Chapter 6 Time Value of Money Concepts
QUESTIONS FOR REVIEW OF KEY TOPICS
Question 6–1
Interest is the amount of money paid or received in excess of the amount
borrowed or lent.
Question 6–2
Compound interest includes interest not only on the original invested amount but
also on the accumulated interest from previous periods.
Question 6–3
If interest is compounded more frequently than once a year, the effective rate or
yield will be higher than the annual stated rate.
Question 6–4
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).
Question 6–5
The present value of a single amount is the amount of money today that is
equivalent to a given amount to be received or paid in the future.
Question 6–6
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.
Question 6–7
An annuity is a series of equal-sized cash flows occurring over equal intervals of
time.
Solutions Manual, Vol.1, Chapter 6 6–1
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
,Answers to Questions (continued)
Question 6–8
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.
Question 6–9
Table 2 lists the present value of $1 factors for various time periods and interest
rates. The factors in Table 4 are simply the summation of the individual PV of $1
factors from Table 2.
Question 6–10
Present
Value
?
0 Year 1 Year 2 Year 3 Year 4
___________________________________________
$200 $200 $200 $200
n = 4, i = 10%
Question 6–11
Present
Value
?
0 Year 1 Year 2 Year 3 Year 4
___
____
___
____
_____________________________
$200 $200 $200 $200
n = 4, i = 10%
6–2 Intermediate Accounting, 9/e
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
,Answers to Questions (concluded)
Question 6–12
A deferred annuity exists when the first cash flow occurs more than one period
after the date the agreement begins.
Question 6–13
The formula for computing present value of an ordinary annuity incorporating the
ordinary annuity factors from Table 4 is:
PVA = Annuity amount x Ordinary annuity factor
Solving for the annuity amount,
Annuity amount =
The annuity factor can be obtained from Table 4 at the intersection of the 8%
column and 5 period row.
Question 6–14
Annuity amount =
Annuity amount = $125.23
Question 6–15
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.
Solutions Manual, Vol.1, Chapter 6 6–3
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
, BRIEF EXERCISES
Brief Exercise 6–1
Fran should choose the second investment opportunity. More rapid compounding
has the effect of increasing the actual rate, which is called the effective rate, at which
money grows per year. For the second opportunity, there are four, three-month
periods paying interest at 2% (one-quarter of the annual rate). $10,000 invested will
grow to $10,824 ($10,000 x 1.0824*). The effective annual interest rate, often referred
to as the annual yield, is 8.24% ($824 ÷ $10,000), compared to just 8% for the first
opportunity.
Future value of $1: n = 4, i = 2% (from Table 1)
Brief Exercise 6–2
Bill will not have enough accumulated to take the trip. The future value of his
investment of $23,153 is $347 short of $23,500.
FV = $20,000 (1.15763) = $23,153
Future value of $1: n = 3, i = 5% (from Table 1)
Brief Exercise 6–3
FV factor = $26,600 = 1.33
$20,000
Future value of $1: n = 3, i = ? (from Table 1, i = approximately 10%)
6–4 Intermediate Accounting, 9/e
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
QUESTIONS FOR REVIEW OF KEY TOPICS
Question 6–1
Interest is the amount of money paid or received in excess of the amount
borrowed or lent.
Question 6–2
Compound interest includes interest not only on the original invested amount but
also on the accumulated interest from previous periods.
Question 6–3
If interest is compounded more frequently than once a year, the effective rate or
yield will be higher than the annual stated rate.
Question 6–4
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).
Question 6–5
The present value of a single amount is the amount of money today that is
equivalent to a given amount to be received or paid in the future.
Question 6–6
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.
Question 6–7
An annuity is a series of equal-sized cash flows occurring over equal intervals of
time.
Solutions Manual, Vol.1, Chapter 6 6–1
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
,Answers to Questions (continued)
Question 6–8
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.
Question 6–9
Table 2 lists the present value of $1 factors for various time periods and interest
rates. The factors in Table 4 are simply the summation of the individual PV of $1
factors from Table 2.
Question 6–10
Present
Value
?
0 Year 1 Year 2 Year 3 Year 4
___________________________________________
$200 $200 $200 $200
n = 4, i = 10%
Question 6–11
Present
Value
?
0 Year 1 Year 2 Year 3 Year 4
___
____
___
____
_____________________________
$200 $200 $200 $200
n = 4, i = 10%
6–2 Intermediate Accounting, 9/e
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
,Answers to Questions (concluded)
Question 6–12
A deferred annuity exists when the first cash flow occurs more than one period
after the date the agreement begins.
Question 6–13
The formula for computing present value of an ordinary annuity incorporating the
ordinary annuity factors from Table 4 is:
PVA = Annuity amount x Ordinary annuity factor
Solving for the annuity amount,
Annuity amount =
The annuity factor can be obtained from Table 4 at the intersection of the 8%
column and 5 period row.
Question 6–14
Annuity amount =
Annuity amount = $125.23
Question 6–15
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.
Solutions Manual, Vol.1, Chapter 6 6–3
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
, BRIEF EXERCISES
Brief Exercise 6–1
Fran should choose the second investment opportunity. More rapid compounding
has the effect of increasing the actual rate, which is called the effective rate, at which
money grows per year. For the second opportunity, there are four, three-month
periods paying interest at 2% (one-quarter of the annual rate). $10,000 invested will
grow to $10,824 ($10,000 x 1.0824*). The effective annual interest rate, often referred
to as the annual yield, is 8.24% ($824 ÷ $10,000), compared to just 8% for the first
opportunity.
Future value of $1: n = 4, i = 2% (from Table 1)
Brief Exercise 6–2
Bill will not have enough accumulated to take the trip. The future value of his
investment of $23,153 is $347 short of $23,500.
FV = $20,000 (1.15763) = $23,153
Future value of $1: n = 3, i = 5% (from Table 1)
Brief Exercise 6–3
FV factor = $26,600 = 1.33
$20,000
Future value of $1: n = 3, i = ? (from Table 1, i = approximately 10%)
6–4 Intermediate Accounting, 9/e
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
