Time Value of Money

Just as you pay rent for your room or apartment, you also pay "rent" for money you borrow. This "rent" is called interest.

Example:

Borrow $100 now (called principal) for 1 year

Interest at 10% per year

Lump sum repayment at end of year is $110

We see that $100 now is equivalent to $110 a year from now at the stated interest terms.

A contractor’s working capital could be invested if it were not needed as working capital.

Therefore, the interest that could have been earned was not, so it is really a cost of doing business; just as is the interest paid on borrowed capital.

A contractor’s idle equipment isn’t earning revenue but its cost, principal and interest, must be paid.

Ability to keep assets employed helps drive decision to buy, lease or rent.

Tax impact on profit must be considered

~ Business expense deductions

~ Interest payment deductions

~ Depreciation deductions for equipment

Time Value of Money - Formulas

Single Payments:

Undisplayed Graphic

Uniform series End-of-period payments:

Undisplayed Graphic

Tables of compounded amount factor values are arranged by i and n values. Their use speeds calculations.

Undisplayed Graphic

Time Value of Money - Depreciation

Depreciation is the loss of value of equipment over a period of time (I.e., a declining book value).

Tax depreciation is an artificial dollar value devised primarily to facilitate deduction accounting for income tax purposes.

Actual depreciation (or appreciation) is the actual change in market value of equipment.

Depreciation accounting is the systematic division of the depreciable value of equipment into annual depreciation allocations over a set period of years.

Depreciation accounting requires knowledge of:

~equipment acquisition cost

~economic life or depreciable life (n)

~ resale/salvage value (unless depreciated to zero value)

~tax law

Commonly used depreciation methods:

~straight line (SL)

~declining balance (DB)

~sum-of-the-year digits (SOYD)

Federal income tax depreciation methods changed due to the "Economic Recovery Tax Act" of 1981 introducing an "Accelerated Cost Recovery System" (ACRS) depreciation method.

Under ACRS all property has a 3-, 5-, 10- or 15-year recovery period depending on its type. Each period has a fixed schedule of depreciation percentages.

(Ex: 3-yr period is 25%, 38% & 37% for 1981 - 1984)

Under ACRS, actual life is neglected and salvage value is figured at zero.

Straight-line (SL)

~most commonly figured as cost per unit of time but can be based on cost per unit of work

Undisplayed GraphicDeclining balance (DB)

~an accelerated method of depreciation using an equal fraction times each year’s book value

~uses a selected DB multiple

Undisplayed Graphic

~ depreciation value = current book value × DB rate

new current book value = previous current book value - depreciation value

~ do not let book value go below salvage value or zero

Sum-of-year digits (SOYD)

~an accelerated method of depreciation using a changing fraction times depreciable value

~see Collier’s Cost Analysis text for more explanation

Equations for Four Depreciation Methods

Undisplayed Graphic

Abbreviations:

Dm = annual depreciation in year m

P = purchase price of depreciable asset

F = salvage value (resale value) of asset

n = life of depreciable asset

BVm = book value at end of any year, m, after depreciation for that year

m = age of asset at time of calculation

SOY = sum of the ordinal digits for each of the years 1 through n,

Undisplayed Graphic

R = depreciation rate for declining balance depreciation

for double declining balance, R = 2/n ;

for 1½ declining balance, R = 1.5/n ;

for 1¼ declining balance, R = 1.25/n

Time Value of Money - Example Problem

A machine is purchased for $9,000. Its estimated economic life is 10 years, after which it will be sold for $1,000. Find the depreciation and book value in the first three years using SL, DDB and SOYD at 6%.

Interest Table

Interest Tables

n

i = 0.5%

P/F*

P/A*

A/F*

A/P*

F/P*

F/A*

1

0.9950249

0.9950249

1.0000000

1.0050000

1.005000

1.000000

2

0.9900745

1.9850990

0.4987531

0.5037531

1.010025

2.005000

3

0.9851488

2.9702480

0.3316722

0.3366722

1.015075

3.015025

4

0.9802475

3.9504960

0.2481328

0.2531328

1.020151

4.030100

5

0.9753707

4.9258660

0.1980100

0.2030100

1.025251

5.050251








6

0.9705181

5.8963850

0.1645955

0.1695955

1.030378

6.075502

7

0.9656896

6.8620740

0.1407285

0.1457285

1.035529

7.105880

8

0.9608852

7.8229590

0.1228289

0.1278289

1.040707

8.141409

9

0.9561047

8.7790640

0.1089074

0.1139074

1.045911

9.182116

10

0.9513479

9.7304120

0.0977706

0.1027706

1.051140

10.228030








11

0.9466149

10.6770300

0.0886590

0.0936590

1.056396

11.279170

12

0.9419053

11.6189300

0.8106640

0.0860664

1.061678

12.335560

13

0.9372192

12.5561500

0.0746422

0.0796422

1.066986

13.397240

14

0.9325565

13.4887100

0.0691361

0.0741361

1.072321

14.464230

15

0.9279169

14.4166200

0.0643644

0.0693644

1.077683

15.536550








16

0.9233004

15.3399300

0.0601894

0.0651894

1.083071

16.614230

17

0.9187068

16.2586300

0.0565058

0.0615058

1.088487

17.697300

18

0.9141362

17.1727700

0.0532317

0.0582317

1.093929

18.785790

19

0.9095882

18.0823600

0.0503025

0.0553025

1.099399

19.879720

20

0.9050629

18.9874200

0.0476665

0.0526665

1.104896

20.979120








21

0.9005601

19.8879800

0.0452816

0.0502816

1.110420

22.084010

22

0.8960797

20.7840600

0.0431138

0.0481138

1.115972

23.194430

23

0.8916216

21.6756800

0.0411347

0.0461347

1.121552

24.310400

24

0.8871857

22.5628700

0.0393206

0.0443206

1.127160

25.431960

25

0.8827718

23.4456400

0.0376519

0.0426519

1.132796

26.559120

* Note: Find the value of the denominator given the value of the numerator

(for example, P/F means find P, given F; P/A means find P given A,

etc.)

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