SOLUTIONS FOR APPC

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Appendix C-1

APPENDIX C

Present Value Concepts

SOLUTIONS TO BRIEF EXERCISES

BRIEF EXERCISE C-1

1. 12% 6 2. 8% 2010% 15 10% 5 4% 24 6% 8

BRIEF EXERCISE C-2

(a) i = 8%? $30,000

0 1 2 3 4 5 6 7 8

Discount rate from Table 1 is .54027 (8 periods at 8%). Present va

of $30,000 to be received in 8 years discounted at 8% is therefo$16,208.10 ($30,000 X .54027).

(b) i = 9%

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

0 1 2 3 4 5 6

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

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Appendix C-2

BRIEF EXERCISE C-3

i = 10%? $600,000

0 1 2 3 4 5

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

BRIEF EXERCISE C-4

i = 9%? $700,000

0 1 2 3 4 5 6 7 8

Discount rate from Table 1 is .50187 (8 periods at 9%). Present value $700,000 to be received in 8 years discounted at 9% is therefore $351,3($700,000 X .50187). LaRussa Company should invest $351,309 to ha$700,000 in eight years.

BRIEF EXERCISE C-5

i = 10%? $36,000

0 1 2 3 4

Discount rate from Table 1 is .68301 (4 periods at 10%). Present value$36,000 to be received in 4 years discounted at 10% is therefore $24,588($36,000 X .68301). Polley should receive $24,588.36 upon the sale of the note

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Appendix C-3

BRIEF EXERCISE C-6

i = 8%? $60,000

0 1 2 3

Discount rate from Table 1 is .79383 (3 periods at 8%). Present value$60,000 to be received in 3 years discounted at 8% is therefore $47,629($60,000 X .79383). Marichal Company should receive $47,629.80 upon isance of the zero-interest bearing note.

BRIEF EXERCISE C-7

i = 6%

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

0 1 2 3 4 14 15

Discount rate from Table 2 is 9.71225. Present value of 15 payments$40,000 each discounted at 6% is therefore $388,490 ($40,000 X 9.7122

Colaw Company should pay $388,490 for this annuity contract.

BRIEF EXERCISE C-8

i = 11%

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

0 1 2 3 4

Discount rate from Table 2 is 3.10245. Present value of 4 payments$100,000 each discounted at 11% is therefore $310,245 ($100,000 X 3.1024Sauder Enterprises invested $310,245 to earn $100,000 per year for four years

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Appendix C-4

BRIEF EXERCISE C-9

i = 4%? $200,000

Diagramfor

Principal

0 1 2 3 4 19 20

i = 4%

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

forInterest

0 1 2 3 4 19 20

Present value of principal to be received at maturity:

$200,000 X 0.45639 (PV of $1 due in 20 periodsat 4% from Table 1) ...................................................................... $ 91,278.0

Present value of interest to be received periodicallyover the term of the bonds: $10,000 X 13.59033(PV of $1 due each period for 20 periods at 4%from Table 2) .................................................................................. 135,903.3

Present value of bonds........................................................................ $227,181.3

BRIEF EXERCISE C-10

The bonds will sell at par 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 periodsat 5% from Table 1) ...................................................................... $ 75,37

Present value of interest to be received periodicallyover the term of the bonds: $10,000 X 12.46221

(PV of $1 due each period for 20 periods at 5%from Table 2) .................................................................................. 124,62Present value of bonds........................................................................ $200,00

*Rounded.

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Appendix C-5

BRIEF EXERCISE C-11

i = 9%? $75,000

Diagramfor

Principal

0 1 2 3 4 5 6

i = 9%

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

forInterest

0 1 2 3 4 5 6

Present value of principal to be received at maturity:$75,000 X .59627 (PV of $1 due in 6 periodsat 9% from Table 1) ....................................................................... $44,720.2

Present value of interest to be received annuallyover the term of the note: $6,000 X 4.48592(PV of $1 due each period for 6 periods at9% from Table 2) ............................................................................ 26,915.5

Present value of note received .......................................................... $71,635.7

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Appendix C-6

BRIEF EXERCISE C-12

i = 5%? $1,000,000

Diagramfor

Principal

0 1 2 3 4 14 15 16

i = 5%? $40,000 $40,000 $40,000 $40,000 $40,000 $40,000 $40,000

Diagramfor

Interest

0 1 2 3 4 14 15 16

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)................................................................... $458,11Present 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)............................................................................... 433,51

Present value of bonds and cash proceeds.................................. $891,62

BRIEF EXERCISE C-13

i = 11%

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

0 1 2 3 4 5 6 7 8

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

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Appendix C-7

BRIEF EXERCISE C-14

i = 5%

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

0 1 2 3 4 11 12

Discount rate from Table 2 is 8.86325. Present value of 12 payments$78,978 each discounted at 5% is therefore $700.001.75 ($78,978 X 8.8632Martinez Company should receive $700,001.75 from the issuance of the note

BRIEF EXERCISE C-15

i = 12%

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

0 1 2 3

To determine the present value of the future cash flows, discount the fut

cash flows at 12%, using Table 1.

Year 1 ($30,000 X .89286) = $ 26,785.80Year 2 ($40,000 X .79719) = 31,887.60Year 3 ($60,000 X .71178) = 42,706.80Present value of future cash flows $101,380.20

To achieve a minimum rate of return of 12%, Durler Company should pay more than $101,380.20. If Durler pays less than $101,380.20 its rate of retuwill be greater than 12%.

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Appendix C-8

BRIEF EXERCISE C-16

i = ?$2,745 $10,000

0 1 2 3 4 14 15

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. Carla Garcia will receiv9% return.

BRIEF EXERCISE C-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 column. Sara Altom therefomust wait 7 years to receive $100,000.

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Appendix C-10

BRIEF EXERCISE C-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 C-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 C-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 C-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 C-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).

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Appendix C-11

BRIEF EXERCISE C-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 C-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 C-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

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