f-fin analysis-class 1 & 2

7/31/2019 F-Fin Analysis-Class 1 & 2

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FINANCIAL ANALYSIS

Classes - 1 & 2


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SESSION PLAN

TIME VALUE OF MONEY


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1. Money has time value.

2. A rupee today is more valuable than a rupee a year hence.

3. Money has, thus, a future value and a present value.

4. Alternatives can be assessed by either(a) compounding to find future value

(through Compounding Techniques) or

(b) discounting to find present value

(through Discounting Techniques)

5. Financial managers rely primarily on present value

techniques for decision making as they are at zero

time (t = 0) when making decisions.


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Mr Y invests Rs 1,000 at 10 % interest compounded annually.

At the end of the first year, he will have Rs 1,100.

This amount will constitute the principal for the next year.At the end of the 2nd year he would have Rs 1,210.00.

This would represent the principal for the third year.

And so on

Annual CompoundingYear 1 2 3

Beginning amount Rs 1,000.00 Rs 1,100.00 Rs 1,210.00

Interest rate 10% 10% 10%

Amount of interest 100.00 110.00 121.00

Ending principal 1,100.00 1,210.00 1,331.00

COMPOUNDING TECHNIQUES


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Mr X invests Rs 1,000 in a two-year time deposit scheme of a bank at6 % interest compounded semi-annually.

He will be paid 3 per cent interest compounded over four periodseach of six months duration.

Calculations are given below :-

6 months 1 Year 18 months 2 years

Beginning amount Rs 1,000.00 Rs 1,030.00 Rs 1,060.90 Rs 1,092.73

Interest rate 0.03 0.03 0.03 0.03

Amount of interest 30.00 30.90 31.83 32.78

Ending principal 1,030.00 1,060.90 1,092.73 1,125.51


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In the last example, there will be 8 compounding periods and the rateof interest for each period will be 1.5 %, that is (1/4 of 6 %)

Relevant calculations are given below.

Period(months)

Beginningamount

Interestfactor

Amount ofinterest

Beginningprincipal

Endingprincipal

3 Rs 1,000.000 0.015 Rs 15.000 Rs 1,000.000 Rs 1,015.000

6 1,015.000 0.015 15.225 1,015.000 1,030.225

9 1,030.225 0.015 15.453 1,030.225 1,045.678

12 1,045.678 0.015 15.685 1,045.678 1,061.363

15 1,061.363 0.015 15.920 1,061.363 1,077.283

18 1,077.283 0.015 16.159 1,077.283 1,093.442

21 1,093.442 0.015 16.401 1,093.442 1,109.843

24 1,109.843 0.015 16.647 1,109.843 1,126.490


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Effect of compounding more than once a yearcan also be calculated by the following formula.

A = P (1 + i )n x mm

where m is the number of times compounding is made per year.For semi-annual compounding, m would be 2, and for quarterlycompounding it would be 4.If interest is compounded monthly, weekly and daily, m would be

12, 52 and 365 respectively.

Using the formula in the last example:1. For semi-annual compounding, Rs 1,000 [1 + (0.06/2)]2x2

= Rs 1,000 (1+ 0.03)4 = Rs 1,125.51

2. For quarterly compounding, Rs 1,000 [1 + (0.06/4)]4x2

= Rs 1,000 (1+ 0.015)8 = Rs 1,126.49


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a stream of equal, annual cash flows

Mr X deposits Rs 2,000 for 5 years in his saving account paying 5 %interest compounded annually. How much money will he have at thebeginning of the 5th year.

Annual Compounding of Annuity

End ofyear

Amountdeposited

Number ofyears

FVIF @ 5 % forvarious periods

Future value(2) (4)

1 2 3 4 5

1 Rs 2,000 4 1.216 Rs 2,432

2 2,000 3 1.158 2,316

3 2,000 2 1.103 2,206

4 2,000 1 1.050 2,100

5 2,000 0 1.000 2,000

11,054


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However, in this case the calculations can be cut shortsince the compound interest factor is to be multiplied bythe same rupee amount (Rs 2,000) each year

Amount at the end of 5 years = Rs 2,000 (1.216) + Rs 2,000

(1.158) + Rs 2,000 (1.103) + Rs 2,000 (1.050) + Rs 2,000(1.000)

Taking out the common factor Rs 2,000, = Rs 2,000 (1.216 +1.158 + 1.103 + 1.050 + 1.000) = Rs 2,000 (5.527) = Rs

11,054.Or, by using FVIFA tables we look for the 5 % column and

the row for the fifth year and multiply the factor by theannuity amount of Rs 2,000. Thus we multiply Rs 2,000 by

5.526 to get our answer = Rs 11,052.


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PRESENT VALUE TABLESFind the present value of Rs 2,000 to be received 5 years fromnow, assuming 10 % rate of interest.

We have to look in the 10 % column of the fifth year in PVIF Table .The relevant PVIF as per Table is 0.621.

Therefore present value = Rs 2,000 (0.621) = Rs 1,242

Present value interest factor (PVIF) is the multiplier used tocalculate the present value of an amount to be received in thefuture, at a particular discount rate.

P = A (PVIF)


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Yearend

Cashflows

PVIF at 10% Present value(2) (3)

1 2 3 4

12345

Rs 5001,0001,5002,0002,500

0.9090.8260.7510.6830.621

Rs 454.50826.00

1,126.501,366.001,552.50

5,325.50

PRESENT VALUEof a mixed stream of Cash Flows


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PRESENT VALUE of an AnnuityPV of a 5 yr annuity of 1000 at 10% is calculated as follows:

P = 1,000 (0.909) + 1,000 (0.826) + 1,000 (0.751) +

1,000(0.683) + 1,000 (0.621) = Rs 3,790Simplifying the equation by taking out 1,000 as common

factor outside the equation,

P = Rs 1,000 (0.909 + 0.826 + 0.751 + 0.683 + 0.621) = Rs

1,000 (3.790) = Rs 3,790

Therefore, the method of determining PV of an annuity isP = A (PVIFA) = Rs 1,000 (3.791) = Rs 3,791


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Find the present value of an annuity of Rs 1,00,000 for a

period of 10 years at a 10 % rate of interest?

: The PVIFA of a 10 year annuity at 10 % is to be

found from the 10th row (representing time period)

against the 10 % interest column. This value is 6.145.Multiplying this factor by the annuity amount ofRs.1,00,000, we find that the sum of the present value ofannuity is Rs 6,14,500

ILLUSTRATION - 1


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ABC company expects cash inflows from its investments - Rs2,00,000 and Rs 1,50,000 at the end of the first two years

respectively and then expects annuity payment of Rs 1,00,000 forthe next eight years. Find the present value of cash inflowsassuming 10 % rate of interest.

Solution We can solve the problem by applying the long method offinding the present values for each years amount by consultingPVIF Table. But we would like to apply the short-cut procedure asmost of the payments are part of an annuity.

ILLUSTRATION - 2


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1. Both the methods of adjusting time value of money,compounding and discounting, yield identical results.

2. Farther in the future a sum is to be received, the lower is its PV.

3. Greater the discount rate, lower is the PV and vice versa.

4. Longer the period of time, lower is the PV and vice versa.

5. At the discount rate of 0 %, the PVIF = 1, i.e. the future value ofthe funds equals their present value.

IN SHORT


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(INFINITE LIFE ANNUITIES)PERPETUITIES

An annuity that goes on for ever is called a perpetuity.

The PV of perpetuity of Rs C is given by the formula where i

is the interest rate.

Example : Find the PV of Rs 500 in perpetuity, discounted at 5 %

Answer : 500 / 5% = 10,000

5 % of 10,000 = 500


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M/s XYZ Ltd is establishing a sinking fund to retire Rs 5,00,000/- 8 %debentures, 10 years from today. The company plans to put a fixedamount into the fund each year for 10 years. Interest rate is 6% p.a.

What equal annual contributions must be made to accumulate Rs5,00,000, 10 years from now if the first payment will be made (a) atthe end of the current year, (b) at the beginning of the current year?

Answer (a) : FVIFA indicates that the annuity factor for 10 years at 6per cent is 13.181. In order to have Rs 5,00,000 the required amount

would be Rs 5,00,000 13.181 = Rs 37,933.39. If Rs 37,933.39 isdeposited at the end of each year for ten years, there will be Rs5,00,000 in the account.

Answer (b) : 500,000 x .943 / 13.181 = 35,771.19

or 500,000 / 1.06 / 13.181 = 35,786.22

ILLUSTRATION - 3


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ILLUSTRATION - 4A particular debenture (face value 1,000) pays interest at 8 % p.a. Thedebenture is to be redeemed after 10 years at a premium of 5%.Interest is paid half yearly. Find its current worth?

Answer : As it is compounded semi-annually, there will be 20compounding periods and the discount rate will be 8 % / 2 = 4%

It is like an annuity of Rs 40 (4% of 1,000) for 20 years.

The PVIFA for 20 years at 4% is 13.59

So PV of total interest receivable = 40 x 13.59 = 543.60.

The PV of the maturity amount of 1,050 (redemption @ 5% premium)will be 1050 x 0.463 (PVIF at 8% for 10 years) = Rs 486.15

The total present value = Rs 543.60 + Rs 486.15 = Rs 1,029.75


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ILLUSTRATION - 5

A machine costing Rs 10 lakhs has a five year life. Itsper annum running costs are Rs 2 lakhs and annualincremental revenues are Rs 5 lakhs. Should one buy it?

Assume no taxes and 10% interest rate.

Answer:PVIFA (10%, 5 years) = 3.791And 300,000(5 lakhs 2 lakhs) x 3.791 = 11,37,300

So it should be bought as NPV is positive


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ILLUSTRATION - 6Which of the following is the best investment option and why :-

1. A Rs 1000/- face value, 10% debenture, paying interest every six months,

and maturing at par after 10 years, currently available at par.

2. A Rs 1000/- face value zero coupon bond which will mature in 10 years at par

and is currently available for Rs 375/-

3. A Rs 1000/- face value, 10% bond, which pays interest annually, and willmature at par after 10 years, currently available at 2% discount.

Answer1. 50 x PVIFA (5%, 20 periods) = 50 x 12.462 = 623.10

1000 x PVIF (10%, 10 years) = 1000 x 0.386 = 386.00 Total 1009.10So NPV = 1009.10 1000.00 = 9.10

2. NPV = 386.00 375.00 = 11.00

3. 100 x PVIFA (10%, 10 years) = 50 x 6.145 = 614.50

1000 x PVIF (10%, 10 years) = 1000 x 0.386 = 386.00 Total 1000.50

So NPV = 1000.50

980.00 = 20.50SO (2) IS THE BEST OPTION


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1. Compounding techniques2. Discounting techniques3. Annuities

4. Perpetuities5. Present & Future Value Tables6. Illustrations


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Volume / cost / Profit Analysis


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f-fin analysis-class 1 & 2

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