Time Value of Money Concepts: Chapter Six
LO6-7: Compute the present value of an ordinary annuity, an annuity due, and a deferred annuity.
PVA = annuity amount x present value of an ordinary annuity of $1 (found by using interest rate & number of compounding periods) PVAD = annuity amount x present value of an annuity due of $1 (found by using interest rate & number of compounding periods) ***in the present value of an annuity due, no interest needs to be removed from the first cash payment
Interest rates are typically stated as what?
annual rates
What is the effective annual rate often referred to as?
annual yield
In situations when the compounding period is less than a year, the interest rate rate per compounding period is determined how?
by dividing the annual rate by the number periods: Semiannually = (annual rate) / 2 Quarterly = (annual rate) / 4 Monthly = (annual rate) / 12
LO6-5: Explain the difference between an ordinary annuity and an annuity due situation.
in an ordinary annuity, cash flows occur at the end of each period (the first cash flow of an ordinary annuity is made on compounding period after the date of which the agreement begins; the final cash flow takes place on the last day covered by the agreement) in an annuity due, cash flows occur at the beginning of each period (the first payment of an annuity due is made on the first day of the agreement, and the last payment is made one period before the end of the agreement)
LO6-6: Compute the future value of both an ordinary annuity and an annuity due.
in the future value of an ordinary annuity, the last cash payment will not earn any interest FVA = annuity amount x future value of an ordinary annuity of $1 (found by using interest rate & number of compounding periods) in the future value of an annuity due, the last cash payment will earn interest FVAD = annuity amount x future value of an annuity due of $1 (found by using interest rate & number of compounding periods) ***note: if unequal amounts are invest each year, we can't solve the problem by using the annuity tables; the future value of each payment would have to be calculated separately
Compound Interest
includes interest not only on the initial investment but also on the accumulated interest in previous periods
Effective Interest Rate
is the rate at which money actually will grow during a full year
Time Value of Money
means that money can be invested today to earn interest and grow to a larger dollar amount in the future
LO6-1: Explain the difference between simple and compound interest.
simple interest: is computed by multiplying an initial investment times both the applicable interest rate and the period of time for which the money is used. SI = (Initial Investment) x (Interest Rate) x (Period of Time) compound interest: occurs when money remains invested for multiple periods. it results in increasingly larger interest amounts for each period of the investment. The reason is that interest is then being generated not only on the initial investment amount but also on the accumulated interest earned in previous periods.
Interest
the amount of money paid or received in excess of the amount borrowed or lent
LO6-9: Briefly describe how the concept of the time value of money is incorporated into the valuation of bonds, long-term leases, and pension obligations.
the concepts are necessary when valuing assets and liabilities for financial reporting purposes; most accounting applications that incorporate the time value of money involve the concept of present value
LO6-2: Compute the future value of a single amount.
the future value of a single amount is the amount of money that a dollar will grow to at some point in the future FV = I(1+i)^n where: I = amount invested at the beginning of the period i = interest rate n = number of compounding periods ***the future value can be determined by using Table 1, Future Value of $1, which contains the future value of $1 invested for various periods of time, n, and at various rates, i so, FV = I x FV factor it is important to remember that the "n" in the future value formula refers to the number of compounding periods, not necessarily the number of years
LO6-3: Compute the present value of a single amount.
the present value of a single amount is today's equivalent to a particular amount in the future FV = PV(1+I)^n PV = FV/ (1+I)^n the table with Present Value of $1 provides the solutions of 1/(1+i)^n for various interest rates (i) and compounding periods (n); these amounts represent the present value of $1 to be received at the end of the different periods ***the calculation of future value requires the addition of interest, while the calculation of present value requires the removal of interest accountants use PV calculations much more frequently than FV
LO6-4: Solve for either the interest rate or the number of compounding periods when present value and future value of a single amount are known.
there are four variables in the process of adjusting single cash flow amounts for the time value of money: the present value, the future value, the number of compounding periods (n), and the interest rate (i) ***if you know any three of these, you can fid the fourth if the unknown variable is the annuity amount or interest rate: compute: PV/ FV ***then use the PRESENT VALUE OF $1 TABLE to search the correct row or column in order to solve for the missing variable
LO6-8: Solve for unknown values in annuity situations involving present value.
there are four variables: 1. present value of an ordinary annuity (PVA) ore present value of an annuity due (PVAD) 2. the amount of each annuity payment 3. the number of periods, n 4. the interest rate, i if you know any three of these, you can solve for the fourth essentially: PV = annuity amount x table factor (whatever you're dealing with in the problem) + single payment x present value of $1 value