Full file at Solution-Manual-for-Accounting-Principles,-11th-Edition

APPENDIX G

Time Value of Money

SOLUTIONS TO BRIEF EXERCISES

BRIEF EXERCISE G-1

1.(a) 12%62.(a) 8% 20

(b) 10%15(b) 10%5

(c) 4%24(c) 6%8

BRIEF EXERCISE G-2

(a)i = 8%

? / $30,000

012345678

Discount rate from Table 1 is .54027 (8 periods at 8%). Present value of $30,000 to be received in 8 years discounted at 8% is therefore $16,208.10 ($30,000 X .54027).

(b)i = 9%

?$30,000$30,000$30,000$30,000$30,000$30,000

0123456

Discount rate from Table 2 is 4.48592 (6 periods at 9%). Present value of 6 payments of $30,000 each discounted at 9% is therefore $134,577.60 ($30,000 X 4.48592).

BRIEF EXERCISE G-3

i = 10%

? / $600,000

012345

Discount rate from Table 1 is .62092 (5 periods at 10%). Present value of $600,000 to be received in 5 years discounted at 10% is therefore $372,552 ($600,000 X .62092). Chaffee Company should therefore invest $372,552 to have $600,000 in five years.

BRIEF EXERCISE G-4

i = 9%

? / $700,000

012345678

Discount rate from Table 1 is .50187 (8 periods at 9%). Present value of $700,000 to be received in 8 years discounted at 9% is therefore $351,309 ($700,000 X .50187). Lloyd Company should invest $351,309 to have $700,000 in eight years.

BRIEF EXERCISE G-5

i = 10%

? / $36,000

01234

Discount rate from Table 1 is .68301 (4 periods at 10%). Present value of $36,000 to be received in 4 years discounted at 10% is therefore $24,588.36 ($36,000 X .68301). Drake should receive $24,588.36 upon the sale of the note.

BRIEF EXERCISE G-6

i = 8%

?$60,000

0123

Discount rate from Table 1 is .79383 (3 periods at 8%). Present value of $60,000 to be received in 3 years discounted at 8% is therefore $47,629.80 ($60,000 X .79383). Delgado Company should receive $47,629.80 upon issuance of the zero-interest bearing note.

BRIEF EXERCISE G-7

i = 6%

?$40,000$40,000$40,000$40,000$40,000$40,000

012341415

Discount rate from Table 2 is 9.71225. Present value of 15 payments of $40,000 each discounted at 6% is therefore $388,490 ($40,000 X 9.71225). Shea Company should pay $388,490 for this annuity contract.

BRIEF EXERCISE G-8

i = 11%

?$100,000$100,000$100,000$100,000

01234

Discount rate from Table 2 is 3.10245. Present value of 4 payments of $100,000 each discounted at 11% is therefore $310,245 ($100,000 X 3.10245). Littleton Company invested $310,245 to earn $100,000 per year for four years.

BRIEF EXERCISE G-9

i = 4%

?$200,000

Diagram
for
Principal

012341920

i = 4%

?$10,000$10,000$10,000$10,000$10,000$10,000

Diagram
for
Interest

012341920

Present value of principal to be received at maturity:

$200,000 X 0.45639 (PV of $1 due in 20 periods

at 4% from Table 1)...... $91,278.00

Present value of interest to be received periodically

over the term of the bonds: $10,000 X 13.59033

(PV of $1 due each period for 20 periods at 4%

from Table 2)...... 135,903.30

Present value of bonds...... $227,181.30

BRIEF EXERCISE G-10

The bonds will sell at face value or $200,000. This may be proven as follows:

Present value of principal to be received at maturity:

$200,000 X .37689 (PV of $1 due in 20 periods

at 5% from Table 1)...... $75,378*

Present value of interest to be received periodically

over the term of the bonds: $10,000 X 12.46221

(PV of $1 due each period for 20 periods at 5%

from Table 2)...... 124,622*

Present value of bonds...... $200,000*

*Rounded.

BRIEF EXERCISE G-11

i = 9%

?$75,000

Diagram
for
Principal

0123456

i = 9%

?$6,000$6,000$6,000$6,000$6,000$6,000

Diagram
for
Interest

0123456

Present value of principal to be received at maturity:

$75,000 X .59627 (PV of $1 due in 6 periods

at 9% from Table 1)...... $44,720.25

Present value of interest to be received annually

over the term of the note: $6,000 X 4.48592

(PV of $1 due each period for 6 periods at

9% from Table 2)...... 26,915.52

Present value of note received...... $71,635.77

BRIEF EXERCISE G-12

i = 5%

?$1,000,000

Diagram
for
Principal

01234141516

i = 5%

?$40,000$40,000$40,000$40,000$40,000$40,000$40,000

Diagram
for
Interest

01234141516

Present value of principal to be received at maturity:

$1,000,000 X 0.45811 (PV of $1 due in 16 periods

at 5% from Table 1)...... $458,110

Present value of interest to be received periodically

over the term of the bonds: $40,000 X 10.83777

(PV of $1 due each period for 16 periods at 5%

from Table 2)...... 433,511

Present value of bonds and cash proceeds...... $891,621

BRIEF EXERCISE G-13

i = 11%

?$2,800$2,800$2,800$2,800$2,800$2,800$2,800$2,800

012345678

Discount rate from Table 2 is 5.14612. Present value of 8 payments of $2,800 each discounted at 11% is therefore $14,409.14 ($2,800 X 5.14612). Bill Broadman should not purchase the tire retreading machine because the present value of the future cash flows is less than the purchase price of the
retreading machine.

BRIEF EXERCISE G-14

i = 5%

?$78,978$78,978$78,978$78,978$78,978$78,978

012341112

Discount rate from Table 2 is 8.86325. Present value of 12 payments of $78,978 each discounted at 5% is therefore $700.001.75 ($78,978 X 8.86325). Martinez Company should receive $700,001.75 from the issuance of the note.

BRIEF EXERCISE G-15

i = 12%

?$30,000$40,000$60,000

0123

To determine the present value of the future cash flows, discount the future cash flows at 12%, using Table 1.

Year 1 ($30,000 X .89286) =$ 26,785.80

Year 2 ($40,000 X .79719) =31,887.60

Year 3 ($60,000 X .71178) = 42,706.80

Present value of future cash flows$101,380.20

To achieve a minimum rate of return of 12%, Preet Company should pay no more than $101,380.20. If Preetpays less than $101,380.20 its rate of return will be greater than 12%.

BRIEF EXERCISE G-16

i = ?

$2,745$10,000

012341415

Present value = Future amount X Present value of 1 Factor

$2,745= $10,000 X .2745

The .2745 for 15 periods is found in the 9% column. Monica Ramirez will receive a 9% return.

BRIEF EXERCISE G-17

i = 10%

$51,316$100,000

n = ?

Present value = Future amount X Present value of 1 Factor

$51,316= $100,000 X .51316

The .51316 at 10% is found in the 7 years row. Hellen Bos therefore must wait 7 years to receive $100,000.

BRIEF EXERCISE G-18

i = ?

?$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000

01234561920

$11,469.92

n = 20

Present value = Annuity X Present value of an annuity

$11,469.92= $1,000 X 11.46992

The 11.46992 for 20 periods is found in the 6% column. Natasha Anapova will therefore earn a rate of return of 6%.

BRIEF EXERCISE G-19

i = 8%

$1,000$1,000$1,000$1,000$1,000$1,000

$8,559.48

n = ?

Present value = Annuity X Present value of an annuity

$8,559.48= $1,000 X 8.55948

The 8.55948 at an interest rate of 8% is shown in the 15-year row. Kaley Perrytherefore will receive 15 payments.

BRIEF EXERCISE G-20

(a)$10,000 X .79383 = $7,938.30.

(b)$10,000 X .79031 = $7,903.10.

(c)$10,000 X .71178 = $7,117.80.

(d)$10,000 X .70496 = $7,049.60.

BRIEF EXERCISE G-21

(a)$10,000 X .74726 = $7,472.60.

(b)$10,000 X .83962 = $8,396.20.

(c)$10,000 X .62092 = $6,209.20.

(d)$10,000 X .75132 = $7,513.20.

BRIEF EXERCISE G-22

Option one has a present value of $39,500.

Option two has a present value of [$10,000 + ($8,000 X 3.79079)] = $40,326.32.

Choose option one (lower cost).

BRIEF EXERCISE G-23

(a)$10,000 X 3.79079 = $37,907.90

(b)Receipt X 6.71008 = $50,000; Receipt = $50,000/6.71008 = $7,451.48

(c)$11,971 X Factor = $70,000; Factor = $70,000/$11,971 = 5.84746;

5.84746 is approximately the factor for 15 years, 15%

BRIEF EXERCISE G-24

Present value of $5,000 option: $5,000 X 6.71008 = $33,550.

Present value of $9,000 option: $9,000 X 3.99271 = $35,934.

Present value of $30,000 option: $30,000.

Select the $9,000 option (highest present value).

BRIEF EXERCISE G-25

$24,000 cost – $2,400 down payment = $21,600.

Payment X 7.36009 = $21,600.

Payment = $21,600/7.36009 = $2,934.75

BRIEF EXERCISE G-26

(a)$40,000 X .62741 = $25,096

2,000 X 6.20979 = 12,420

$37,516

(b)$40,000 X .73069 = $29,228

2,000 X 6.73274 = 13,465

$42,693

BRIEF EXERCISE G-27

(a)$90,000 X .55684 = $50,116

4,050 X 8.86325 = 35,896

$86,012

(b)$90,000 X .62460 = $56,214

4,050 X 9.38507 = 38,010

$94,224


download full file at