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Compounding and Discounting
The time value of money means that the current value of a dollar is higher than a dollar promised at some point in the future (Ross et al., 2017, p. 98). Essentially, the money that one has today can reach a higher value than the same amount of money in the future. The value of money is determined in two ways to determine the present and the future: compounding and discounting.
Compounding is placing money in an account today for a promised rate of return for more than one period, usually months or years. Accrued interest is reinvested in the same account at the end of each investment period, compounding one's investment. The value of the investment at the end of the series of periods is the future value and can be calculated based on the value of the initial investment, interest, and additional investments.
Discounting is the opposite of compounding. One knows how much will be needed in the future, future value, so investments are made that account for how much money is needed to invest at a specific rate of return ("Compounding and" n.d., para. 2). If, for example, a person wanted to have a future value of $5,000.00 they would need to calculate the present value at the promised rate of return. If the rate of return were 3%, one would need to invest $4854.37. The equation used to calculate present value is present value x rate of return = future value. In this case, it would be $4854.37 x 1.03 = $5000.00.
Importance
Managers and investors can use compounding and discounting to evaluate investments. They must consider money's present and future value when considering these investments. For example, if a company were to invest in a project that costs $12,000 to finance yet is only expected to yield $10,000 in five years, it is not worth investing in as the present value of money is higher than the future value. Similarly, if the same project produces $12,000today and requires a payment of $10,000 in five years, it would be a good investment as the front payment will compound to well over $10,000 in those five years (Merritt, 2011, para. 5)
Annuities
"There are two basic types of annuities: ordinary annuities and annuities due" ("Annuities," n.d., para. 2). An ordinary annuity requires payments to be made at the end of each period for a specified number of periods, where an annuity due requires the payment to occur at the beginning of the period. An example of an ordinary annuity would be car payments, and an example of an annuity due would be insurance payments for that same car. The car payment covers the period leading up to the payment due date, whereas the insurance payments for that same
car cover the period following the payment due date. These payments also apply to those who receive ordinary or annuity-due payments, such as the financier and insurer of the car.
Importance
Understanding when payments are due, at the beginning or end of a period, can assist managers in having predictable inflows and outflows of cash (Annuities, n.d.). Knowing when cash is going out and coming in is essential, as managers need to know what cash assets are available to them to meet their financial needs. Investors can gauge the cash flow to determine a company's liquidity and long-term
solvency.
References
Annuities. (n.d.).Lumen Boundless Finance.Retrieved fromhttps://courses.lumenlearning.com/boundless-finance/chapter/annuities/
Annuities and the future value and present value of multiple cash flows. (n.d.).Investopedia.Retrieved fromhttps://www.investopedia.com/walkthrough/corporate-finance/3/discounted-
cash-flow/annuities.aspxCompounding and discounting. (n.d.).Clint Burdett Strategic
Consulting.Retrieved from HTTP://www.clintburdett.com/process/10_costs/costs_01_discounting.htm#.WiijRFW
nE_4https://www.theatlantic.com/business/archive/2015/10/the-recession-hurt-
americans-retirement-accounts-more-than-everyone-thought/410791/
Merritt, C. (2011, October 2). What is the relationship between discounting and compounding? Retrieved fromhttps://www.sapling.com/12115675/relationship-
between-discounting-compounding
Ross, S.A., Westerfield, R.W., & Jordan, B.D. (2017).Essentials of corporate finance(9ed.).New York, NY: McGraw-Hill Education.Gregory Lind -
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Work through the following scenario to understand future value and the concept of compounding interest.
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formula is
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Rate =r= i
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Present Value =
years
%
M
1.
0
S (t) et dt.
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Help
Save &
The difference between an ordinary annulty and an annulty due Is:
Multiple Choice
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an ordinary annuity represents a future value and an annuity due represents a present value.
an ordinary annuity assumes the cash flows occur at the beginning of the period and an annuity due assumes the cash flows occur at the end of the period.
an ordinary annuity assumes the cash flows occur at the end of the period and an annuity due assumes the cash flows occur at the beginning of the period.
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Compute the following:
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There are three categories of cash flows: single cash flows, also referred to as “lump sums,” a stream of unequal cash flows, and annuities.
Based on your understanding of annuities, answer the following questions.
Which of the following statements about annuities are true? Check all that apply.
An annuity due earns more interest than an ordinary annuity of equal time.
An annuity due is an annuity that makes a payment at the end of each period for a certain time period.
Ordinary annuities make fixed payments at the end of each period for a certain time period.
A perpetuity is a constant, infinite stream of equal cash flows that can be thought of as an infinite annuity.
Which of the following is an example of an annuity?
A lump-sum payment made to a life insurance company that promises to make a series of equal payments later for some period of time
An investment in a certificate of deposit (CD)
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