Accounting Chapter 6 The rate of interest is determined by dividing

EXERCISE 6.8 (10–15 minutes)

(a)

Present value of an ordinary annuity of 1

for 4 periods @ 8%

3.31213

Annual withdrawal

(b)

Fund balance at June 30, 2022

Future value of an ordinary annuity at 8%

EXERCISE 6.9 (5–10 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 approxi–

mates that number:

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 $148,644, which is 6.72748—the value $1.00 would

accumulate to at 10% for the unknown number of interest periods. The

factor 6.72748 or its approximate is then located in the Future Value of

1 Table by reading down the 10% column to the 20–period line; thus, 20 is

the unknown number of years Chopra must wait to become a millionaire.

EXERCISE 6.11 (10–15 minutes)

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

€155,820 (10 X €15,582) – €100,000 = €55,820.

EXERCISE 6.12 (10–15 minutes)

Building A—PV = $610,000.

Building B—

Building C—

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

Cash purchase price

$650,000

PV of rental income

– 47,059

Net present value

$602,941

EXERCISE 6.13 (15–20 minutes)

Time diagram:

Messier, SA

PV = ? i = 5% (10% ÷ 2)

PV – OA = ? Principal

Formula for the interest payments:

PV – OA = R (PVF – OAn, i)

Formula for the principal:

PV = FV (PVFn, i)

EXERCISE 6.14 (15–20 minutes)

Time diagram:

i = 8%

R =

PV – OA = ? $200,000 $200,000 $200,000

Formula: PV – OA = R (PVF – OAn, i)

OR

Time diagram:

i = 8%

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 begin–

ning of the current year:

EXERCISE 6.15 (15–20 minutes)

(a)

i = 6%

PV = $1,000,000 FV = $1,898,000

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

amount to establish the foundation.

PV = $300,000 FV = ?

0 1 2 8 9

EXERCISE 6.16 (10–15 minutes)

Amount to be repaid on March 1, 2027.

Time diagram:

i = 6% per six months (12% ÷ 2 payments annually)

PV = $90,000 FV = ?

Amount of annual contribution to debt retirement fund.

Time diagram:

i = 10%

R R R R R FV – AD =

R = ? ? ? ? ? $288,643

EXERCISE 6.16 (Continued)

1.

Future value of ordinary annuity of 1 for 5 periods

at 10% ……………………………………………………………………

6.10510

2.

Factor (1 + .10) ………………………………………………………….

3.

Future value of an annuity due of 1 for 5 periods

at 10% ……………………………………………………………………

6.71561

EXERCISE 6.17 (10–15 minutes)

Time diagram:

i = 11%

R R R

PV – OA = £421,087 ? ? ?

EXERCISE 6.18 (10–15 minutes)

Time diagram:

i = 8%

PV – OA = ? ¥400,000 ¥400,000 ¥400,000 ¥400,000 ¥400,000

0 1 2 13 14 15

n = 15

EXERCISE 6.19 (10–15 minutes)

Time diagram:

i = 8%

PV – AD = ?

R =

¥400,000 ¥400,000 ¥400,000 ¥400,000 ¥400,000

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

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

competing contracts. The student is required to decide which contract to accept.

Problem 6.4 (Time 20–30 minutes)

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

annuity and annuity due for three different cash payment situations. The student must then decide

which cash payment plan should be undertaken.

Time and Purpose of Problems (Continued)

Problem 6.9 (Time 30–35 minutes)

Problem 6.10 (Time 30–35 minutes)

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

lease. The computations for this problem are relatively complicated.

Problem 6.11 (Time 25–30 minutes)

Problem 6.12 (Time 20–25 minutes)

Problem 6.13 (Time 20–25 minutes)

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

value techniques to determine a warranty liability.

Problem 6.14 (Time 20–25 minutes)

Problems 6.15 (Time 20–25 minutes)

SOLUTIONS TO PROBLEMS

PROBLEM 6.1

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

the note would be estimated to value the building.

Time diagram:

i = 9%

PV = ? FV = ¥24,000,000

Formula: PV = FV (PVFn, i)

PROBLEM 6.1 (Continued)

(b) Time diagram:

i = 11%

Principal

¥100,000 x 300 = ¥30,000,000

Interest = ¥30,000,000 x 9% Interest

PV – OA = ? ¥2,700,000 ¥2,700,000 ¥2,700,000 ¥2,700,000

Present value of the principal

FV (PVF10, 11%) = ¥30,000,000 (.35218) …………….

= ¥10,565,400

Present value of the interest payments

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

(c) Time diagram:

i = 8%

PV – OA = ? ¥400,000 ¥400,000 ¥400,000 ¥400,000 ¥400,000

PROBLEM 6.1 (Continued)

(d) Time diagram:

i = 12%

PV – OA = ?

¥2,000,000 ¥500,000 ¥500,000 ¥500,000 ¥500,000 ¥500,000 ¥500,000 ¥500,000 ¥500,000

(e) Time diagram:

i = 11%

PV – OA = ? ¥12,000,000 ¥12,000,000 ¥12,000,000 ¥12,000,000

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 = ? ? ? ? ? ? ? ?

(b) Time diagram:

i = 12%

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 12% ……………………………………….

133.33387

Factor (1 + .12) ………………………………………………

(c) Time diagram:

i = 9%

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

0 1 2 3 n

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

0

1

2

3 4

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