Accounting Chapter 6 The recommended method of payment would be the

EXERCISE 6.8 (10–15 minutes)

(a)

Present value of an ordinary annuity of 1

for 4 periods @ 8%

3.31213

Annual withdrawal

X $20,000

(b)

Fund balance at June 30, 2023

Future value of an ordinary annuity at 8%

EXERCISE 6.9 (10 minutes)

The rate of interest is determined by dividing the future value by the

present value and then finding the factor in the FVF table with n = 2 that

EXERCISE 6.10 (10–15 minutes)

(a) The number of interest periods is calculated by first dividing the

future value of $1,000,000 by $92,296, which is 10.83471—the value

$1.00 would accumulate to at 10% for the unknown number of interest

periods. The factor 10.83471 or its approximate is then located in the

EXERCISE 6.11 (10–15 minutes)

(a) Total interest = Total payments—Amount owed today

$162,745 (10 X $16,274.53) – $100,000 = $62,275.

EXERCISE 6.12 (10–15 minutes)

Building A—PV = $600,000.

Building C—

Rent X (PV of ordinary annuity of 25 periods at 12%) = PV

$7,000 X 7.84314 = PV

$54,902 = PV

Cash purchase price

$650,000

PV of rental income

– 54,902

Net present value

$595,098

EXERCISE 6.13 (15–20 minutes)

Time diagram:

Hincapie, Inc.

PV = ? i = 5% (.10 ÷ 2)

Formula for the interest payments:

PV–OA = R (PVF–OAn, i)

Formula for the principal:

PV = FV (PVFn, i)

PV = $2,000,000 (PVF30, 5%)

EXERCISE 6.14 (15–20 minutes)

Time diagram:

i = 8%

R =

PV–OA = ? $700,000 $700,000 $700,000

Formula: PV–OA = R (PVF–OAn, i)

OR

Time diagram:

i = 8%

R =

PV–OA = ? $700,000 $700,000 $700,000

EXERCISE 6.14 (Continued)

(i) Present value of the expected annual pension payments at the end of

the 10th year:

PV–OA = R (PVF–OAn, i)

(ii) Present value of the expected annual pension payments at the

beginning of the current year:

PV = FV (PVFn, i)

EXERCISE 6.15 (15–20 minutes)

(a)

i = 8%

PV = $1,000,000 FV = $1,999,000

(b) By setting aside $300,000 now, Andrew can gradually build the fund

to an amount to establish the foundation.

PV = $300,000 FV = ?

$? $? $? FV = $1,399,300

0 1 2 8 9

EXERCISE 6.16 (10–15 minutes)

Amount to be repaid on March 1, 2028.

Time diagram:

i = 3% per six months (.06 ÷ 2)

PV = $70,000 FV = ?

Formula: FV = PV (FVFn, i)

Amount of annual contribution to retirement fund.

Time diagram:

i = 5%

R R R R R FV–AD =

R = ? ? ? ? ? $126,428

EXERCISE 6.16 (Continued)

1.

Future value of ordinary annuity of 1 for 5 periods

at 5%

5.52563

2.

Factor (1 + .5)

3.

*Future value of an annuity due of 1 for 5 periods

at 5%

EXERCISE 6.17 (10–15 minutes)

Time diagram:

i = 11%

R R R

PV–OA = $365,755 ? ? ?

Formula: PV–OA = R (PV–OAn, i)

$365,755 = R (PVF–OA25, 11%)

EXERCISE 6.18 (10–15 minutes)

Time diagram:

i = 8%

PV–OA = ? $300,000 $300,000 $300,000 $300,000 $300,000

The recommended method of payment would be the 15 annual payments of

$300,000, since the present value of those payments ($2,567,844) is less

than the alternative immediate cash payment of $2,600,000.

EXERCISE 6.19 (10–15 minutes)

Time diagram:

i = 8%

PV–AD = ?

R =

$300,000 $300,000 $300,000 $300,000 $300,000

Formula:

Using Table 6-4 Using Table 6-5

PV–AD = R (PVF–OAn, i) PV–AD = R (PVF–ADn, i)

EXERCISE 6.20 (15–20 minutes)

Expected

Cash Flow Probability Cash

Estimate X Assessment = Flow

(a) $ 4,800 20% $ 960

(b) $ 5,400 30% $ 1,620

7,200 50% 3,600

8,400 20% 1,680

Total Expected

Value $ 6,900

EXERCISE 6.21 (10–15 minutes)

Estimated

Cash Probability Expected

Outflow X Assessment = Cash Flow

$200 10% $ 20

EXERCISE 6.22 (15–20 minutes)

(a) This exercise determines the present value of an ordinary annuity or

expected cash flows as a fair value estimate.

Cash flow Probability Expected

Estimate X Assessment = Cash Flow

$ 380,000 20% $ 76,000

(b) This fair value is based on unobservable inputs—Killroy’s own data on

the expected future cash flows associated with the trade name. This

TIME AND PURPOSE OF PROBLEMS

Problem 6.1 (Time 15–20 minutes)

Purpose—to present an opportunity for the student to determine how to use the present value tables in

Problem 6.2 (Time 15–20 minutes)

Purpose—to present an opportunity for the student to determine solutions to four present and future

Problem 6.3 (Time 20–30 minutes)

Purpose—to present the student with an opportunity to determine the present value of the costs of

Problem 6.4 (Time 20–30 minutes)

Purpose—to present the student with an opportunity to determine the present value of two lottery

Problem 6.5 (Time 20–25 minutes)

Purpose—to provide the student with an opportunity to determine which of four insurance options results

Problem 6.6 (Time 25–30 minutes)

Purpose—to present an opportunity for the student to determine the present value of a series of

Problem 6.7 (Time 30–35 minutes)

Purpose—to present the student an opportunity to use time value concepts in business situations.

Problem 6.8 (Time 20–30 minutes)

Purpose—to present the student with an opportunity to determine the present value of an ordinary

Time and Purpose of Problems (Continued)

Problem 6.9 (Time 30–35 minutes)

Purpose—to present the student with the opportunity to work three different problems related to time

Problem 6.10 (Time 30–35 minutes)

Purpose—to present the student with the opportunity to assess whether a company should purchase or

Problem 6.11 (Time 25–30 minutes)

Purpose—to present the student an opportunity to apply present value to retirement funding problems,

Problem 6.12 (Time 20–25 minutes)

Purpose—to provide the student an opportunity to explore the ethical issues inherent in applying time

Problem 6.13 (Time 20–25 minutes)

Purpose—to present the student an opportunity to compute expected cash flows and then apply

Problem 6.14 (Time 20–25 minutes)

Purpose—to present the student an opportunity to compute expected cash flows and then apply

Problems 6.15 (Time 20–25 minutes)

Purpose—to present the student an opportunity to estimate fair value by computing expected cash

SOLUTIONS TO PROBLEMS

PROBLEM 6.1

(a) Given no established fair value for the building, the fair value of the

note would be used to estimate the fair value of the building.

Time diagram:

i = 9%

PV = ? FV = $240,000

n = 3

Formula: PV = FV (PVFn, i)

PROBLEM 6.1 (Continued)

(b) Time diagram:

i = 11%

Principal

$300,000 (300 x $1,000)

Interest

PV – OA = ? $27,000 $27,000 $27,000 $27,000 ($300,000 x .09)

FV (PVF10, 11%) = $300,000 (.35218) ………………..

Present value of the interest payments

R (PVF – OA10, 11%) = $27,000 (5.88923) ………….

159,009

Combined present value (purchase price) …………….

$264,663

(c) Time diagram:

i = 8%

PV – OA = ? $4,000 $4,000 $4,000 $4,000 $4,000

PROBLEM 6.1 (Continued)

(d) Time diagram:

i = 12%

PV – OA = ?

$20,000 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000

(e) Time diagram:

i = 11%

PV – OA = ? $120,000 $120,000 $120,000 $120,000

0 1 2 8 9

n = 9

PROBLEM 6.2

(a) Time diagram:

i = 8% FV – OA = $90,000

R R R R R R R R

R = ? ? ? ? ? ? ? ?

0 1 2 3 4 5 6 7 8

n = 8

(b) Time diagram:

i = 8%

FV – AD =

R R R R 500,000

R = ? ? ? ?

PROBLEM 6.2 (Continued)

1.

Future value of an ordinary annuity of 1 for

25 periods at 8% …………………………………………

73.10594

Factor (1 + .08) ………………………………………………

(c) Time diagram:

i = 9%

PV = $20,000 FV = $47,347

Future value approach

Present value approach

FV = PV (FVFn, i)

PV = FV (PVFn, i)

$47,347 = $20,000 (FVFn, 9%)

$20,000 = $47,347 (PVFn, 9%)

PROBLEM 6.2 (Continued)

(d) Time diagram:

i = ?

PV = FV =

$19,553 $27,600

Future value approach

Present value approach

FV = PV (FVFn, i)

PV = FV (PVFn, i)

or

$27,600 = $19,553 (FVF4, i)

$19,553 = $27,600 (PVF4, i)

= $27,600 ÷ $19,553

= $19,553 ÷ $27,600