the lump-sum option is discounted to reflect the present value of the payment annuity. ![]() The lottery agency would prefer that you took the annual payment because it would not have to give up as much liquidity all at once it could hold on to its liquidity longer. If you win the lottery, for example, you are typically offered a choice of payouts for your winnings: a lump sum or an annual payment over twenty years. the rate at which time affects value (r).Īlmost any calculator and the many readily available software applications can do the math for you, but it is important for you to understand the relationships between time, risk, opportunity cost, and value.the amount of the future cash flows (the same for each),.To calculate the present value of an annuity, you need to know You could think of your paycheck as an annuity, as are many living expenses, such as groceries and utilities, for which you pay roughly the same amount regularly. Fixed-rate bond interest payments are an annuity, as are stable stock dividends over long periods of time. Most consumer loan repayments are annuities, as are, typically, installment purchases, mortgages, retirement investments, savings plans, and retirement plan payouts. When there are regular payments at regular intervals and each payment is the same amount, that series of cash flows is an annuity A series of cash flows in which equal amounts happen at regular, periodic intervals. Often, the series of cash flows is such that each cash flow has the same future value. The present value (PV) of the series of cash flows is equal to the sum of the present value of each cash flow, so valuation is straightforward: find the present value of each cash flow and then add them up. It is quite common in finance to value a series of future cash flows (CF), perhaps a series of withdrawals from a retirement account, interest payments from a bond, or deposits for a savings account. Discuss the relationships of those factors to the annuity’s value.Identify the factors you need to know to calculate the value of an annuity. ![]()
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