Ch 6: Time Value of Money
Future Value of an Annuity Due
- since payment made at beginning (ex. 3 years) calculate with n=3, n=2, n=1 -future value can be found by using the future value of an annuity due (FVAD) factor from Table 5, Future Value of an Annuity Due of $1 -FVAD= [(1+i)^n −1 / i] × (1+i)
Future Value of an Ordinary Annuity
- since payment made at end (ex. 3 years) calculate with n=2, n=1, n=0 -calculate the future value of the annuity by separately calculating the FV of each payment and then adding these amounts together -FVA= (1+i)^n - 1 / i
ordinary annuity
-An ordinary annuity exists when the cash flows occur at the end of each period. -Ex. an installment note payable dated December 31, 2018, might require the debtor to make three equal annual payments, with the first payment due on December 31, 2019, and the last one on December 31, 2021
Explain the difference between an ordinary annuity and an annuity due.
-An ordinary annuity exists when the cash flows occur at the end of each period. -In an annuity due the cash flows occur at the beginning of each period.
Present Value of an Ordinary Annuity
-Ex. invest a single amount today in a savings account earning 10% interest compounded annually that is equivalent to investing $10,000 at the end of each of the next three years -present value can be found by separately calculating the PV of each of the three payments and then summing those individual present values as follows -n=1, n=2, n=3 -PVA = [1 - (1/(1+i)^n)) / i]
Present Value of a Deferred Annuity
-Exists when the first cash flow occurs more than one period after the date the agreement begins -Ex. considering acquiring an investment that will provide three equal payments of $10,000 each to be received at the end of three consecutive years. However, the first payment is not expected until December 31, 2020. The time value of money is 10%. How much would you be willing to pay for this investment? -n=3, n=4, n=5
annuity due
-In an annuity due the cash flows occur at the beginning of each period. -Ex. A 3 yr lease of a building that begins on December 31, 2018, and ends on December 31, 2021, may require first year's lease payment in advance on December 31, 2018. The third and last payment would take place on December 31, 2020, the beginning of the third year of the lease
Define interest
-Interest is the amount of money paid or received in excess of the amount borrowed or lent.
Single Cash Amount Approach
-Monetary assets and monetary liabilities represent cash or fixed claims/commitments to receive/pay cash in the future and are valued at the present value of these fixed cash flows. All other assets and liabilities are nonmonetary. -note receivable vs note payable
Expected Cash Flow Approach
-Provides framework for using future cash flows in accounting measurement when uncertainty is present -objective in valuing an asset or liability using present value is to approximate fair value of that asset or liability
Explain the difference between simple and compound interest. (p. 314)
-Simple interest is: Investment × Interest rate × Time period -Compound interest Includes interest not only on the initial investment but also on the accumulated interest earned in previous periods
Compute the present value of a single amount. (p. 316)
-present value of a single amount is today's equivalent to a particular amount in the future. -PV = FV/(1+i)^n
Compute the future value of a single amount. (p. 315)
-single amount is the amount of money that a dollar will grow to at some point in the future. -FV = I(1 + i)^n FV = Future value of the invested amount I = Amount invested at the beginning of the period
What is a deferred annuity?
A deferred annuity exists when the first cash flow occurs more than one period after the date the agreement begins.
Annuity
An annuity is a series of equal-sized cash flows occurring over equal intervals of time.
Explain how the time value of money concept is incorporated into the valuation of certain leases.
Companies frequently acquire the use of assets by leasing rather than purchasing them. Leases usually require the payment of fixed amounts at regular intervals over the life of the lease. Certain leases are treated in a manner similar to an installment sale by the lessor and an installment purchase by the lessee. In other words, the lessor records a receivable and the lessee records a liability for the several installment payments. For the lessee, this requires that the leased asset and corresponding lease liability be valued at the present value of the lease payments.
Present Value of an Annuity Due
Ex. suppose that the three equal payments of $10,000 are to be made at the beginning of each of the three years -n=0, n=1, n=2 -PVAD=PVA[(1−(1+i)^n)/i] x (1+i)
What would cause the annual interest rate to be different from the annual effective rate or yield?
If interest is compounded more frequently than once a year, the effective rate or yield will be higher than the annual stated rate.
effective rate
More rapid compounding increases the actual rate, at which money grows per year
Identify the three items of information necessary to calculate the future value of a single amount.
The three items of information necessary to compute the future value of a single amount are the original invested amount, the interest rate (i), and the number of compounding periods (n).
