7. Financial

You can use the Financial Sticky Note to perform a variety of financial calculations.

Important!
Financial calculation rules and practices can differ according to country, geographic area, or financial institution.
It is up to you to determine whether the calculation results produced by the Financial Sticky Note are compatible with the financial calculation rules that apply to you.

7-1. Financial Calculation Basic Operations

7-1-1. Financial Sticky Note

7-1-2. Financial Calculation Example

The examples below explain basic operations using the Financial calculation.
Example: What is the final value after two years (730 days) of a $3,000 investment earning 5.0% simple interest? Also calculate the final value during the same period for the same investment when the simple interest rate is 3%.

1. Click anywhere on the Paper to display the Sticky Note menu.

2. Click to display a Financial Sticky Note.

3. Click [Simple Interest].

・This displays the Simple Interest Sticky Note.

4. Input the following information: Days = 730; I% (annual interest rate) = 5; PV (present value) = −3000.

5. Click [SI] and then [SFV].

・This displays the calculation results for simple interest (SI) and simple future value (SFV = principal + interest).

6. Change the I% value to 3, click [SI], and then [SFV].

・The SI and SFV values are updated in accordance with the new I% value.

7-2. Configuring Financial Settings

1. Click the Settings button () in the Paper header.

2. Click [Financial Settings].

・This displays the Financial Settings dialog box.

3. You can use this screen to configure settings below.

  • Days in Year
    • 360 days: Specifies calculation according to a 360 days.
    • 365 days: Specifies calculation according to a 365 days.
  • Payment Date
    • Beginning of period: Specifies the beginning of period as the payment data.
    • End of period: Specifies the end of period as the payment data.
  • Odd Period
    • Compound (CI): Specifies compound interest to the odd period when performing a Compound Interest calculation.
    • Simple (SI): Specifies simple interest to the odd period when performing a Compound Interest calculation.
    • Off: Specifies no interest to the odd period when performing a Compound Interest calculation.
  • Compounding Frequency
    • Annual: Specifies once a year compounding.
    • Semi-annual: Specifies twice a year compounding.
  • Bond Interval
    • Term: Uses a number of payments as term for bond calculation.
    • Date: Uses a date as term for bond calculation.
  • Profit Amount/Ratio
    • Amount (PRF): Uses amount (PRF) for break-even point calculations.
    • Ratio (r%): Uses profit ratio (r%) for break-even point calculations.
  • Break-Even Value
    • Quantity: Uses quantity for break-even point calculations.
    • Sales: Uses sales amount for break-even point calculations.

4. After settings are the way you want, click [OK].

Note

・Initial default settings are shown below.

  • Days in Year: 365 days
  • Payment Date: End of period
  • Odd Period: Off
  • Compounding Frequency: Annual
  • Bond Interval: Term
  • Profit Amount/Ratio: Amount (PRF)
  • Break-Even Value: Quantity

The table below shows setting items for each type of Financial calculation.

Financial Calculation Setting Items
Simple Interest Days in Year
Compound Interest Payment Date, Odd Period
Amortization Payment Date
Day Count Days in Year
Bond Calculation Days in Year, Compounding Frequency, Bond Interval
Break-Even Point Profit Amount/Ratio, Break-Even Value

Note

  • Clicking the button in the upper right corner of the Sticky Note displays certain Financial setting items. The setting items that appear depend on the type of financial calculation being performed. These settings are applied to the displayed Sticky Note.

7-3. Simple Interest

Simple Interest lets you calculate interest (without compounding) based on the number of days money is invested.

7-3-1. Simple Interest Fields

The following fields appear on the Simple Interest calculation.

Field Description
Days Number of days in investment period
I% Annual interest rate (as a percent)
PV Present value (initial investment)
SI Calculates and displays simple interest
SFV Calculates and displays simple future value (principal + interest)

7-3-2. Calculation Formulas

365-day Mode

$ SI' = \cfrac{Dys}{360}\times{PV}\times{i} \qquad (i=\cfrac{I\%}{100}) $


360-day Mode

$ SI' = \cfrac{Dys}{360}\times{PV}\times{i} \qquad (i=\cfrac{I\%}{100}) $
$ SI = -SI' $
$ SFV = -(PV + SI') $

7-4. Compound Interest

Compound Interest lets you calculate interest based on compounding parameters you specify.

7-4-1. Compound Interest Fields

The following fields appear on the Compound Interest calculation.

Field Description
N Number of installment periods
I% Annual interest rate (as a percent)
PV Present value (initial investment)
PMT Amount paid each period
FV Future value
P/Y Number of installment periods per year
C/Y Number of times interest is compounded per year

7-4-2. Calculation Formulas

・When calculating PV, PMT, FV, n

$ I \% \ne 0 $

$ PV = \cfrac{-\alpha\times{PMT}-\beta\times{FV}}{\gamma} $
$ PMT = \cfrac{-\gamma\times{PV}-\beta\times{FV}}{\alpha} $
$ FV = \cfrac{-\gamma\times{PV}-\alpha\times{PMT}}{\beta} $
$ n = \cfrac{log\left\{\cfrac{(1+iS)\times{PMT}-FV\times{i}}{(1+iS)\times{PMT}+PV\times{i}}\right\}}{\log{(1+i)}} $


$ I \% = 0 $

$ PV = -(PMT\times{n}+FV) $
$ PMT = -\cfrac{PV + FV}{n} $
$ FV = -(PMT\times{n}+PV) $
$ n = -\cfrac{PV+FV}{PMT} $


$ \alpha=(1+i\times{S})\times\cfrac{1-\beta}{i} $

When “Odd Period” is “Off” When “Odd Period” is “CI” When “Odd Period” is “SI”
\( \beta= \) \( \left(1+i\right)^{-n} \) \( \left(1+i\right)^{-Ing\left(n\right)} \)
\( \gamma= \) 1 \( \left(1+i\right)^{Frac\left(n\right)} \) \( 1+i \times{Frac\left(n\right)} \)

When “Payment Date” is “End” When “Payment Date” is “Begin”
\( S= \) 0 1

When \( P/Y \) = \( C/Y \) = 1 When \( P/Y \) ≠ 1 and/or \( C/Y \) ≠ 1
$ i= $ $ \cfrac{I \%}{100} $ $ {\left(1+\cfrac{I\%}{100\times\left[C/Y \right]}\right)}^{\cfrac{C/Y}{P/Y}}-1 $

・When calculating \( I \) %
i (effective interest rate) is calculated using Newton’s Method.
$ \gamma\times{PV}+\alpha\times{PMT}+\beta\times{FV}=0 $
$ I $ % is calculated from i using the formulas below:

When \( P/Y \) = \( C/Y \) = 1 When \( P/Y \) ≠ 1 and/or \( C/Y \) ≠ 1
$ I \% = $ $ i\times{10} $ $ \left( {\left( 1+i \right) }^{\cfrac{P/Y}{C/Y}}-1 \right) \times C/Y \times{100} $

Interest (\( I \)%) calculations are performed using Newton’s Method, which produces approximate values whose precision can be affected by various calculation conditions. Interest calculation results produced by this application should be used keeping the above in mind, or results should be confirmed separately.

7-5. Cash Flow

Cash Flow lets you calculate the value of money paid out or received in varying amounts over time.

7-5-1. Cash Flow Fields

The following fields appear on the Cash Flow calculation.

Field Description
Cash List of income or expenses (up to 80 entries)
I% Annual interest rate (as a percent)
NPV Net present value
IRR Interest rate of return
PBP Payback period
NFV Net future value

7-5-2. To specify the list to be used by Cash Flow

1. On the Cash Flow Sticky Note, click the "Cash" field.

2. On the menu that appears, click "Add List".

  • This displays a Data Sticky Note.

3. Input data to be used by Cash Flow into the Data Sticky Note.

4. Input the list name at the top of data you input.

5. On the Cash Flow Sticky Note, click the "Cash" field.

6. On the menu that appears, select the list to be used by Cash Flow.

Note

  • When a variable is defined as a list type variable, it will appear in the "Cash" field pulldown menu. You can use a list type variable to perform Cash Flow calculations.

7-5-3. Calculation Formulas

$ NPV=CF_{0}+\cfrac{CF_{1}}{\left(1+i\right)}+\cfrac{CF_{2}}{{\left(1+i\right)}^{2}}+\cfrac{CF_{3}}{{\left(1+i\right)}^{3}}+ \cdots +\cfrac{CF_{n}}{{\left(1+i\right)}^{n}} \qquad \left(i=\cfrac{I\%}{100}\right) $

$ n $: natural number up to 80

$ NFV=NPV\times{\left(1+i\right)}^{n} $

IRR is calculated using Newton’s Method.

$ 0=CF_{0}+\cfrac{CF_{1}}{\left(1+i\right)}+\cfrac{CF_{2}}{{\left(1+i\right)}^{2}}+\cfrac{CF_{3}}{{\left(1+i\right)}^{3}}+ \cdots +\cfrac{CF_{n}}{{\left(1+i\right)}^{n}} $

In this formula, NPV = 0, and the value of IRR is equivalent to i×100. It should be noted, however, that minute fractional values tend to accumulate during the subsequent calculations performed automatically, so NPV never actually reaches exactly zero. IRR becomes more accurate the closer that NPV approaches to zero.

$ PBP=\begin{cases}0 .................. \left(CF_{0}\geq0\right)\\n-\cfrac{NPV_{n}}{NPV_{n+1}-NPV_{n}}...\left(Other\space than\space those\space above\right)\end{cases} $

$ NPV_{n}=\sum_{k=0}^n\cfrac{CF_{k}}{{\left(1+i\right)}^k} $

$ n $: smallest positive integer that satisfies the conditions
$ NPV_{n}\leq 0 $, $0 \leq NPV_{n+1} $, or 0

7-6. Amortization

Amortization lets you calculate the interest and principal portions of a payment or payments.

7-6-1. Amortization Fields

The following fields appear on the Amortization calculation.

Field Description
PM1 Number of first installment period in interval under consideration
PM2 Number of last installment period in interval under consideration
I% Annual interest rate (as a percent)
PV Present value (initial investment)
PMT Amount paid each period
P/Y Number of installment periods per year
C/Y Number of times interest is compounded per year
BAL Balance of principal after PM2
INT Interest portion of PM1
PRN Principal portion of PM1
ΣINT Total interest paid from PM1 to PM2 (inclusive)
ΣPRM Total principal paid from PM1 to PM2 (inclusive)

7-6-2. Calculation Formulas

a: Interest portion of payment PM1 (INT)
\( INT_{PM1}=\mid{BAL_{PM1-1}}\mid\times\left(PMT_{sign}\right) \)
b: Principal portion of payment PM1 (PRN)
\( PRN_{PM1}=PMT+BAL_{PM1-1}\times{i} \)
c: Principal balance upon completion of payment PM2 (BAL)
\( BAL_{PM2}=BAL_{PM2-1}+PRN_{PM2} \)
d: Total principal paid from payment PM1 to payment PM2 (ΣPRN)
\( \sum_{PM1}^{PM2}PRN=PRN_{PM1}+PRN_{PM1+1}+ \) ... \( +PRN_{PM2} \)
e: Total interest paid from payment PM1 to payment PM2 (ΣINT)
・a + b = one repayment (PMT)
\( \sum_{PM1}^{PM2}INT=INT_{PM1}+INT_{PM1+1}+...+INT_{PM2} \)
\( BAL_{0}=PV................ \) Payment: End (Format tab)
\( INT_{1}=0,PRN_{1}=PMT... \) Payment: Begin (Format tab)

Converting between the Nominal Interest Rate and Effective Interest Rate
The nominal interest rate (\( I \)% value input by user) is converted to an effective interest rate (\( I \)%') for installment loans where the number of annual payments is different from the number of annual compoundings calculation periods.

$ I\%'=\left\{{\left(1+\cfrac{I\%}{100\times\left[C/Y\right]}\right)}^{\cfrac{\left[C/Y\right]}{\left[P/Y\right]}}-1\right\}\times100 $

The following calculation is performed after conversion from the nominal interest rate to the effective interest rate, and the result is used for all subsequent calculations.

$ i=I \%' \div 100 $

7-7. Interest Conversion

Interest Conversion lets you calculate the effective or nominal interest rate for interest that is compounded multiple times during a year.

7-7-1. Interest Conversion Fields

The following fields appear on the Interest Conversion calculation.

Field Description
N Number of times interest is compounded per year
EFF Effective interest rate (as a percent)
APR Nominal interest rate (as a percent)

7-7-2. Calculation Formulas

$ EFF=\left[{\left(1+\cfrac{APR/100}{n}\right)}^{n}-1\right]\times100 $
$ APR=\left[{\left(1+\cfrac{EFF}{100}\right)}^{\cfrac{1}{n}}-1\right]\times{n}\times100 $

7-8. Cost/Sell/Margin

Cost/Sell/Margin lets you calculate the cost, selling price, or margin of profit on an item, given the other two values.

7-8-1. Cost/Sell/Margin Fields

The following fields appear on the Cost/Sell/Margin calculation.

Field Description
Cost Production cost
Sell Selling price
Margin Margin of profit (portion of selling price not absorbed by cost of production)

7-8-2. Calculation Formulas

$ CST=SEL\left(1-\cfrac{MRG}{100}\right) $
$ SEL=\cfrac{CST}{1-\cfrac{MRG}{100}} $
$ MRG\left(\%\right)=\left(1-\cfrac{CST}{SEL}\right)\times100 $

7-9. Day Count

Day Count lets you calculate the number of days between two dates, or the date that is a specified number of days from another date.

7-9-1. Day Count Fields

The following fields appear on the Day Count calculation.

Field Description
d1 Date 1
d2 Date 2
Days Number of days from d1 to d2

7-10. Depreciation

Depreciation lets you calculate the amount that a business expense can be offset by income (depreciated) over a given year.

Note

  • You can also click [SL] to calculate depreciation using straight-line method, [FP] using fixed-percentage method, or [DB] using declining-balance method. Each depreciation method will produce a different residual value after depreciation (RDV) for the applicable year (j).

7-10-1. Depreciation Fields

The following fields appear on the Depreciation calculation.

Field Description
N Number of times interest is compounded per year
I% Annual interest rate (as a percent)
PV Present value (initial investment)
FV Future value
\( j \) Year for which depreciation is being calculated
YR1 Number of depreciable months in first year
SL Calculate depreciation for year j using the straight-line method
FP Calculate depreciation for year j using the fixed-percentage method
SYD Calculate depreciation for year j using the sum-of-the-years’-digits method
DB Calculate depreciation for year j calculated using the declining-balance method
RDV Residual value after depreciation for year \( j \)

7-10-2. Calculation Formulas

・Straight-Line Method

$ SL_{1}=\cfrac{\left(PV-FV\right)}{n}\times\cfrac{YR1}{12} $
$ SL_{j}=\cfrac{\left(PV-FV\right)}{n} $
$ SL_{n+1}=\cfrac{\left(PV-FV\right)}{n}\times\cfrac{12-YR1}{12} $
$ (YR1 \ne 12) $

・Fixed-Percentage Method

$ FP_{1}= PV\times\cfrac{I\%}{100}\times\cfrac{YR1}{12} $
$ FP_{j}=\left(RDV_{j-1}+FV\right)\times\cfrac{I\%}{100} $
$ FP_{n+1}=RDV_{n} \qquad \left(YR1\neq12\right) $
$ RDV_{1}=PV-FV-FP_{1} $
$ RDV_{j}=RDV_{j-1}-FP_{j} $
$ RDV_{n+1}=0 \qquad \left(YR1\neq12\right) $

・Sum-of-the-Years’-Digits Method

$ Z=\cfrac{n\left(n+1\right)}{2} $
$ n'=n-\cfrac{YR1}{12} $
$ Z'=\cfrac{\left(Intg\left(n'\right)+1\right)+\left(Intg\left(n'\right)+2\times{Frac\left(n'\right)}\right)}{2} $
$ SYD_{1}=\cfrac{n}{Z}\times\cfrac{YR1}{12}\left(PV-FV\right) $
$ SYD_{j}=\left(\cfrac{n'-j+2}{Z'}\right)\left(PV-FV-SYD_{1}\right) \qquad \left(j\neq1\right) $
$ SYD_{n+1}=\left(\cfrac{n'-\left(n+1\right)+2}{Z'}\right)\left(PV-FV-SYD_{1}\times\cfrac{12-YR1}{12}\right) \qquad \left(YR1\neq12\right) $
$ RDV_{1} = PV-FV-SYD_{1} $ $ RDV_{j} = RDV_{j-1}-SYD_{j} $

・Declining-Balance Method

$ DB_{1}=PV\times\cfrac{I\%}{100n}\times\cfrac{YR1}{12} $
$ RDV_{1}=PV-FV-DB_{1} $
$ DB_{j}=\left(RDV_{j-1}+FV\right)\times\cfrac{I\%}{100n} $
$ RDV_{j}=RDV_{j-1}-DB_{j} $
$ DB_{n+1}=RDV_{n} \qquad \left(YR1\neq12\right) $
$ RDV_{n+1} \qquad \left(YR1\neq12\right) $

7-11. Bond Calculation

Bond Calculation lets you calculate the purchase price or the annual yield of a bond.

7-11-1. Bond Calculation Fields

The following fields appear on the Bond Calculation.

Field Description
d1 Purchase date
d2 Redemption date
N Number of periods
RDV Redemption value
CPN Annual coupon rate
PRC Price of bond
YLD Yield to maturity (as a percent)
INT Interest accumulated during partial year portion of investment period
Cost Cost of bond (price plus partial year interest)

7-11-2. Calculation Formulas

・Terms in the formulas

  • PRC: price per $100 of face value
  • RDV: redemption price per $100 of face value
  • CPN: coupon rate (%)
  • YLD: annual yield (%)
  • M: number of coupon payments per year
    (1 = Annual, 2 = Semi-annual)
  • N: number of coupon payments until maturity (n is used when “Term” is specified for “Bond Interval”.)
  • INT: accrued interest
  • CST: price including interest
  • A: accrued days
  • D: number of days in coupon period where settlement occurs
  • B: number of days from purchase date until next coupon payment date = D – A

・PRC when “Date” is specified for “Bond Interval”

For one or fewer coupon period to redemption:
$ PRC=\cfrac{RDV+CPN/M}{1+\left(B/D\times\left(YLD/100\right)/M\right)}+A/D\times{CPN/M} $
For more than one coupon period to redemption:
$ PRC=-\cfrac{RDV}{{\left(1+\left(YLD/100\right)/M\right)}^{ \left( N-1+B/D \right) }} \quad - \sum_{k=1}^N\cfrac{CPN/M}{{\left(1+\left(YLD/100\right)/M\right)}^{\left( N-1+B/D \right) }} \quad + A/D\times{CPN/M} $
$ INT=-A/D\times{CPN/M} \qquad CST=PRC\times{INT} $

・PRC when “Term” is specified for “Bond Interval”

$ PRC=-\cfrac{RDV}{{\left(1+\left(YLD/100\right)/M\right)}^{n}} \quad -\sum_{k=1}^N\cfrac{CPN/M}{{\left(1+\left(YLD/100\right)/M\right)}^{k}} \qquad INT=0 \qquad CST=PRC $

・YLD

The Financial performs annual yield (YLD) calculations using Newton’s Method, which produces approximate values whose precision can be affected by various calculation conditions. Because of this, annual yield calculation results should be used keeping the above in mind, or results should be confirmed separately.

7-12. Break-Even Point

Break-Even Point lets you calculate the amount you must sell to break even or to obtain a specified profit, as well as the profit or loss on particular sales.

7-12-1. Break-Even Point Fields

The following fields appear on the Break-Even Point calculation.

Field Description
PRC Selling price per unit
VCU Variable cost per unit
FC Fixed costs
PRF Amount of profit realized
QBE Number of units to be sold
SBE Amount that must be obtained from sales to break even
$r$% Proportion of sales amount retained as a profit (as a percent)

7-12-2. Calculation Formulas

・Profit (Profit Amount/Ratio Setting: Amount (PRF))

$ QBE=\cfrac{FC+PRF}{PRC-VCU} $
$ SBE=\cfrac{FC+PRF}{PRC-VCU}\times{PRC} $

・Profit Ratio (Profit Amount/Ratio Setting: Ratio (r%))

$ QBE=\cfrac{FC}{PRC\times\left(1-\cfrac{r\%}{100}\right)-VCU} $
$ SBE=\cfrac{FC}{PRC\times\left(1-\cfrac{r\%}{100}\right)-VCU}\times{PRC} $

7-13. Margin of Safety

Margin of Safety lets you calculate how much sales can be reduced before losses are incurred.

7-13-1. Margin of Safety Fields

The following fields appear on the Margin of Safety calculation.

Field Description
SAL Amount obtained from sales
SBE Break-even sales (amount that must be obtained from sales to break even)
MOS Margin of safety (portion of sales amount above break-even point)

7-13-2. Calculation Formulas

$ MOS=\cfrac{SAL+SBE}{SAL} $

7-14. Operating Leverage

Operating Leverage lets you calculate the degree of change in net earnings arising from a change in sales amount.

7-14-1. Operating Leverage Fields

The following fields appear on the Operating Leverage calculation.

Field Description
SAL Amount currently obtained from sales
VC Variable cost for this level of production
FC Fixed costs
DOL Degree of operating leverage

7-14-2. Calculation Formulas

$ DOL=\cfrac{SAL-VC}{SAL-VC-FC} $

7-15. Financial Leverage

Financial Leverage lets you calculate the degree of change in net earnings arising from a change in interest paid.

7-15-1. Financial Leverage Fields

The following fields appear on the Financial Leverage calculation.

Field Description
EBIT Earnings before interest and taxes
INT Interest to be paid to bondholders
DFL Degree of financial leverage

7-15-2. Calculation Formulas

$ DFL=\cfrac{EBIT}{EBIT-INT} $

7-16. Combined Leverage

Combined Leverage lets you calculate the combined effects of operation and financial leverages.

7-16-1. Combined Leverage Fields

The following fields appear on the Combined Leverage calculation.

Field Description
SAL Amount obtained from sales
VC Variable cost for this level of production
FC Fixed costs
INT Interest to be paid to bondholders
DCL Degree of combined leverage

7-16-2. Calculation Formulas

$ DCL=\cfrac{SAL-VC}{SAL-VC-FC-INT} $

7-17. Quantity Conversion

Quantity Conversion lets you calculate the number of items sold, selling price, or sales amount given the other two values. It also lets you calculate the number of items manufactured, unit variable cost, or total variable cost given the other two values.

7-17-1. Quantity Conversion Fields

The following fields appear on the Combined Leverage calculation.

Field Description
SAL Amount obtained from sales
PRC Selling price per unit
QTY Number of units sold
VC Variable cost for this level of production
VCU Variable cost per unit
QTY Number of units manufactured

7-17-2. Calculation Formulas

\( SAL=PRC\times{QTY} \)
\( VC=VCU\times{QTY} \)