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FM1


Unit 2 


CONCEPTS IN VALUATION


 

In our economics life, money is not free. Money has time value. Interest rates give money its time value. If the investor has some spare cash or funds, he can invest it in savings deposit in a bank and receive more money later. If the investor wants to borrow money, he must repay a larger amount in the future due to interest. The result is that Rs. 100 in hand today, is worth more than Rs. 100 to be received a year from now. This is because Rs. 100 today can be invested to provide Rs. 100 plus interest after a year. The interest rates in the economy provide money with its time value. There are two types of decisions which requires some consideration of time value. The first decision involves investing money now in order to receive future cash benefits. The other decision involves borrowing now to take current expenditure at a cost of having less money in the future. The intelligent investor requires familiarity with the concepts of compound interest.

 


 

In the world of finance and investment, time does have a value, Rs. 100 today are more valuable than Rs. 100 a year later. This is because capital can be employed productively to generate positive returns. Again, individuals normally prefer current consumption to future consumption. Even in case of inflation, Rs. 100 today represents greater real purchasing power as compared to Rs. 100 one year later. The longer the term of a loan, the greater the amount that must be paid due to interest. Bonds are worthless to an investor, if the maturity is longer. Therefore, this makes sense under the general framework of the time value of money.

 


 

(a)               PRESENT VALUE: A present value is the discounted value of one or more future cash

Flows.

 

(b)               FUTURE VALUE: A future value is the compounded value of a present value.

 

(c)               DISCOUNT FACTOR: The discount factor is the present value of a rupee received in

The future.

 

(d)               COMPOUNDING FACTOR: The compounding factor is the future value of a rupee.

 

Discount and compounding factors are functions of two things: (i) the interest rate used, and (ii) the time between the present value and the future value. The discount factor decreases as time increases. The discount factor also decreases as interest rate increases.

 


RELATIONSHIP

 

There are two techniques of adjusting the time value of money:

 

I. Compounding Technique

II. Discounting or present Value Technique

 

I. Compounding Technique

The time preference for money encourages person to receive the money at present instead of waiting for future. But he may like if he is duly compensated for the waiting time by way of ensuring more money in future.

 

For example, a person being offered Rs. 100 today may wait for a year if he is ensured of Rs. 100 at eh end of one year (taking his preference for an interest of 10% p.a).

The future value at the end of period 1 can be calculated by a simple formula given below:

 

FV = PV (1+i)n

 

Where, FV = Future value at the end of period 1

PV = Value of money at time 0 i.e. original sum of money

I = Rate of interest

n = Number of years

 

Taking the example given above, the value of money after 2 years is given below:

FV = PV (1+i)n

= 100 (1+.10)2

= Rs. 121

 

II. Discounting or Present Value Technique

Present value is the exact opposite of compound or future value. While future value shows how much a sum of money becomes at some future period, present value shows what the value is today of some future sum of money. The present value of money to be received on future date will be less because we have lost the opportunity of investing it at some interest.

 

For example, there is an opportunity to buy a debenture today and we get back Rs. 1000 after one year. What will you be willing to pay for the debenture today if your time preference for money is 10% p.a? We can calculate the present value of Rs. 1000 to be received after one year at 10% time preference rate as below:

 

PV = FV / (1+i)t

 

The basic time value of money relationships is presented in the following equations:

 

PV = FV x DF

FV = PV XCF

 

Where, PV = Present value

FV = Future value

DF = Discounting factor =   1    

(1 + R)t

 

CF = Compounding factor = (1 + R)t

Where,  R = Rate of interest

t = time in years.

 


 

The future value of an amount invested or borrowed at a given rate of interest can be calculated if the maturity period is given. Suppose, a deposit of Rs. 5,000 gets 10 percent interest compounded annually for a period of 3 years, the future value will be:

PV X CF = 5,000 (1.10)3 = 5,000 x 1.311 = Rs. 6,655.

 

Illustration 1:

Shashikant deposit Rs. 1, 00,000 with a bank which pays 10 percent interest compounded annually, for a period of 3 years. How much amount he would get a maturity?

Solution:

 

FV  = PV X CF

= 1,00,000 x (1.10)3

= 1,00,000 x 1.331

= Rs. 1,33,100

 

Mr. Shashikant will get Rs. 1,33,100 after 3 years.

 


 

An annuity is a series of payments of a fixed amount for a specified number of periods. When payment is made at the end of each year, it is called ordinary annuity. On the other hand, when the payments are made at the beginning of the year, it is called an annuity due. Normally, it is assumed that the first annuity payment occurs at the end of the first year.

 

FVa = A x  (1 + R)t 1

R

Where,A = Periodic cash payments

R = Annual interest rate

t = time in years / duration of annuity

 

The value of (1+R)t – 1 can be determined by using the Time value of money tables.

R

 

The Future Value Interest Factors (FVIFA) for various years are a shown in table:

 

Year

FVIF

@ 8%

FVIF @ 10%

FVIF @ 12%

FVIF @14%

1

1.0000

1.0000

1.0000

1.0000

2

2.0800

2.1000

2.1200

2.1400

3

3.2464

3.3100

3.3744

3.4396

4

4.5061

4.6410

4.7793

4.9211

5

5.8666

6.1051

6.3528

6.6101

6

7.3359

7.7156

8.1152

8.5355

7

8.9228

9.4872

10.089

10.730

8

10.636

11.435

12.299

13.232

9

12.487

13.579

14.775

16.085

10

14.486

15.937

17.548

19.337

 

Illustration 2:

Four equal annual payments of Rs. 5,000 are made into a deposit account that pays 8 percent interest per year. What is the future value of this annuity at the end of 4 years?

Solution

The future value of annuity FVa  = A x (1 + R) t – 1

R

= Rs. 5,000 x FVIFA @ 8%

= Rs. 5,000 x 4.5061

= Rs. 22530.50

 


 

Sometimes, investor should know how long it will take to double his money at a given rate of interest. In this case, a rule of thumb called the rule of 72, can be used. This rule works pretty well for most of the interest rates. The rule of 72 says that it will take seventy-two years to double your money at 1 percent interest. You can calculate the doubling by dividing 72 by the interest rate. You can also estimate the interest rate required to double your money in the given number of years by dividing number of years into 72.

 

For example, if the interest rate is 12 percent, it will take 6 years to double your money (72+23). On the other hand, if you want to double your money in 6 years, the interest rate should be 12 percent (72+6).

 

A more accurate method used for doubling your money is using the rule of 69. According to this rule, the doubling period of an investment is = 0.35 + 69 Thus the doubling period of Interest rate investment of different rates of interest can be determined as follows:

 

(1)               Interest rate 12%

 

0.35 + 69 = 0.35 + 5.75 = 6.1 years

12

 

(2)               Interest rate 15%

 

0.35 + 69 = 0.35 + 4.60 = 4.95 years

15

 

Illustration 3:

If the interest rate is 10%, what are the doubling periods of an investment at this rate?

 

Solution

(a)               As per rule of 72, the doubling period will be

 

72 = 7.2 years

10

(b)              As per the rule of 69, the doubling period will be

= 0.35 + 69

10

= 0.35 + 6.9 = 7.25 years

 

PRESENT VALUE:

 

Many times, investors like to know the present value which grows to a given future value. Suppose, you want to save some money from your salary to but a scooter after 5 years. You should know how much money should be put into bank now in order to get the future value after 5 years. The present value is simply the inverse of compounding used in determining future value. The general relationship between future value and present value is given in the following formula:

 

PV = FV x DF

= FV x       1     

(1+R)

 

Illustration 4:

Find the present value of Rs. 50,000 to be received at the end of four years at 12 percent interest compounding quarterly.

 

Solution:

 

PV = FV x PVIF at 12%

= Rs. 50,000 x 0.623

= Rs. 31,150

 


 

The annuity includes the constant amount in which cash flows are identical in every period. Many financial decisions involve constant cash flows, however, some important decisions are concerned with uneven cash flows. For example, investment in shares is expected to pay an increasing series of dividends over time. The capital budgeting projects also do not normally provide constant cash flows.

 

In order to deal with uneven payment streams, we have to multiply each payment by the appropriate PVIF and then sum these products to obtain the present value of an uneven series of payments.

 

Illustration 5:

Mr. Shah has invested Rs. 50,000 on Xerox machine on 1st Jan. 2002. He estimates net cash income from Xerox machine in next 5 years as under.

 

Year

Estimated inflows

2002

12,000

2003

15,000

2004

18,000

2005

25,000

2006

30,000

 

At the end of 5th year Machine will be sold at Scarp value of Rs. 5,000. Advise him whether his project to viable, considering interest rate of 10% p.a.

 

Solution:

Calculation of Present Value of Future Cash Flows:

 

Year

Inflows (Rs)

PVIF at 10%

PV of Inflows

(Rs.)

2002

12,000

0.9091

10,909

2003

15,000

0.8264

12,396

2004

18,000

0.7513

13,523

2005

25,000

0.6830

17,075

2006

2006

30,000

5,000

0.6209

21,732

 

 

 

75,635

 

Note: It is assumed that the net cash income is received at the end of the year.

 

Considering 10% interest rate, the net present value of all future cash flows is Rs. 75,635 which is higher than present net cash flow of Rs. 50,000. Thus, the project is viable.

 


 

Many times investors want to know the present value which must be invested today in order to provide an annuity for several future periods. For example, a grandfather wants to deposit enough money today to meet the tuition fees of his grand-son for the next three years. The interest rate is 8%. The present value of this annuity is the sum of the present values of all the future inflow of the annuities. The present value of an annuity can be expressed in the following formula:

 

PVA1  = A x 1    +    1    +    1    

(1+R)3          (1+R)2          (1+R)1

 

=  (1+R)t-1

R(1+R)t

 

Where  PVA1  = Present value of an annuity with a duration of t’ periods

A  = Constant periodic flow R = Interest Rate

 

The present value interest factors for an annuity (PVIF) can be determined by using the Time Value of Money Tables. The (PVIF) for various years are given below:

 

Year

PVIF

@ 8%

PVIF @ 10%

PVIF @ 12%

PVIF @ 14%

1

0.9259

0.9091

0.8929

0.8772

2

1.7833

1.7355

1.6901

1.6467

3

2.5771

2.4869

2.4018

2.3216

4

3.3121

3.1700

3.0373

2.9140

5

3.9927

3.7908

3.6048

3.4331

6

4.6229

4.3553

4.1114

3.8887

7

5.2064

4.8684

4.5638

4.2883

8

5.7466

5.3349

4.9676

4.6389

9

6.2469

5.7590

5.3282

4.9464

10

6.7101

6.1446

5.6502

5.2161

 

For all positive interest rates, PVIFA for the present value of an Annuity is always less than the number of periods the annuity runs, whereas FVIFA for the future value of an annuity is equal to or greater than the number of periods.

 

Illustration 6:

What is the present value of a 4 years’ annuity of Rs. 8,000 at 12% interest?

 

Solution:

 

PVA   = (1+R)t-1

R(1+R)t

 

The value of (1+R)t 1 as per table is 3.0373

R(1+R)t

 

= Rs. 8,000 x PVIF at 12%

= Rs. 8,000 x 3.0373

= Rs. 24.298

 


 

Net Present Value (NPV) is the most suitable method used for evaluating the capital investment projects. Under this method, cash inflow and outflows associated with each project are worked out. The present value of cash inflows is calculated by discounting the cash flows at the rate of return acceptable to the management. The cash outflows represent the investment and commitments of cash in the project at various points of time. It is generally determined on the basis of cost of capital suitably adjusted to allow for the risk element involved in the project. The working capital is taken as a cash outflow in the initial year. The cash inflow represents the net profit after tax but before depreciation. Depreciation is a non-cash expenditure hence it is added back to the net profit after tax in order to determine the cash inflows. The Net Present Value of cash inflows and the present value of cash outflows. If the NPV is positive the project is accepted, and if it is negative, the project is rejected.

 

Discounted cash flow is an evaluation of the future net cash flows generated by a project. This method considers the time value of money concept and hence it is considered better for evaluation of investment proposals. If these are mutually exclusive projects, this method is more useful. The Net Present Value is determined as follows:

 

NPV = Present value of future cash inflows – Present value of cash outflows.

 

Illustration 7:

 

An investment of Rs. 40,000 made on 1/4/2002 provides inflows as follows:

 

Date

Alternative I

Alternative II

01/04/03

20,000

10,000

01/04/04

10,000

20,000

01/04/05

10,000

10,000

01/04/06

10,000

10,000

 

Which alternative would you prefer in the investor’s expected return is 10%? Give reason(s) for your preference.

 

Solution:

 

Calculation of Present Values:

Alternative I

 

Date

Amount

Discount Factor

PV (Rs)

01/04/03

20,000

0.9091

18,182

01/04/04

10,000

0.8264

8,264

01/04/05

10,000

0.7513

7,513

01/04/06

10,000

0.6830

6,830

 

 

 

40,789

 

Alternative II

 

Date

Amount

Discount Factor

PV (Rs)

01/04/03

10,000

0.9091

9,091

01/04/04

20,000

0.8264

16,528

01/04/05

10,000

0.7513

7,513

01/04/06

10,000

0.6830

6,830

 

 

 

39,962

 

The net present value of all future cash flows is Rs. 40,789 in case of Alternative I and Rs. 39,962 in case of II. The NPV in case of alternative is higher at 10% discounting factor. Hence, alternative I is preferred for investment.

 

Illustration 8:

 

A Finance company has introduced a scheme of investment of Rs. 40,000. The returns would be Rs. 8000, 10000, 11000 and 12000 in the next five years. The indicated rate of interest is 10%. Compute the present value of the investment and advice regarding the investment.

 

Solution:

 

(i)                 Present value of investment = Rs. 40,000.

(ii)               Present value of returns:

 

Year

Returns (Rs)

PVIF (10%)

Present Value (Rs.)

1

8,000

0.9091

7,273

2

9,000

0.8264

7,438

3

10,000

0.7513

7,513

4

11,000

0.6830

7,513

5

12,000

0.6209

7,451

 

 

 

37,188

 

(iii)      Present value of investment is Rs. 37,188 which is lower than investment of Rs. 40,000. The net present value (i.e. 37,188 - 40,000 = Rs. 2,812) is negative. Hence the investment is not profitable at 10% interest.

 

Illustration 9:

 

The share of Ridhi Ltd (Rs.10) was quoting at Rs. 102 on 01.04.2002 and the price rose to Rs. 132 on 01.04.2005. Dividends were received at 10% on 30th June each year. Cost of funds was 10%. Is it a worth-while investment, considering the time value of money? (Present value factor at 10% were 0.909, 0.826 and 0.751).

Solution:

 

Calculation of Present Value of Cash inflows:

Year

Inflow (Rs)

Present Value Factor

Present Value (Rs.)

1

1

0.909

0.909

2

1

0.826

0.826

3

1 + 132 = 133

0.751

99.883

 

 

Present Value

101.618

 

 

(-) Present Value of Cash Outflow

102.000

 

 

Net Present Value

-0.382

 

Considering the time value of money, the NPV is negative, hence, it is not a wise investment.

 

Illustration 10:

XYZ & Co. Is considering investing in a project requiring a capital outlay of Rs. 2,00,000. Forecast for annual income after tax is as follows:

 

Year

1

2

3

4

5

Profit After Tax (Rs.)

1,00,000

1,00,000

80,000

80,000

40,000

Depreciation is 20% on Straight Line Basis

 

 

 

 

 

 

Evaluate the project on the basis of Net Present Value taking 14% discounting factor and advise whether XYZ & Co. Should invest in the project or not? The Present value of Re. 1 at 14% discounting rate are 0.8772, 0.7695, 0.6750, 0.5921 and 0.5194.

Solution:

Depreciation = 20% of 2,00,000 = Rs. 40,000 Profit after tax is given.

The cash inflow after tax (CFAT) = Profit After Tax (PAT) + Depreciation.

 

Year

PAT

+

Depreciation

CFAT

DF

P.V.

1

1,00,000

40,000

1,40,000

0.8772

1,22,808

2

1,00,000

40,000

1,40,000

0.7695

1,07,730

3

80,000

40,000

1,20,000

0.6750

81,000

4

80,000

40,000

1,20,000

0.5921

71,052

5

40,000

40,000

80,000

0.5194

41,552

 

 

 

 

Present Value of Cash Inflow

4,24,142

 

 

 

 

Present Value of Cash Outflow

2,00,000

 

 

 

 

Net Present Value

2,24,142

 

Net Present Value is positive, hence XYZ & Co should invest in the project.

 

Illustration 11:

Find out the present value of a debenture from the following:

 

Face value of debenture

Rs.

1,000

Annual Interest Rate

 

15%

Expected return

 

12%

Maturity Period

 

5 years

 

(Present values of Re. 1 at 12% are, 0.8929, 0.7972, 0.7118, 0.6355 and 0.5674)

Solution:

 

PVd  = I (PVAF) + FV (DF)

= I (PVAF 12% for 5 years) + FV (DF 12% for 5 years)

= 150 (3,6048) + 1,000 (0.5674)

= Rs. 540.72 + 567.40

= Rs. 1108.12

 

Illustration 12:

 

Mr. Vishwanathan is planning to buy a machine which would generate cash flow as follows:

 

Year

0

1

2

3

4

Cash Flow

(25000)

6000

8000

15000

8000

 

If discount rate is 10%, is it worth to invest in machine?

 

Year

1

2

3

4

Discount Factor

0.909

0.826

0.751

0.683

 

Solution:

 

Calculation of Net Present Value

Year

Cash Flow

(Rs.)

Discount Factor

Present Value (Rs.)

1

6,000

0.909

5,454

2

8,000

0.826

6,608

3

15,000

0.751

11,265

4

8,000

0.683

5,464

 

 

Present value of cash inflow

28,791

 

 

(-) Present Value of cash outflow

25,000

 

 

Net Present Value

3,791

 

As the NPV is positive, it is worth investing in the machine.

 

Illustration 13:

A machine cost Rs. 80,000 and is expected to produce the following cash flows:

 

Year

1

2

3

4

5

6

7

Cash Flow

(Rs)

50000

57000

35000

60000

40000

30000

60000

 

If the cost of capital is 12 percent, is it worth buying the machine?

 

Solution:

 

Calculation of Net Present Value

Year

Cash Inflow

D.F. @ 12%

Present Value (Rs.)

1

50,000

0.8929

44,645

2

57,000

0.7972

45,440

3

35,000

0.7118

24,913

4

60,000

0.6355

38,130

5

40,000

0.5674

22,696

6

30,000

0.5066

15,198

7

60,000

0.4523

27,138

 

 

Present Value of Cash Inflow

2,18,160

 

 

Present Value of outflow

2,80,000

 

 

Net Present Value

(61840)

 

As the Net Present Value is negative, it is not worth buying the machine.

 

Illustration 14:

Find the compounded value of annuity where three equal yearly payments of Rs. 2000 are deposited into an account that yields 7% compound interest.

 

Solution:

The future value of annuity FVa (for 3 years) = A x (1 + R)t – 1

R

= Rs. 2,000 (FVAFA @ 7%

= Rs. 2,000 x 3.215

= Rs. 6,430

 

Illustration 15:

Calculate the compound value when Rs. 10,000 are invested for 3 years and the interest on it is compounded at 10% p.a semi-annually.

 

Solution:

 

FV  = PV x CF

FV  = PV x (1 + R)t

= 10,000 X (1 + 2 ) 2 x 3

= 10,000 (1.05) 6

= Rs. 10,000 x 1.340

= Rs. 13,400

 


 

When the present value of cash inflows is exactly equal to the present value of cash outflows we are getting a rate of return which is equal to our discounting rate. In this case the rate of return we are getting is the actual return on the project. This rate is called the IRR.

 

In the net present value calculation we assume that the discount rate (cost of capital) is known and determine the net present value of the project. In the internal rate of return calculation, we set the net present value equal to zero and determine the discount rate (internal rate of return) which satisfies this condition.

 

Both the discounting methods NPV and IRR relate the estimates of the annual cash outlays on the investment to the annual net of tax cash receipt generated by the investment. As a general rule, the net of tax cash flow will be composed of revenue less taxes, plus depreciation. Since discounting techniques automatically allow for the recovery of the capital outlay in computing time-adjusted rates of return, it follows that depreciation provisions implicitly form part of the cash inflow.

 

Internal rate of return method consists of finding that rate of discount that reduces the present value of cash flows (both inflows and outflows attributable to an investment project to zero. In other words, this true rate is that which exactly equalises the net cash proceeds over a project's life with the initial investment outlay.

 

If the IRR exceeds the financial standard (i.e. cost of capital), then the project is prima facie acceptable. Instead of being computed on the basis of the average or initial investment, the IRR is based on the funds in use from period to period.

 

The actual calculation of the rate is a hit-and-miss exercise because the rate is unknown at the outset, but tables of present values are available to aid the analyst. These tables show the present value of future sums at various rates of discount and are prepared for both single sums and recurring annual payments.

 

What Does IRR Mean?

 

There are two possible economic interpretations of internal rate of return: (i) Internal rate of return represents the rate of return on the unrecovered investment balance in the project. (ii) Internal rate of return is the rate of return earned on the initial investment made in the project.

 

Formula for calculating IRR:

 

NPV i.e 0 =  CF0 +   CF1 +   CF2 +   CF3 +   CFn 

(1+IRR)1        (1+IRR)2        (1+IRR)3        (1+IRR)n

Where,

CF0   = Initial Investment

CF1, CF2, CF3, CFn = Cash flows of respective years

n   = each period

NPV   = Net Present Value

IRR   = Internal Rate of Return

 

Evaluation

 

A popular discounted cash flow method, the internal rate of return criteria has several virtues:

         It takes into account the time value of money.

         It considers the cash flow stream in its entirety.

         It makes sense to businessmen who want to think in terms of rate of return and find an absolute quantity, like net present value, somewhat difficult to work with.

 

The internal rate of return criteria, however, has its own limitations.

         It may not be uniquely defined. If the cash flow stream of a project has more than one change in sign, there is a possibility that there are multiple rates of return.

         The internal rate of return figure cannot distinguish between lending and borrowing and hence a high internal rate of return need not necessarily be a desirable feature.

 

The internal rate of return criterion can be misleading when choosing between mutually exclusive projects that have substantially different outlays. Consider projects P and Q

Cash Flows

Period 0 & 1

Internal rate of return (%)

Net present value (assuming k = 12%)

P - 10,000 + 20,000

100

7,857

Q - 50,000 + 75,000

50

16,964

 

Both the projects are good, but Q, with its higher net present value, contributes more to the wealth of the stockholders. Yet from an internal rate of return point of view P looks better than Q. Hence, the internal rate of return criterion seems unsuitable for ranking projects of different scale.

 


 

Table A- 1 Present Value of Re. 1:

 

PVIF =      1    

(1 + k)n

 

Period

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

1

.9901

.9804

.9709

.9615

.9524

.9434

.9346

.9259

.9174

.9091

2

.9803

.9612

.9426

.9246

.9070

.8900

.8734

.8573

.8417

.8264

3

.9706

.9423

.9151

.8890

.8638

.8396

.8163

.7938

.7722

.7513

4

.9610

.9238

.8885

.8548

.8227

.7921

.7629

.7350

.7084

.6830

5

.9515

.9057

.8626

.8219

.7835

.7473

.7130

.6806

.6499

.6209

6

.9420

.8880

.8375

.7903

.7462

.7050

.6663

.6302

.5963

.5645

7

.9327

.8706

.8131

.7599

.7107

.6651

.6227

.5835

.5470

.5132

8

.9235

.8535

.7894

.7307

.6768

.6274

.5820

.5403

.5019

.4665

9

.9143

.8368

.7664

.7026

.6446

.5919

.5439

.5002

.4604

.4241

10

.9053

.8203

.7441

.6756

.6139

.5584

.5083

.4632

.4224

.3855

11

.8963

.8043

.7224

.6496

.5847

.5268

.4751

.4289

.3875

.3505

12

.8874

.7885

.7014

.6246

.5568

.4970

.4440

.3971

.3555

.3186

13

.8787

.7730

.6810

.6006

.5303

.4688

.4150

.3677

.3262

.2897

14

.8700

.7579

.6611

.5775

.5051

.4423

.3878

.3405

.2992

.2633

15

.8613

.7430

.6419

.5553

.4810

.4173

.3624

.3152

.2745

.2394

16

.8528

.7284

.6232

.5339

.4581

.3936

.3387

.2919

.2519

.2176

17

.8444

.7142

.6050

.5134

.4363

.3714

.3166

.2703

.2311

.1978

18

.8360

.7002

.5874

.4936

.4155

.3503

.2959

.2502

.2120

.1799

19

.8277

.6864

.5703

.4746

.3957

.3305

.2765

.2317

.1945

.1635

20

.8195

.6730

.5537

.4564

.3769

.3118

.2584

.2145

.1784

.1486

21

.8114

.6598

.5375

.4388

.3589

.2942

.2415

.1987

.1637

.1351

22

.8034

.6468

.5219

.4220

.3418

.2775

.2257

.1839

.1502

.1228

23

7954

.6342

.5067

.4057

.3256

.2618

.2109

.1703

.1378

.1117

24

.7876

.6217

.4919

.3901

.3101

.2470

.1971

.1577

.1264

.1015

25

.7798

.6095

.4776

.3751

.2953

.2330

.1842

.1460

.1160

.0923

26

.7720

.5976

.4637

.3607

.2812

.2198

.1722

.1352

.1064

.0839

27

.7644

.5859

.4502

.3468

.2678

.2074

.1609

.1252

.0976

.0763

28

.7568

.5744

.4371

.3335

.2551

.1956

.1504

.1159

.0895

.0693

29

.7493

.5631

.4243

.3207

.2429

.1846

.1406

.1073

.0882

.0630

30

.7419

.5521

.4120

.3083

.2314

.1741

.1314

.0994

.0754

.0573

 

Table A-1 (continued)

 

Period

12%

14%

15%

16%

18%

20%

24%

28%

32%

36%

1

.8929

.8772

.8696

.8621

.8475

.8333

.8065

.7813

.7576

.7353

2

.7972

.7695

.7561

.7432

.7182

.6944

.6504

.6104

.5739

.5407

3

.7118

.6750

.6575

.6407

.6086

.5787

.5245

.4768

.4348

.3975

4

.6355

.5921

.5718

.5523

.5158

.4823

.4230

.3725

.3294

.2923

5

.5674

.5194

.4972

.4761

.4371

.4019

.3411

.2910

.2495

.2149

6

.5066

.4556

.4323

.4104

.3704

.3349

.2751

.2274

.1890

.1580

7

.4523

.3996

.3759

.3538

.3139

.2791

.2218

.1776

.1432

.1162

8

.4039

.3506

.3269

.3050

.2660

.2326

.1789

.1388

.1085

.0854

9

.3606

.3075

.2843

.2630

.2255

.1938

.1443

.1084

.0822

.0628

10

.3220

.2697

.2472

.2267

.1911

.1615

.1164

.0847

.0623

.0462

11

.2875

.2366

.2149

.1954

.1619

.1346

.0938

.0662

.0472

.0340

12

.2567

.2076

.1869

.1685

.1372

.1122

.0757

.0517

.0357

.0250

13

.2292

.1821

.1625

.1452

.1163

.0935

.0610

.0404

.0271

.0184

14

.2046

.1597

.1413

.1252

.0985

.0779

.0492

.0316

.0205

.0135

15

.1827

.1401

.1229

.1079

.0835

.0649

.0397

.0247

.0155

.0099

16

.1631

.1229

.1069

.0930

.0708

.0541

.0320

.0193

.0118

.0073

17

.1456

.1078

.0929

.0802

.0600

.0451

.0258

.0150

.0089

.0054

18

.1300

.0946

.0808

.0691

.0508

.0376

.0208

.0118

.0068

.0039

19

.1161

.0829

.0703

.0596

.0431

.0313

.0168

.0092

.0051

.0029

20

.1037

.0728

.0611

.0514

.0365

.0261

.0135

.0072

.0039

.0021

21

.0926

.0638

.0531

.0443

.0309

.0217

.0109

.0056

.0029

.0016

22

.0826

.0560

.0462

.0382

.0262

.0181

.0088

.0044

.0022

.0012

23

.0738

.0491

.0402

.0329

.0222

.0151

.0071

.0034

.0017

.0008

24

.0659

.0431

.0349

.0284

.0188

.0126

.0057

.0027

.0013

.0006

25

.0588

.0378

.0304

.0245

.0160

.0105

.0046

.0021

.0010

.0005

26

.0525

.0331

.0264

.0211

.0135

.0087

.0037

.0016

.0007

.0003

27

.0469

.0291

.0230

.0182

.0115

.0073

.0030

.0013

.0006

.0002

28

.0419

.0255

.0200

.0157

.0097

.0061

.0024

.0010

.0004

.0002

29

.0374

.0224

.0174

.0135

.0082

.0051

.0020

.0008

.0003

.0001

30

.0334

.0196

.0151

.0116

.0070

.0042

.0016

.0006

.0002

.0001

 

Table A- 2 Present Value of an Annuity of Re. 1 per period for n periods:

 

1 -   1    

(1+k)n

k

 

PVIFA =    1    

(1+k)1

 

No. of payments

1%

2%

3%

4%

5%

6%

7%

8%

9%

1

0.9901

0.9804

0.9709

0.9615

0.9524

0.9434

0.9346

0.9259

0.9174

2

1.9704

1.9416

1.9135

1.8861

1.8594

1.8334

1.8080

1.7833

1.7591

3

2.9410

2.8839

2.8286

2.7751

2.7232

2.6730

2.6243

2.5771

2.5313

4

3.9020

3.8077

3.7171

3.6299

3.5460

3.4651

3.3872

3.3121

3.2397

5

4.8534

4.7135

4.5797

4.4518

4.3295

4.2124

4.1002

3.9927

3.8897

6

5.7955

5.6014

5.4172

5.2421

5.0757

4.9173

4.7665

4.6229

4.4859

7

6.7282

6.4720

6.2303

6.0021

5.7864

5.5824

5.3893

5.2064

5.0330

8

7.6517

7.3255

7.0197

6.7327

6.4632

6.2098

5.9713

5.7466

5.5348

9

8.5660

8.1622

7.7861

7.4353

7.1078

6.8017

6.5152

6.2469

5.9952

10

9.4713

8.9826

8.5302

8.1109

7.7217

7.3601

7.0236

6.7101

6.4177

11

10.3676

9.7868

9.2526

8.7605

8.3064

7.8869

7.4987

7.1390

6.8052

12

11.2551

10.5753

9.9540

9.3851

8.8633

8.3838

7.9427

7.5361

7.1607

13

12.1337

11.3484

10.6350

9.9856

9.3936

8.8527

8.3577

7.9038

7.4869

14

13.0037

12.1062

11.2961

10.5631

9.8986

9.2950

8.7455

8.2442

7.7862

15

13.8651

12.8493

11.9379

11.1184

10.3797

9.7122

9.1079

8.5595

8.0607

16

14.7179

13.5777

12.5611

11.6523

10.8378

10.1059

9.4466

8.8514

8.3126

17

15.5623

14.2919

13.1661

12.1657

11.2741

10.4773

9.7632

9.1216

8.5436

18

16.3983

14.9920

13.7535

12.6593

11.6896

10.8276

10.0591

9.3719

8.7556

19

17.2260

15.6785

14.3238

13.1339

12.0853

11.1581

10.3356

9.6036

8.9501

20

18.0456

16.3514

14.8775

13.5903

12.4622

11.4699

10.5940

9.8181

9.1285

21

18.8570

17.0112

15.4150

14.0292

12.8212

11.7641

10.8355

10.0168

9.2922

22

19.6604

17.6580

15.9369

14.4511

13.1630

12.0416

11.0612

10.2007

9.4424

23

20.4558

18.2922

16.4436

14.8568

13.4886

12.3034

11.2722

10.3711

9.5802

24

21.2434

18.9139

16.9355

15.2470

13.7986

12.5504

11.4693

10.5288

9.7066

25

22.0232

19.5235

17.4131

15.6221

14.0939

12.7834

11.6536

10.6748

9.8226

26

22.7952

20.1210

17.8768

15.9828

14.3753

13.0032

11.8258

10.8100

9.9290

27

23.5596

20.7069

18.3270

16.3296

14.6430

13.2105

11.9867

10.9352

10.0266

28

24.3164

21.2813

18.7641

16.6631

14.8981

13.4062

12.1371

11.0511

10.1161

29

25.0658

21.8444

19.1885

16.9837

15.1411

13.5907

12.2777

11.1584

10.1983

30

25.8077

22.3965

19.6004

17.2920

15.3725

13.7648

12.4090

11.2578

10.2737

 

Table A-2 (continued)

 

No. Of payments

10%

12%

14%

15%

16%

18%

20%

24%

28%

32%

1

0.9091

0.8929

0.8772

0.8696

0.8621

0.8475

0.8333

0.8065

0.7813

0.7576

2

1.7355

1.6901

1.6467

1.6257

3.6052

1.5656

1.5278

1.4568

1.3916

1.3315

3

2.4869

2.4018

2.3216

2.2832

2.2459

2.1743

2.1065

1.9813

1.8684

1.7663

4

3.1699

3.0373

2.9137

2.8550

2.7982

2.6901

2.5887

2.4043

2.2410

2.0957

5

3.7908

3.6048

3.4331

3.3522

3.2743

3.1272

2.9906

2.7454

2.5320

2.3452

6

4.3553

4.1114

3.8887

3.7845

3.6847

3.4976

3.3255

3.0205

2.7594

2.5342

7

4.8684

4.5638

4.2883

4.1604

4.0386

3.8115

3.6046

3.2423

2.9370

2.6775

8

5.3349

4.9676

4.6389

4.4873

4.3436

4.0776

3.8372

3.4212

3.0758

2.7860

9

5.7590

5.3282

4.9464

4.7716

4.6065

4.3030

4.0310

3.5655

3.1842

2.8681

10

6.1446

5.6502

5.2161

5.0188

4.8332

4.4941

4.1925

3.6819

3.2689

2.9304

11

6.4951

5.9377

5.4527

5.2337

5.0286

4.6560

4.3271

3.7757

3.3351

2.9776

12

6.8137

6.1944

5.6603

5.4206

5.1971

4.7932

4.4392

3.8514

3.3868

3.0133

13

7.1034

6.4235

5.8424

5.5831

5.3423

4.9095

4.5327

3.9124

3.4272

3.0404

14

7.3667

6.6282

6.0021

5.7245

5.4675

5.0081

4.6106

3.9616

3.4587

3.0609

15

7.6061

6.8109

6.1422

5.8474

5.5755

5.0916

4.6755

4.0013

3.4834

3.0764

16

7.8237

6.9740

6.2651

5.9542

5.6685

5.1624

4.7296

4.0333

3.5026

3.0882

17

8.0216

7.1196

6.3729

6.0472

5.7487

5.2223

4.7746

4.0591

3.5177

3.0971

18

8.2014

7.2497

6.4674

6.1280

5.8178

5.2732

4.8122

4.0799

3.5294

3.1039

19

8.3649

7.3658

6.5504

6.1982

5.8775

5.3162

4.8435

4.0967

3.5386

3.1090

20

8.5136

7.4694

6.6231

6.2593

5.9288

5.3527

4.8696

4.1103

3.5458

3.1129

21

8.6487

7.5620

6.6870

6.3125

5.9731

5.3837

4.8913

4.1212

3.5514

3.1158

22

8.7715

7.6446

6.7429

6.3587

6.0113

5.4099

4.9094

4.1300

3.5558

3.1180

23

8.8832

7.7184

6.7921

6.3988

6.0442

5.4321

4.9245

4.1371

3.5592

3.1197

24

8.9847

7.7843

6.8351

6.4338

6.0726

5.4510

4.9371

4.1428

3.5619

3.1210

25

9.0770

7.8431

6.8729

6.4642

6.0971

5.4669

4.9476

4.1474

3.5640

3.1220

26

9.1609

7.8957

6.9061

6.4906

6.1182

5.4804

4.9563

4.1511

3.5656

3.1227

27

9.2372

7.9426

6.9352

6.5135

6.1364

5.4919

4.9636

4.1542

3.5669

3.1233

28

9.3066

7.9844

6.9607

6.5335

6.1520

5.5016

4.9697

4.1566

3.5679

3.1237

29

9.3696

8.0218

6.9830

6.5509

6.1656

5.5098

4.9747

4.1585

3.5687

3.1240

30

9.4269

8.0552

7.0027

6.5660

6.1772

5.5168

4.9789

4.1601

3.5693

3.1242

 

Table A-3 Future Value of Re. 1 at the end of n Periods.

 

FVIF = (1+k)n

 

Period

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

1

1.0100

1.0200

1.0300

1.0400

1.0500

1.0600

1.0700

1.0800

1.0900

1.1000

2

1.0201

1.0404

1.0609

1.0816

1.1025

1.1236

1.1449

1.1664

1.1881

1.2100

3

1.0303

1.0612

1.0927

1.1249

1.1576

1.3910

1.2250

1.2597

1.2950

1.3310

4

1.0406

1.0824

1.1255

1.1699

1.2155

1.2625

1.3108

1.3605

1.4116

1.4641

5

1.0510

1.1041

1.1593

1.2167

1.2763

1.3382

1.4026

1.4693

1.5386

1.6105

6

1.0615

1.1262

1.1941

1.2653

1.3401

1.4185

1.5007

1.5869

1.6771

1.7716

7

1.0721

1.1487

1.2299

1.3159

1.4071

1.5036

1.6058

1.7138

1.8280

1.9487

8

1.0829

1.1717

1.2668

1.3686

1.4775

1.5938

1.7182

1.8509

1.9926

2.1436

9

1.0937

1.1951

1.3048

1.4233

1.5513

1.6895

1.8385

1.9990

2.1719

2.3579

10

1.1046

1.2190

1.3439

1.4802

1.6289

1.7908

1.9672

2.1589

2.3674

2.5937

11

1.1157

1.2434

1.3842

1.5395

1.7103

1.8983

2.1049

2.3316

2.5804

2.8531

12

1.1268

1.2682

1.4258

1.6010

1.7959

2.0122

2.2522

2.5182

2.8127

3.1384

13

1.1381

1.2936

1.4685

1.6651

1.8856

2.1329

2.4098

2.7196

3.0658

3.4523

14

1.1495

1.3195

1.5126

1.7317

1.9799

2.2609

2.5785

2.9372

3.3417

3.7975

15

1.1610

1.3459

1.5580

1.8009

2.0789

2.3966

2.7590

3.1722

3.6425

4.1772

16

1.1726

1.3728

1.6047

1.8730

2.1829

2.5404

2.9522

3.4259

3.9703

4.5950

17

1.1843

1.4002

1.6528

1.9479

2.2920

2.6928

3.1588

3.7000

4.3276

5.0545

18

1.1961

1.4282

1.7024

2.0258

2.4066

2.8543

3.3799

3.9960

4.7171

5.5599

19

1.2081

1.4568

1.7535

2.1068

2.5270

3.0256

3.6165

4.3157

5.1417

6.1159

20

1.2202

1.4859

1.8061

2.1911

2.6533

3.2071

3.8697

4.6610

5.6044

6.7275

21

1.2324

1.5157

1.8603

2.2788

2.7860

3.3996

4.1406

5.0338

6.1088

7.4002

22

1.2447

1.5460

1.9161

2.3699

2.9253

3.6035

4.4304

5.4365

6.6586

8.1403

23

1.2572

1.5769

1.9736

2.4647

3.0715

3.8197

4.7405

5.8715

7.2579

8.9543

24

1.2697

1.6084

2.0328

2.5633

3.2251

4.0489

5.0724

6.3412

7.9111

9.8497

25

1.2824

1.6406

2.0938

2.6658

3.3864

4.2919

5.4274

6.8485

8.6231

10.834

26

1.2953

1.6734

2.1566

2.7725

3.5557

4.5494

5.8074

7.3964

9.3992

11.918

27

1.3082

1.7069

2.2213

2.8834

3.7335

4.8223

6.2139

7.9881

10.245

13.110

28

1.3213

1.7410

2.2879

2.9987

3.9201

5.1117

6.6488

8.6271

11.167

14.421

29

1.3345

1.7758

2.3566

3.1187

4.1161

5.4184

7.1143

9.3173

12.172

15.863

30

1.3478

1.8114

2.4273

3.2434

4.3219

5.7435

7.6123

10.062

13.267

17.449

 

Table A – 3 (continued)

 

Period

12%

14%

15%

16%

18%

20%

24%

28%

32%

36%

1

1.1200

1.1400

1.1500

1.1600

1.1800

1.2000

1.2400

1.2800

1.3200

1.3600

2

1.2544

1.2996

1.3225

1.3456

1.3924

1.4400

1.5376

1.6384

1.7424

1.8496

3

1.4049

1.4815

1.5209

1.5609

1.6430

1.7280

1.9066

2.0972

2.3000

2.5155

4

1.5735

1.6890

1.7490

1.8106

1.9388

2.0736

2.3642

2.6844

3.0360

3.4210

5

1.7623

1.9254

2.0114

2.1003

2.2878

2.4883

2.9316

3.4360

4.0075

4.6526

6

1.9738

2.1950

2.3131

2.4364

2.6996

2.9860

3.6352

4.3980

5.2899

6.3275

7

2.2107

2.5023

2.6600

2.8262

3.1855

3.5832

4.5077

5.6295

6.9826

8.6054

8

2.4760

2.8526

3.0590

3.2784

3.7589

4.2998

5.5895

7.2058

9.2170

11.703

9

2.7731

3.2519

3.5179

3.8030

4.4355

5.1598

6.9310

9.2234

12.166

15.916

10

3.1058

3.7072

4.0456

4.4114

5.2338

6.1917

8.5944

11.805

16.059

21.646

11

3.4785

4.2262

4.6524

5.1173

6.1759

7.4301

10.657

15.111

21.198

29.439

12

3.8960

4.8179

5.3502

5.9360

7.2876

8.9161

13.214

19.342

27.982

40.037

13

4.3635

5.4924

6.1528

6.8858

8.5994

10.699

16.386

24.758

36.937

54.451

14

4.8871

6.2613

7.0757

7.9875

10.147

12.839

20.319

31.691

48.756

74.053

15

5.4736

7.1379

8.1371

9.2655

11.973

15.407

25.195

40.564

64.358

100.71

16

6.1304

8.1372

9.3576

10.748

14.129

18.488

31.242

51.923

84.953

136.96

17

6.8660

9.2765

10.761

12.467

16.672

22.186

38.740

66.461

112.13

186.27

18

7.6900

10.575

12.375

14.462

19.673

26.623

48.038

85.070

148.02

253.33

19

8.6128

12.055

14.231

16.776

23.214

31.948

59.567

108.89

195.39

344.53

20

9.6463

13.743

16.366

19.460

27.393

38.337

73.864

139.37

257.91

468.57

21

10.803

15.667

18.821

22.574

32.323

46.005

91.591

178.40

340.44

637.26

22

12.100

17.861

21.644

26.186

38.142

55.206

113.57

278.35

449.39

866.67

23

13.552

20.361

24.891

30.376

45.007

66.247

140.83

292.30

593.19

1178.6

24

15.178

23.212

28.625

35.236

53.108

79.496

174.63

374.14

783.02

1602.9

25

17.000

26.461

32.918

40.874

62.668

95.396

216.54

478.90

1033.5

2180.0

26

19.040

30.166

37.856

47.414

73.948

114.47

268.51

612.99

1364.3

2964.9

27

21.324

34.389

43.535

55.000

87.259

137.37

332.95

784.63

1800.9

4032.2

28

23.883

39.204

50.065

63.800

102.96

164.84

412.86

1004.3

2377.2

5483.8

29

26.749

44.693

57.575

74.008

121.50

197.81

511.95

1285.5

3137.9

7458.0

30

29.959

50.950

66.211

85.849

143.37

237.37

634.81

1645.5

4142.0

10143.

 

Table A – 4 Sum of an Annuity of Re. 1 per period of n Periods :

 

FVIFA    = (1+k)n – 1

k

No. Of Periods

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

1

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

2

2.0100

2.0200

2.0300

2.0400

2.0500

2.0600

2.0700

2.0800

2.0900

2.1000

3

3.0301

3.0604

3.0909

3.1216

3.1525

3.1836

3.2149

3.2464

3.2781

3.3100

4

4.0604

4.1216

4.1836

4.2465

4.3101

4.3746

4.4399

4.5061

4.5731

4.6410

5

5.1010

5.2040

5.3091

5.4163

5.5256

5.6371

5.7507

5.8666

5.9847

6.1051

6

6.1520

6.3081

6.4684

6.6330

6.8019

6.9753

7.1533

7.3359

7.5233

7.7156

7

7.2135

7.4343

7.6625

7.8983

8.1420

8.3938

8.6540

8.9228

9.2004

9.4872

8

8.2857

8.5830

8.8923

9.2142

9.5491

9.8975

10.259

10.636

11.028

11.435

9

9.3685

9.7546

10.159

10.582

11.026

11.491

11.978

12.487

13.021

13.579

10

10.462

10.949

11.463

12.006

12.577

13.180

13.816

14.486

15.192

15.937

11

11.566

12.168

12.807

13.486

14.206

14.971

15.783

16.645

17.560

18.531

12

12.682

13.412

14.192

15.025

15.917

16.869

17.888

18.977

20.140

21.384

13

13.809

14.680

15.617

16.626

17.713

18.882

20.140

21.495

22.953

24.522

14

14.947

15.973

17.086

18.291

19.598

21.015

23.550

24.214

26.019

27.975

15

16.096

17.293

18.598

20.023

21.578

23.276

25.129

27.152

29.360

31.772

16

17.257

18.639

20.156

21.824

23.657

25.672

27.888

30.324

33.003

35.949

17

18.430

20.012

21.761

23.697

25.840

28.212

30.840

33.750

36.973

40.544

18

19.614

21.412

23.414

25.645

28.132

30.905

33.999

37.450

41.301

45.599

19

20.810

22.840

25.116

27.671

30.539

33.760

37.379

41.446

46.018

51.159

20

22.019

24.297

26.870

29.778

33.066

36.785

40.995

45.762

51.160

57.275

21

23.239

25.783

28.676

31.969

35.719

39.992

44.865

50.422

56.764

64.002

22

24.471

27.299

30.536

34.248

38.505

43.392

49.005

55.456

62.873

71.402

23

25.716

28.845

32.452

36.617

41.430

46.995

53.436

60.893

69.531

79.543

24

26.973

30.421

34.426

39.082

44.502

50.815

58.176

66.764

76.789

88.497

25

28.243

32.030

36.459

41.645

47.727

54.864

63.249

73.105

84.700

98.347

26

29.525

33.670

38.553

44.311

51.113

59.156

68.676

79.954

93.323

109.18

27

30.820

35.344

40.709

47.084

54.669

63.705

74.483

87.350

102.72

121.09

28

32.129

37.051

42.930

49.967

58.402

68.528

80.697

95.338

112.96

134.20

29

33.450

38.792

45.218

52.966

62.322

73.639

87.346

103.96

124.13

148.63

30

34.784

40.568

47.575

56.084

66.438

73.639

94.460

113.28

136.30

164.49

 

Table A- 4 (continued)

 

No. Of Period

12%

14%

15%

16%

18%

20%

24%

28%

32%

36%

1

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

2

2.1200

2.1400

2.1500

2.1600

2.1800

2.2000

2.2400

2.2800

2.3200

2.3600

3

3.3744

3.4396

3.4725

3.5056

3.5724

3.6400

3.7776

3.9184

4.0624

4.2096

4

4.7793

4.9211

4.9934

5.0665

5.2154

5.3680

5.6842

6.0156

6.3624

6.7251

5

6.3528

6.6101

6.7424

6.8771

7.1542

7.4416

8.0484

8.6999

9.3983

10.146

6

8.1152

8.5355

8.7537

8.9775

9.4420

9.9299

10.980

12.135

13.405

14.798

7

10.089

10.730

11.066

11.413

12.141

12.915

14.615

16.533

18.695

21.126

8

12.299

13.232

13.726

14.240

15.327

16.499

19.122

22.163

25.678

29.731

9

14.775

16.065

16.785

17.518

19.085

20.798

24.712

29.369

34.895

41.435

10

17.548

19.337

20.303

21.321

23.521

25.958

31.643

38.592

47.061

57.351

11

20.654

23.044

24.349

25.732

28.755

32.150

40.237

50.398

63.121

78.998

12

24.133

27.270

29.001

30.850

34.931

39.580

50.894

65.510

84.320

108.43

13

28.029

32.088

34.351

36.786

42.218

48.496

64.109

84.852

112.30

148.47

14

32.392

37.581

40.504

43.672

50.818

59.195

80.496

109.61

149.23

202.92

15

37.279

43.842

47.580

51.659

60.965

72.035

100.81

141.30

197.99

276.97

16

42.753

50.980

55.717

60.925

72.939

87.442

126.01

181.86

262.35

377.69

17

48.883

59.117

65.075

71.673

87.068

105.93

157.25

233.79

347.30

514.66

18

55.749

68.394

75.836

84.140

103.74

128.11

195.99

300.25

459.44

700.93

19

63.439

78.969

88.211

98.603

123.41

154.74

244.03

385.32

607.47

954.27

20

72.052

91.024

102.44

115.37

146.62

186.68

303.60

494.21

802.86

1298.8

21

81.698

104.76

118.81

134.84

174.02

225.02

377.46

633.59

1060.7

1767.3

22

92.502

120.43

137.63

157.41

206.34

271.03

469.05

811.99

1401.2

2404.6

23

104.60

138.29

159.27

183.60

244.48

326.23

582.62

1040.3

1850.6

3271.3

24

118.15

158.65

184.16

213.97

289.49

392.48

723.46

1332.6

2443.8

4449.9

25

133.33

181.87

212.79

249.21

342.60

471.98

898.09

1706.8

3226.8

6052.9

26

150.33

208.33

245.71

290.08

405.27

567.37

1114.6

2185.7

4260.4

8223.0

27

169.37

238.49

283.56

337.50

479.22

681.85

1383.1

2798.7

5624.7

11197.9

28

190.69

272.88

327.10

392.50

566.48

819.22

1716.0

3583.3

7425.6

15230.2

29

214.58

312.09

377.16

456.30

669.44

984.06

2128.9

4587.6

9802.9

20714.1

30

241.33

356.78

434.74

530.31

790.94

1181.8

2640.9

5873.2

12940.

28172.2

 


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