Fin Calculator Guide

APPLICATION MANUAL

FINANCIAL CALCULATORS FC100V, FC200V Specific Applications in addition to various other applications that can be performed by FC are

summarized below: Simple Interest Calculation

Compound Interest calculation

Cash Flow Calculation

Amortization calculations General and function calculation

Statistics calculations

Interest rate conversion calculations

Cost / selling price / margin calculations

Day or date calculation

Depreciation calculation

Bond (Annual/yield to maturity (YTM) calculations)

Break even point analysis

Explanation

Example

Operation

Simple Interest calculation

Simple Interest calculations as performed mainly by banks and loan providers or person lending or borrowing funds at simple rate of interest. The formula for calculation shall be as follows:

SI = PV x n / 365 x I% PV= Principal

N = Number of interest periods SFV= PV+SI I = Annual interest rate SI = Simple Interest SFV=Interest + principal

Principal (PV) = INR 5000 5000x90/365x9/100 Interest (I %) = 9% Days (n) = 90 SI = solve =110.95 SFV = solve =5110.95

Press key and using the cursor key enter the following data with exe key

1 2 3

For calculating the simple interest bring the cursor key to SI and enter the solve key and the answer appears as 1 above Press ESC key and bring the cursor by using the Key and enter the Solve key and the answer appears as 2 and using the ESC key bring the cursor to ALL key and press SOLVE key and the answer appears as 3 above. Note: The days in a year can be adjusted as 360 days or 365 days depending upon the usage

to adjust press SMPL and then SET key and enter EXE key and chose the option of 360 or 365 days.

Simple Int. Set : 365 or 360 days Dys : 90

I% : 9 PV : 5000 SI : Solve SFV : Solve ALL : Solve

SI= -110.958904

SFV= -5110.958904

SI= -110.958904 SFV=-5110.958904

An amount of 5000/- is borrowed at the rate of 9% per annum for 90 days, calculate the simple interest.

Explanation

Operation

Compound Interest calculation

Most of the banks and person dealing with funds use the word compounding interest annually, semi-annually or quarterly etc. to understand better compound interest would mean calculating the interest on interest also. The mathematical formula shall be as follow:

• C.I. = P , where C.I. = compound interest

• If the interest rates for the successive fixed periods are r1%, r2%, r3% ..., then A (amount) is given by

A=P ... ….., where A= amount & principal , P= principal

For example continue with the same example in previous sheet. If the period is 3 years then CI would be C.I. =5000 x {(1+ .09)³-1} = 1475.145 A =5000 + 1475.145 = 6475.145

Press CMPD key Input the following using scroll and exe keys

* Use of option PMT is explained in next page Note: Using scroll key please enter the P/Y = 1 and C/Y = 1 as the same represents the

Installments per year and Compounding per year respectively. If the compounding is semi annually then C/Y should be selected as 2 and for quarterly the same should be selected as 4.

Note: Press ESC key to come back to previous screen Note: To clear variables from the memory is to press SHIFT key and 9 key and EXE

key and chose the correct option to clear either setup, memory or all

variables from the memory

Set : begin / end select End using scroll and exe key N : press 3 and enter exe key I% : press 9 and enter exe key PV : press 5000 and enter exe key PMT : leave blank or press 0 and enter exe key* FV : Press solve key, see the answer appears as -6475.145

EMI calculation CMPD continues…. A very important tool for finance companies having the business of lending money and all those also borrowing money and in the need to know that how much monthly installment need to be paid for a particular loan. Typically a person needs to know the present value of amount borrowed/lend and the interest rate to be paid also the total number of installments to be used while returning the amount

borrowed. i.e. PV = amount borrowed or lend i.e. INR 50000 I% = interest rate i.e. 12% p.a. i= I%/12/100 = 0.010 N = number of installments per year i.e. 15 years = 180 times A typical way of calculating the EMI shall be taking the help of computer or a long sheet of

paper and lot of time in computing and yet not very sure about the way of doing. The formula shall be as follows: PV x i x (1+ i)ⁿ = (1+ i)ⁿ-1

= 50000 x 0.01 x (1.01)180

(1.01)180

- 1

= 600.08

EMI calculation without a calculator having the solving power like this is just impossible and doing little simulations and variations in interest, principal etc, the working becomes very tough, but the use of FC 200V is very simple, faster and economical, let’s see Press CMPD key and using the scroll and exe key enter the following data

Set = End key N = Press 180 and enter Exe key (15 years x 12 months) I% = Press 12 and enter Exe key PV = 50000 exe key PMT = Solve key FV = Press 0 and enter Exe key P/Y =12 as the installments per year is 12 the duration of loan is 15 years C/Y =12 as the compounding also is monthly so in a year 12 compounding

Scroll back to PMT key and enter solve key as the answer flashes -600.08. Is it not quite amazing the result is produced in less than a minute as against probably one

hour? Now we can use variation just like mortgage calculators available on the web and computer spreadsheets e.g.

1. Calculate the PV if we know how much maximum EMI can be paid

2. Calculate the maximum Rate of interest can be borne if EMI, period and PV is known

3. Calculate the Number of periods (i.e years) wherein loan can be repaid if PV, I%

and EMI is known

Just in simple way skip the term we want to know and enter the data in rest of the terms as before, using the scroll key come back to the term we want to know and press solve key and result is available.

Set = End key N = 180 periods (15 years x 12 months) I% = 12 PV = solve key PMT = -600.08

FV =0 P/Y =12 as the installments per year is 12 the duration of loan is 15 years C/Y =12 as the compounding also is monthly so in a year 12 compounding

Set = End key N = 180 periods (15 years x 12 months) I% = Solve key PV = 50000 PMT = -600.08 FV =0 P/Y =12 as the installments per year is 12 the duration of loan is 15 years C/Y =12 as the compounding also is monthly so in a year 12 compounding

Set = End key N = Solve key I% = 12 PV = 50000 PMT = -600.08 FV =0 P/Y =12 as the installments per year is 12 the duration of loan is 15 years C/Y =12 as the compounding also is monthly so in a year 12 compounding

Explanation

Example

Cash Flow Calculation

The application mainly is used by analysis to appraise an investment proposal having a fixed stream of cash inflow after a fixed period of cash outflow. Typically an investor need to know the following to do the analysis i.e. cash outflow and cash inflow and certain financial tools to help him to take the decision, the tools could be Internal Rate of Return (IRR), Net Present Value (NPV), Net Future Value (NFV) and Payback Period (PBP) PBP The payback period is defined as the number of years required to recover a project’s

cost. NPV The net present value (NPV) method discounts all cash flows at the project’s cost of

capital and then sums those cash flows. Accept project if NPV > 0.

IRR The internal rate of return (IRR) is defined as the discount rate which forces a project’s NPV to equal to zero.

Accept project if IRR > cost of capital.

A typical cash flow shall work out as follows Cash Inflow Cash Outflow

An investment would outlay an expenditure of INR 100000 in the year0 and thereafter for the next four years it generates the cash inflow at a consistent flow of 40000 per year. The PBP shall work out to be like 100000/40000=2.50 years

The NPV shall be as follows: Particulars cash In/Out Discounted Cash Flow @12%

Year 0 -100000 -100000 -100000.00 Year 1 40000 40000/ (1.12)¹ 35714.28 Year 2 40000 40000/ (1.12)² 31887.75

Year 3 40000 40000/ (1.12)³ 28471.21 Year 4 40000 40000/ (1.12)Q 25420.72 Net present value +21493.96

As you know, money devalues over time. The rate at which it does is commonly referred to as the "discount rate". Therefore, let's say you have a payment/income profile as shown above and we assume a discount rate of 12%. If you take the difference between the net present value of the payments and the net present value of the returns, you get the net present value of the investment. In the case shown above that turns out to be 121493.96-100000=21493.96.

IRR

If we equate the net present value to zero we get the internal rate of return, a rate which puts cash outflow-discounted cash inflow equal to zero, the significance of IRR is that for example the IRR for the above said case is 21.86% and if the money devalues at 22% then you make nothing on your investment. So prudence say that you must make investment that fetches you return greater than 22%. The IRR can be derived only be trial and error method and a guessed cost of capital should be estimated otherwise the trial and error method also takes long time and is irritating. The common method used for IRR is CFº+ CF₁ +CF₂ +CF₃ +CF₄ = 0

(1+r) (1+r) ² (1+r) ³ (1+r) ⁴

In the given case if we discount the cash flow by an estimated rate of capital of 21% shall give us the NPV equal to +1617.64 Again using the trial method we forward the rate to 22% and see the NPV coming out to be as -254.38 but the object is to bring the discounted cost of capital equal to Zero so by using the trial and error method we use the following

Formula

1617.64 21% + ----------------- X 1 1617.64+254.38 = 21.86% We have seen how cumbersome procedure is used to calculate the IRR and NPV imagine a person evaluating the 50-100 proposals a day shall get mad and crazy. The solution provided

by FC 200 V is quite simple and we just have to input the data as follows:

Operation

For calculating the NPV at the discounted rate of 12% Press Cash Key and using the scroll and exe key input the data as follow

*remember to remove the I%=12% / 21.86% otherwise the PBP shall be calculated on DCF@12% and the result shall be 3.15 years / 3.99 years Is it not very simple and clean way of computing complex things, yes thanks to FC 200V Remember to be patient while solving IRR as calculator processes the data at the speed of _ Note: Data editor can input the maximum number of 80 variables in case of 1-var is selected

or 40 in case of 2- var is selected (i.e. X, Y or X and Freq ) and 26 in case of X, Y and Freq is selected. To choose the option Press STAT Key and chose 1- Var press exe and AC key and select again CASH key and in the case of more than one variable using the same procedure above select other than 1-Var mode.

I% : input 12 enter exe key Csh : Press exe key and input that cash out flow and cash inflow Cash outflows should be represented as (-) and inflow as (+) : using ESC key and scroll key press following

NPV : Press solve key and the result shall be +21493.96 IRR : Press solve key and the result shall be 21.86% PBP : Press solve key and the result shall be 2.50 years* NFV : Press solve key and the result shall be +60000*

Explanation

Example

Operation

Interest rate conversion calculations

The conversion of annual interest rate into effective interest rate is usually used when the compounding per year is more than one. The conventional way of calculating EEF (effective interest rate) is:

EEF = 1+ APR/100

n- 1 x 100 APR Annual percentage rate (%)

n EEF Effective interest rate (%)

N number of compounding

APR = 1+ EEF/100

1/n

- 1 x n x 100

n

Example of converting the annual rate is where an investor gets the return on an investment other than annual basis then his first curiosity shall be to know what my effective annual interest rate is. E.g. Interest rate: 12% compounded semi annually, the EEF shall be 12.36% and if the EEF is 14%

then APR shall be 13.54%. Similarly if the compounding can be quarterly (4) or monthly (12) and accordingly results can be obtained but how complex is to solve the power of 12.

Press CNVR key Input the above data using scroll and exe key Other way could be press i% =14 and press APR key the result shall be 13.54% as described above.

N = Press 2 and enter Exe key I% = Press 12 and enter exe key

EEF = press solve key and the result is 12.36%

Explanation

Operation

Cost / selling price / margin calculations

Cost and their relation with the selling price is very well known, the difference is known as margin which could be profit or loss. The formula for calculation shall be as follows:

CST = SEL * (1-MRG/100) CST= cost SEL= selling price MRG=margin

SEL = CST/ (1-MRG/100)

MRG = (1- (CST/SEL))*100

Select COST Key By inputting any two values the third value can be calculated, by using the following way, it can be done:

Note: By inputting any two variables third variable can be calculated, typically margin is the

selling price less cost and divided by selling price as the %age of sale price, conversely many people use the cost as the base price for generating the %age of value addition to the cost.

CST = Press 1200 and enter exe key SEL = Press 1500 and enter exe key

MRG= press solve key answer shall be 20%

Explanation

Example

Amortization calculations

Amortization means "the systemic payment plan -- such as a monthly payment -- so that your

loan is paid off over the specified loan period."

So an amortized loan is for one specific amount that is to be paid off by a certain date, usually

in equal monthly installments. Your car loan and home loan fit that definition. Your credit card

account doesn't because it's a revolving loan with no fixed payoff date.

A part of the payment goes toward the interest cost and the remainder of the payment goes toward the principal amount -- the amount borrowed," Interest is computed on the current amount owed "and thus will become progressively smaller as the ending balance of the loan reduces." In simple meaning when you borrow money the first repayment of loan installment, the interest is on the full amount of loan but as you continue to pay back the principal amount keeps on reducing so is the interest amount.

But if you want to know the breakup of any EMI or installment into Principal and Interest it shall be a quite difficult task for common man. Let us understand the concept of amortization in simple amortization calculator. The concept

of PMT, interest, FV, BAL, INT, PRN, ∑INT, ∑ PRN ETC can be understood with an easy example.

In the given case the PV = 10000 and interest rate is 2% and the PMT working out to be 286.43 over a period of 3 years i.e. N=36 months, please note the Amortization table helps you to calculate the interest and principal on any of the installment specified. The requirement is to know the PMT = EMI = -286.43 (remember EMI can be calculated by CMPD key), PV=principal = 10000 and Interest = i%=2. You can calculate between any month to any month i.e. PM1 to PM2, remember that PM2 needs to be greater than PM1.

0

60

120

180

240

300

Amount

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

Months

Break up of PMT

InterestPrincipal

Loan Calculator

Enter Values Loan Summary

Loan Amount $10,000.00

Scheduled

Payment $ 286.43

Annual Interest

Rate 2.00 %

Scheduled

Number of

Payments 36

Loan Period

in Years 3

Actual Number

of Payments 36

Number of Payments

Per Year 12

Total Early

Payments $ -

Start Date

of Loan 01/04/2004 Total Interest $ 311.33

Optional

Extra

Payments

Lender Name: Anil Chaudhry

Pm

tNo

.

Payment

Date

Beginning

Balance

Scheduled

Payment

Extra

Payment

Total

Payment Principal Interest

Ending

Balance

1 01/05/2004 $ 10,000.00 $ 286.43 $ - $ 286.43 $ 269.76 $ 16.67 $ 9,730.24

2 01/06/2004 9,730.24 286.43 - 286.43 270.21 16.22 9,460.03

3 01/07/2004 9,460.03 286.43 - 286.43 270.66 15.77 9,189.37

4 01/08/2004 9,189.37 286.43 - 286.43 271.11 15.32 8,918.26

5 01/09/2004 8,918.26 286.43 - 286.43 271.56 14.86 8,646.70

6 01/10/2004 8,646.70 286.43 - 286.43 272.01 14.41 8,374.69

7 01/11/2004 8,374.69 286.43 - 286.43 272.47 13.96 8,102.22

8 01/12/2004 8,102.22 286.43 - 286.43 272.92 13.50 7,829.30

9 01/01/2005 7,829.30 286.43 - 286.43 273.38 13.05 7,555.92

10 01/02/2005 7,555.92 286.43 - 286.43 273.83 12.59 7,282.09

11 01/03/2005 7,282.09 286.43 - 286.43 274.29 12.14 7,007.80

12 01/04/2005 7,007.80 286.43 - 286.43 274.75 11.68 6,733.05

13 01/05/2005 6,733.05 286.43 - 286.43 275.20 11.22 6,457.85

14 01/06/2005 6,457.85 286.43 - 286.43 275.66 10.76 6,182.18

15 01/07/2005 6,182.18 286.43 - 286.43 276.12 10.30 5,906.06

16 01/08/2005 5,906.06 286.43 - 286.43 276.58 9.84 5,629.48

17 01/09/2005 5,629.48 286.43 - 286.43 277.04 9.38 5,352.44

18 01/10/2005 5,352.44 286.43 - 286.43 277.51 8.92 5,074.93

19 01/11/2005 5,074.93 286.43 - 286.43 277.97 8.46 4,796.96

20 01/12/2005 4,796.96 286.43 - 286.43 278.43 7.99 4,518.53

21 01/01/2006 4,518.53 286.43 - 286.43 278.89 7.53 4,239.64

22 01/02/2006 4,239.64 286.43 - 286.43 279.36 7.07 3,960.28

23 01/03/2006 3,960.28 286.43 - 286.43 279.83 6.60 3,680.45

24 01/04/2006 3,680.45 286.43 - 286.43 280.29 6.13 3,400.16

25 01/05/2006 3,400.16 286.43 - 286.43 280.76 5.67 3,119.40

26 01/06/2006 3,119.40 286.43 - 286.43 281.23 5.20 2,838.18

27 01/07/2006 2,838.18 286.43 - 286.43 281.70 4.73 2,556.48

28 01/08/2006 2,556.48 286.43 - 286.43 282.16 4.26 2,274.32

29 01/09/2006 2,274.32 286.43 - 286.43 282.64 3.79 1,991.68

30 01/10/2006 1,991.68 286.43 - 286.43 283.11 3.32 1,708.57

31 01/11/2006 1,708.57 286.43 - 286.43 283.58 2.85 1,425.00

32 01/12/2006 1,425.00 286.43 - 286.43 284.05 2.37 1,140.95

33 01/01/2007 1,140.95 286.43 - 286.43 284.52 1.90 856.42

34 01/02/2007 856.42 286.43 - 286.43 285.00 1.43 571.42

35 01/03/2007 571.42 286.43 - 286.43 285.47 0.95 285.95

36 01/04/2007 285.95 286.43 - 285.95 285.47 0.48 0.00

Operation

Finding the breakup of any PMT for any month shall be difficult task, however the same shall be quite easy in FC200, see the steps

1. The answer pertains to the principal balance after 25th installment, please refer the table

2. The answer pertains to the interest component in the first installment (PM1) please refer the table

3. The answer pertains to the principal component in the first installment (PM1) please refer the table

4. The answer pertains to the total interest paid from 1st to 25th installment please refer the table

5. The answer pertains to the total principal paid from 1st to 25th installment please refer the table

The simulation from any installment to any installment is possible, quite simple way. Note : for going back to default input screen use ESC key

Press AMRT key Set : End key PM1 : Enter 1 press exe; you may enter any particular month PM2 : Enter 25 Press exe; you may enter any particular month, but should be greater than PM1

N : 36 press exe; (3 years and 12 months in a year) I% : 2 press exe; the interest % PV : 10000 press exe; the principal amount PMT : enter -286.43 press exe; the PMT can be worked out by using CMPD key FV : 0 press exe; should be left blank P/Y : 12 press exe; payments in a year C/Y : 12 press exe; compounding in a year

BAL : SOLVE key : Answer shall be 3119.29₁ INT : SOLVE Key : Answer shall be -16.666₂ PRN : SOLVE Key : Answer shall be -269.76₃ ∑INT : SOLVE key : Answer shall be -280.04₄ ∑PRN : SOLVE Key : Answer shall be -6880.70₅

Explanation

Operation

Day or date calculation

The day’s mode helps you to calculate the number of days from any specific date to any specific date.

The following simulation is possible If days and d1 is known then d2 can be calculated If days and d2 is known then d1 can be calculated If d1 and d2 is known then days can be calculated

d1 is the first date and d2 is the date after the d1 D1 D2 Before entering the data following options are available

The option of setting the day as 360 or 365 is available Mode of entering the date as DMY or MDY, the same can be selected in setup key

Let us see the practical aspect of the same Press DAYS key and using the scroll key enter the following

By leaving any one variable blank and filling the other two variables, we can find the third variable.

Set : 365 D1 : 30072004 i.e. July 30, 2004

D2 : 17052005 i.e. May 17, 2005 Dys : press SOLVE key and the answer shall be 291 days

Days

Explanation

Depreciation calculation

With the help of FC200 we can calculate the following four popular method of

calculating the depreciation on fixed assets: Depreciation means wear and tear of the assets due to its usage. Straight Line Method (SL) Fixed Percentage Method (FP)

Sum of Years Digit Method (SYD) Declining Method or written Down Value Method (WDV)

Straight Line Method= (P-S)/n P= Principal Value S=Salvage value if any N=Number of years

Fixed Percentage Method = (P-S) x FP P= Principal Value S=Salvage value if any N=Number of years

Sum of years Digit Method First Year = N (P-S)

Sum-of –years Second Year = N-1 (P-S) Sum-of –years

Third Year = N-2 (P-S) Sum-of –years . . Last Year = 1 (P-S)

Sum-of –years

For our example, N=5 and the sum of years is 1+2+3+4+5=15

Declining method or WDV Depreciation in First year = (P) x Depreciation rate

Second year and onwards= (Net book value) x Depreciation rate Net book Value = (P-S-Accumulated depreciation) Depreciation rate =

Operation

The following setting values should be done (hypothetical values) Press DEPR key and using the scroll key and EXE key press following values

N = 6 (life of assets in terms of years) I% = 25 (fixed rate of depreciation incase of Fixed percentage method)

= 200 (depreciation factor in case of Declining Method) PV = 12000 (Cost of the assets) FV = 0 (residual value if any)

‘j = 1 (year for which the depreciation is being calculated) YR1 = 12 (number of months in the first year)* *In the initial year of buying the assets it is quite possible that depreciation is allowed only for part of the year in that case required number of months need to be entered. You need to input I% only if you use FP or DB method of depreciation

With the help of FC200V the calculation for any year’s depreciation is possible also the factor for

SL = SOLVE Key SL = 2000 RDV = 10000 ‘j = 1 RDV means the value after depreciation

FP = SOLVE Key FP = 3000 RDV = 9000 ‘j = 1 RDV means the value after depreciation

SYD = SOLVE Key SYD = 3428.57 RDV = 8571.42 ‘j = 1 RDV means the value after depreciation

DB = SOLVE Key DB = 4000 RDV = 8000 ‘j = 1

RDV means the value after depreciation Don’t forget to change the I%=as factor instead of Fixed percentage

Explanation

Break even point analysis

This is a very common term used often by Finance Manager or Production Manager, a point of sales or a point of quantities to sell where the company would break even or

to ore specifically company would neither gain nor lose. The profit at such sales would become Nil or 0%. This tool is very important for Managers as it suggest that company to break even must sell at least N number of quantities.

Let’s see the calculation of Break even (quantities) Break even (quantities) =Fixed Cost / (Selling Price

(Unit) – Variable Cost

(Unit))

Break Even (Values) = Break even (quantities) x Selling price (Unit)

For calculating the BE we need selling price per unit (PRC), variable cost per unit (VCU), Fixed Cost (FC) Using the FC200V Press BEVN key and using the scroll key enter the following values

Press exe key at BEV and input the following Hypothetical data

Set : PRF / Quantities using exe key use appropriate options

PRF / ratio press exe key using again exe key select ant of the following

1. PRF

2. r% or

B-even press exe key and using again exe key select any of the following

1. quantities (QBE)

2. Sales (SBE)

Operation

Using Exe key enter following

*In case the company wants to know how much quantities need to be sold for achieving the profit (PRF) of say 10000, then after selecting PRF above enter the PRF / r% as 10000 and then QBE and SBE can be calculated for a profit target of 10000

* the option can be used if company wants to know that how much quantities need to

be sold for achieving the profit % of say 10%, then after selecting r% above enter the PRF / r% as 10 and then QBE and SBE can be calculated for a profit target of 10%.

Margin of Safety (MOS) Margin of safety denotes that how much sales can be dropped before attaining the

losses. For example if sales are 120000 and SBE is 48000 then MOS shall be 0.60. That denotes that sales from the present levels can be dropped by 60% before

company starts incurring losses. Continuing from the last hypothetical figures where the SBE was 48000 and suppose

the actual sales are 120000 that means the actual sales are more than the Break even

sales of 48000. I.e. Margin of safety is 60% By inputting any two values third value can be calculated DEGREE OF OPERATING LEVERAGE (DOL)

The extent to which a business uses fixed costs (compared to variable costs) in its operations is referred to as "operating leverage." The greater the use of operating leverage (fixed costs, often associated with fixed assets), the larger the increase in profits as sales rise and the larger the increase in loss as sales fall. = Sales less Variable cost / sales less total cost

Degree of operating leverage can be calculated if we know the total sales, total variable cost and the total fixed cost.

Press Exe key on MOS Input the sales SAL : 120000 SBE : 48000 MOS : 0.60

Press Exe key on DOL

Input the sales SAL : 120000 VC : 90000 FC : 10000 DOL press solve key : 1.5

PRC = 100 VCU = 75 FC = 12000 PRF/ R%= 0* QBE = SOLVE key i.e 480 units or if SBE selected above then answer

shall be 48000

DEGREE OF FINANCIAL LEVERAGE (DFL) The degree of financial leverage (DFL) is defined as the percentage change in

earnings per share [EPS] that results from a given percentage change in earnings before interest and taxes (EBIT), and is calculated as follows: DFL = Percentage change in EPS divided by Percentage change in EBIT

This calculation produces an index number which if, for example, is 1.43, means that a 100 percent increase in EBIT would result in a 143 percent increase in earnings per

share

In simple terms the DFL means the impact of Interest expenses on the earnings of the company

DEGREE OF COMBINED LEVERAGE (DCL)

Combined leverage is the product of operating leverage and financial leverage. That is: DTL=DOL*DFL Where: DTL=degree of total leverage. DOL=degree of operating leverage. DFL=degree of financial leverage.

Application of total leverage

1. Degree of total leverage measures the percentage change in EPS that results from a change in one percent in output.

2. It assists in measuring the firm’s total risk.

Press Exe key on DFL EIT (earnings before Interest) :120000 ITR (Interest) : 9000 DFL press solve key : 1.081

Press Exe key on DCL SAL (total sales) :120000 VC (Variable cost) : 90000 FC (Fixed Cost) : 10000 ITR (Interest) : 9000 DCL press Solve : 2.7272

Statistical analysis

Before understanding the concept of Standard deviation, we must understand the term Mean and Variance Mean as a common meaning denotes the center and arithmetically represents the average of the given population or sample data

Variance is a parameter that measures how dispersed a random variable’s probability

distribution is. For two random variables the one on the left is more dispersed than the

one on the right. It has a higher variance. In more common terminology we can say

that it measures the variability from the mean.

Variance can be of two types:

• Population variance

• Sample Variance

High vs. Low Variance

Example of Population variance

The population variance is the mean squared deviation from the population mean:

Here is an example of the variance formula in action.

σ2

= Population Variance

µ = Mean

Example of Sample variance

In practice population variance cannot be computed directly because the entire population is not ordinarily observed. An analogous measure of variability may be determined with sample data. This referred to as sample variance

Sample variance can be calculated in the similar way as Population variance except that

the divisional factor is one number less than the total numbers i.e N

S2

= Sample variance =

X = Sample mean data

Standard Deviation

The standard deviation is the positive square root of the variance:

Population standard deviation:

Sample standard deviation:

Let us take the an example having one variable and calculate above said

Press Setup key and using the scroll key STAT: On/Off key Select On by

pressing EXE

Press STAT key and select type

1

)(12

−

−

=

∑=

n

xx

s

N

i

i

2σσ =

1- 1- Var : exe

2- A + B X : exe

3- _ + cX2 : exe

4- In X : exe

5- e^X : exe

6- a + b^X : exe

7- a +X^B : exe

8- 1/X : exe

2)1(1 −=− σσ

2)1( −σ

Example for 1- Var (single variable)

Press Stat and chose option from type 1-var by pressing exe key and enter the

following data using cursor and exe key

X freq

1 10 1

2 12 1

3 14 1

4 16 1

5 18 1

6 20 1

7 18 1

8 16 1

9 14 1

10 12 1

Press AC key and Shift S-Menu and by selecting the appropriate digit following options

available

Press 1 we get the table __ above

Press 2 we get the option of more data entry

Press 3 we get the option of editing the data

Press 4 we get the option of 1. ∑ x2 2. ∑ x

Press 1 and below screen appears

Sum of variable ∑ x

Press Exe

Press 2 and below screen appears

Press exe

1. Type 2. Data

3. Edit 4. Sum

5. Var 6. MinMax

∑ x2

0

∑ x2

2340

∑ x

150

∑ x

0

Please note for all calculation Press AC key and Shift – S-menu key and then

press the required option

Press AC-Shift-S-Menu and option 5, we get the following screen

Press 1: Press exe Press exe

Press AC – Shift – S-Menu- 5- option 2

Press exe Press AC – Shift – S-Menu- 5- option 3 Press exe

Press AC – Shift – S-Menu- 5- option 4

Press exe Press AC – Shift – S-Menu- 6- we get options of 1: minX and maxX

Press 1 Press exe

1: n 2: X

3: Xσn 4: xσn-1

n

10

n

0

X

0

X

15

Xσn

0

Xσn

3

Xσn-1

0

Xσn-1

3.162277

minX

0

minX

10

Press AC – Shift – S-Menu- 6- we get options of 2

Press exe In case of two variables the frequency column is used for another variable and the calculation

is based on the following formula and the formula shall be based on the following shortcut of variance and Standard Deviation.

σ = ∑ Xb - (∑ X)b/n n

******

maxX

0

maxX

20

Commands when linear regression calculation (A+ BX) is selected

When linear regression calculation is selected the calculation is performed by the following model is selected i.e. a + b X and the calculation are done based on the following:

Using FC200V following calculation is possible

Steps in case of 1-variable Formula Details

Shift (S-menu) 5-Var 1 ‘n Number of variables

Shift (S-menu) 5-Var 2 X Mean of the variables (x data)

Shift (S-menu) 4-sum 2 ∑ x Sum of the variables (x data)

Shift (S-menu) 4-sum 1 ∑Xb Sum of squares of variables ( x data)

Shift (S-menu) 5-Var 3 Xσn Population standard deviation (x data)

Shift (S-menu) 5-Var 4 xσn-1 Sample standard deviation (x data)

Shift (S-menu) 6-MinMax 1 MinX Minimum of x values

Shift (S-menu) 6-MinMax 2 MaxX Maximum of x values

Steps in case of more than 1

variable, in addition to above

Formula Details

Shift (S-menu) 4-sum 4 ∑ y Mean of the variables ( y data)

Shift (S-menu) 4-sum 3 ∑yb Sum of squares of variables ( y data)

Shift (S-menu) 4-sum 5 ∑ xy Sum of products of x data and y data

Shift (S-menu) 4-sum 7 ∑Xby Sum of x2 data X y data

Shift (S-menu) 4-sum 6 ∑Xd Sum of cubes of x data

Shift (S-menu) 4-sum 8 ∑XQ Sum of bi-squares of x data

Shift (S-menu) 5-Var 5 Ӯ Mean of variables (y data)

Shift (S-menu) 5-Var 6 Yσn Population standard deviation (y data)

Shift (S-menu) 5-Var 7 yσn-1 Sample standard deviation (y data)

Shift (S-menu) 6-MinMax 3 MinY Minimum if y values

Shift (S-menu) 6-MinMax 4 MaxY Maximum of y values

Shift (S-menu) 7-Reg 1 A Regression coefficient constant term A

Shift (S-menu) 7-Reg 2 B Regression coefficient term b

Shift (S-menu) 7-Reg 3 ‘r Correlation coefficient r

Shift (S-menu) 7-Reg 4 X^ Estimated value of X

Shift (S-menu) 7-Reg 5 Y^ Estimated value of Y

Example in the case of A+BX

X 2 3 4 5 6 7 8 9

Y 12 13 14 15 16 17 18 19

Steps in case of 1-variable Formula Result

Shift (S-menu) 5-Var 1 ‘n 8

Shift (S-menu) 5-Var 2 X 5.5

Shift (S-menu) 4-sum 2 ∑ x 44

Shift (S-menu) 4-sum 1 ∑Xb 284

Shift (S-menu) 5-Var 3 Xσn 2.291287

Shift (S-menu) 5-Var 4 xσn-1 2.449489

Shift (S-menu) 6-MinMax 1 MinX 2

Shift (S-menu) 6-MinMax 2 MaxX 9

Shift (S-menu) 4-sum 4 ∑ y 124

Shift (S-menu) 4-sum 3 ∑yb 1964

Shift (S-menu) 4-sum 5 ∑ xy 724

Shift (S-menu) 4-sum 7 ∑Xby 4864

Shift (S-menu) 4-sum 6 ∑Xd 2024

Shift (S-menu) 4-sum 8 ∑XQ 15332

Shift (S-menu) 5-Var 5 Ӯ 15.5

Shift (S-menu) 5-Var 6 Yσn 2.291287

Shift (S-menu) 5-Var 7 yσn-1 2.449489

Shift (S-menu) 6-MinMax 3 MinY 12

Shift (S-menu) 6-MinMax 4 MaxY 19

Shift (S-menu) 7-Reg 1 A 10

Shift (S-menu) 7-Reg 2 B 1

Shift (S-menu) 7-Reg 3 ‘r 1

Shift (S-menu) 7-Reg 4 X^ Estimated value y=3 x^=-7

Shift (S-menu) 7-Reg 5 Y^ Estimated value x=3 y^=13

Commands when other types of Regression calculation(s) are selected

1. Quadratic Regression (_CXb), Model equation y= A+BX+CXb

2. Logarithmic Regression (In X), model equation y= A+BInX

3. Exponential Regression (e^X), model equation y= AeBX

4. Power Regression (A*X^B), model equation y= AXB

5. Inverse Regression (1/X), Model equation y= A+B/X

Example in case of quadratic regression equation

X 2 4 6 8 10 12 14 16

Y 3 5 7 9 11 13 15 19

COMMANDS Formula Result


Shift (S-menu) 5-Var 2 X 9


















Shift (S-menu) 7-Reg 1 A 1.75

Shift (S-menu) 7-Reg 2 B 0.70833333

Shift (S-menu) 7-Reg 3 C 0.02083333

Shift (S-menu) 7-Reg 4 X^ If Y=3 then X^1= 1.68154169

Shift (S-menu) 7-Reg 5 x^2 If Y=3 then X^2= -35.6815416

Shift (S-menu) 7-Reg 6 Y^ If X=2 then y^= 3.25

Example in the case of Logarithmic Regression (In X), model equation y= A+BInX

X 2 4 6 8 10 12 14 16

Y 3 5 7 9 11 13 15 19





















Shift (S-menu) 7-Reg 1 A -4.106502688

Shift (S-menu) 7-Reg 2 B 7.111677003

Shift (S-menu) 7-Reg 3 r 0.9370197279

Shift (S-menu) 7-Reg 4 X^ If Y=3 then X^= 2.71630479

Shift (S-menu) 7-Reg 5 Y^ If x=3 then y^= 3.706473061

Example in the case of Exponential Regression (e^X), model equation y= AeBX

X 2 4 6 8 10 12 14 16

Y 3 5 7 9 11 13 15 19





















Shift (S-menu) 7-Reg 1 A 2.964238069

Shift (S-menu) 7-Reg 2 B 0.1218549797

Shift (S-menu) 7-Reg 3 r 0.9778589787



Example in the case of ab Exponential Power Regression (A*b^x), model equation

y= ABX

X 2 4 6 8 10 12 14 16

Y 3 5 7 9 11 13 15 19





Shift (S-menu) 4-sum 1 ∑bX 816








Shift (S-menu) 4-sum 7 ∑ybX 11696

Shift (S-menu) 4-sum 6 ∑dX 10368

Shift (S-menu) 4-sum 8 ∑QX 140352






Shift (S-menu) 7-Reg 1 A 2.964238069

Shift (S-menu) 7-Reg 2 B 1.129590276

Shift (S-menu) 7-Reg 3 r 0.9778589787



Example in the case of Power Regression (A*x^b), model equation y= AXB

X 2 4 6 8 10 12 14 16

Y 3 5 7 9 11 13 15 19





















Shift (S-menu) 7-Reg 1 A 1.550191285

Shift (S-menu) 7-Reg 2 B 0.8643765905

Shift (S-menu) 7-Reg 3 r 0.9959314857



Example in the case of Inverse Regression (1/X), Model equation

y= A+B/X

X 2 4 6 8 10 12 14 16

Y 3 5 7 9 11 13 15 19





















Shift (S-menu) 7-Reg 1 A 15.2498118

Shift (S-menu) 7-Reg 2 B -29.43384607

Shift (S-menu) 7-Reg 3 r -0.8098270919


Shift (S-menu) 7-Reg 5 Ŷ If x=3 then Ŷ= 5.438529776

Bond (Annualized Yield or Yield to Maturity)

The customary way of calculating the yield on Bonds purchased from the market is to typically finding the Internal Rate of Return (IRR) To understand Bond we must understand the complete terminology of the Bonds, e.g. Coupon Rate = CPN = rate of interest payable on the face value of the Bonds Purchase price = PRC = Price at which these bonds are available in the market Redemption value = RDV = Price at which maturity value is paid back to bondholders Term = n = Period of the bond, it can be either Fixed or can be derived from two dates Yield = YLD = the effective rate of interest or YTM. Example

A bond sold in the market at discount of 5% (face value-100, coupon rate-4%) and has a term period of 5 years. Find out its effective return? An investor to this Bond shall enjoy following benefits Period Cash flow

Year 0 -95 Year 1 04 Year 2 04 Year 3 04 Year 4 04 Year 5 104* (*Investor would get the Principal amount also in addition to Interest)

Equate the present value of all Cash flows to Zero and using the trial and error method find out its Yield, using a discount factor of 5%, we get following CF0(5%, 1st year)+CF1(5%, 2nd Year)+CF2(5%, 3rd Year)+CF3(5%, 4th year)+CF5(5%, 5th Year)=0

= (-95*0.9523)+(4*0.90702)+(4*0.86384)+(4*0.82270)+(104*0.78353) =1.39 Similarly using the Discount factor at 5.25% we get the net present value as -0.374649 To be more precise the YTM shall be 5.16% where the discounted cash flows shall be nearly equal to Zero.

Operation: Press BOND key and using scroll and exe key enter the following data:

• The interest option can be selected either Annual or Semi annual and also the period of bond can be either fixed or term

• Fixed period bonds shall give the option of putting two different dates as

purchase date and maturity date • Term period bond give the option of only putting the number of years as the

life of the bond If the Coupon rate is 4% and the Redemption price if 100 and to get the Yield of 8% what should be the purchase price of the bond in the market? The purchase price shall be 84.03 in the market to get the yield of 8% in the bond the Interest accrued on such bond shall be zero and the purchase price including interest shall be 84.03 only

Bond Calc Set: Annual / Term*

N= 5: Press exe RDV=100: press exe CPN= 4: Press exe PRC=-95: press exe YLD=Solve key

YLD=5.159986152

Bond Calc Set: Annual / Term*

N= 5: Press exe RDV=100: press exe CPN= 4: Press exe PRC=Solve Key YLD=8: Press exe

PRC= -84.02915985 INT= 0

CST= =-84.02915985

Defining the setup keys

The initial setup for various key is as per following table and to change the settings value the procedure defined in the next pages shall be followed:

1. Payment Mode: Used in CMPD and AMRT Modes, the calculation of interest is

dependant on the payment mode i.e. in advance (begin) or after the completion of month (end), for choosing the correct option following is the procedure:

Press Setup key and using scroll key select the following menu

Exe Choose 1 2. Date Mode: Used in SMPL, DAYS and BOND Modes, the days in the year can be 365 or

360 days depending upon the usage and practice, the same can changed as followed

Exe Choose 1 3. DN: Used in CMPD mode, these settings specifies whether Simple Interest (SI) or

Compound Interest (CI) is to be used for partial months to change the settings Exe Choose 2

4. Periods: Used in BOND mode , Year: Annual or Semi annual coupons payment per

year, the bond can have the payment of interest either annually or semi annually. The settings can be configured as follows:

Exe Choose 2

Payment: End Payment

1. Begin 2. End

Payment: Begin

Date Mode: 365 Date Mode: 360 Date Mode

1 360

2 365

DN: CI DN: SI DN

1: CI 2: SI

Periods/Y: Annu Date Mode: 365 Periods/year

1 Annual

2 Semi

5. Bond date: used in BOND mode only, Date in case of Bonds purchased the same can

be either having a fixed term or two dates can specified, i.e. Date of purchase and the

date of maturity. The initial settings can be modified as follows: Exe Choose2

6. Date Input: MDY: used in case of DAYS and BOND mode only, the dates can be input

either of the following way, Month/Day/Year (MDY) or Date/Month/Year (DMY), the initial settings of MDY can be modified as follows:

Exe Choose2 7. PRF/Ratio: PRF, used in the case BEVN mode only, Profit or profit percentage can be

specified, the initial settings can be modified as follows: Exe Chose2 8. B-Even : Quantity, used in the case BEVN mode only and the break even can be

calculated either in term of quantity or Sales amount, the initial settings of quantity can be modified as follows:

Exe Chose2

9. Digit Separator : used in all modes and is an option used for making the digit appearing as

123456 Superscript mode 123’456 123456 Subscript mode 123,456 123456 Separator Off 123456

10 Angle, Fix, Sci and Norm modes are used in all modes and the calculations and are easy to understand and modify the initial settings.

Bond date: Date Bond Date

3 Date 4 Term

Bond Date: Term

PRF/Ratio: PRF

Date Mode: 365 Date Input

1 MDY

2 DMY Date Input: MDY

PRF / Ratio 1 PRF

2 R%

PRF/Ratio: r%

B-Even: Sales B- Even 1 Quantity 2 Sales

B-Even: Quantity

11. Stat: on ,used is STAT mode only and is an application which is used when the

statistical calculations are to be performed then the stat mode can be turned on or off by following the following procedure

Exe Choose2 STAT: Off

STAT 1. On 2. Off

STAT: On

Fin Calculator Guide

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