Financial Functions Part Two

PPMT function

PPMT

Returns for a given period the payment on the principal for an investment that is based on periodic and constant payments and a constant interest rate.

PPMT(Rate; Period; NPer; PV [ ; FV [ ; Type ] ]) Rate is the periodic interest rate. Period is the amortizement period. P = 1 for the first and P = NPer for the last period. NPer is the total number of periods during which annuity is paid. PV is the present value in the sequence of payments. FV (optional) is the desired (future) value. Type (optional) defines the due date. F = 1 for payment at the beginning of a period and F = 0 for payment at the end of a period.

How high is the periodic monthly payment at an annual interest rate of 8.75% over a period of 3 years? The cash value is 5,000 currency units and is always paid at the beginning of a period. The future value is 8,000 currency units. =PPMT(8.75%/12;1;36;5000;8000;1) = -350.99 currency units.

calculating; total amortizement rates total amortizement rates amortization installment repayment installment CUMPRINC function mw added two entries

CUMPRINC

Returns the cumulative interest paid for an investment period with a constant interest rate.

CUMPRINC(Rate; NPer; PV; S; E; Type) Rate is the periodic interest rate. NPer is the payment period with the total number of periods. NPER can also be a non-integer value. PV is the current value in the sequence of payments. S is the first period. E is the last period. Type is the due date of the payment at the beginning or end of each period.

What are the payoff amounts if the yearly interest rate is 5.5% for 36 months? The cash value is 15,000 currency units. The payoff amount is calculated between the 10th and 18th period. The due date is at the end of the period. =CUMPRINC(5.5%/12;36;15000;10;18;0) = -3669.74 currency units. The payoff amount between the 10th and 18th period is 3669.74 currency units.

CUMPRINC_ADD function

CUMPRINC_ADD

Calculates the cumulative redemption of a loan in a period.

CUMPRINC_ADD(Rate; NPer; PV; StartPeriod; EndPeriod; Type) Rate is the interest rate for each period. NPer is the total number of payment periods. The rate and NPER must refer to the same unit, and thus both be calculated annually or monthly. PV is the current value. StartPeriod is the first payment period for the calculation. EndPeriod is the last payment period for the calculation. Type is the maturity of a payment at the end of each period (Type = 0) or at the start of the period (Type = 1).

The following mortgage loan is taken out on a house: Rate: 9.00 per cent per annum (9% / 12 = 0.0075), Duration: 30 years (payment periods = 30 * 12 = 360), NPV: 125000 currency units. How much will you repay in the second year of the mortgage (thus from periods 13 to 24)? =CUMPRINC_ADD(0.0075;360;125000;13;24;0) returns -934.1071 In the first month you will be repaying the following amount: =CUMPRINC_ADD(0.0075;360;125000;1;1;0) returns -68.27827

calculating; accumulated interests accumulated interests CUMIPMT function

CUMIPMT

Calculates the cumulative interest payments, that is, the total interest, for an investment based on a constant interest rate.

CUMIPMT(Rate; NPer; PV; S; E; Type) Rate is the periodic interest rate. NPer is the payment period with the total number of periods. NPER can also be a non-integer value. PV is the current value in the sequence of payments. S is the first period. E is the last period. Type is the due date of the payment at the beginning or end of each period.

What are the interest payments at a yearly interest rate of 5.5 %, a payment period of monthly payments for 2 years and a current cash value of 5,000 currency units? The start period is the 4th and the end period is the 6th period. The payment is due at the beginning of each period. =CUMIPMT(5.5%/12;24;5000;4;6;1) = -57.54 currency units. The interest payments for between the 4th and 6th period are 57.54 currency units.

CUMIPMT_ADD function

CUMIPMT_ADD

Calculates the accumulated interest for a period.

CUMIPMT_ADD(Rate; NPer; PV; StartPeriod; EndPeriod; Type) Rate is the interest rate for each period. NPer is the total number of payment periods. The rate and NPER must refer to the same unit, and thus both be calculated annually or monthly. PV is the current value. StartPeriod is the first payment period for the calculation. EndPeriod is the last payment period for the calculation. Type is the maturity of a payment at the end of each period (Type = 0) or at the start of the period (Type = 1).

The following mortgage loan is taken out on a house: Rate: 9.00 per cent per annum (9% / 12 = 0.0075), Duration: 30 years (NPER = 30 * 12 = 360), Pv: 125000 currency units. How much interest must you pay in the second year of the mortgage (thus from periods 13 to 24)? =CUMIPMT_ADD(0.0075;360;125000;13;24;0) returns -11135.23. How much interest must you pay in the first month? =CUMIPMT_ADD(0.0075;360;125000;1;1;0) returns -937.50.

PRICE function prices; fixed interest securities sales values;fixed interest securities mw added two entries

PRICE

Calculates the market value of a fixed interest security with a par value of 100 currency units as a function of the forecast yield.

PRICE(Settlement; Maturity; Rate; Yield; Redemption; Frequency [; Basis]) Settlement is the date of purchase of the security. Maturity is the date on which the security matures (expires). Rate is the annual nominal rate of interest (coupon interest rate) Yield is the annual yield of the security. Redemption is the redemption value per 100 currency units of par value. Frequency is the number of interest payments per year (1, 2 or 4).

A security is purchased on 1999-02-15; the maturity date is 2007-11-15. The nominal rate of interest is 5.75%. The yield is 6.5%. The redemption value is 100 currency units. Interest is paid half-yearly (frequency is 2). With calculation on basis 0, the price is as follows: =PRICE("1999-02-15"; "2007-11-15"; 0.0575; 0.065; 100; 2; 0) returns 95.04287.

PRICEDISC function prices;non-interest-bearing securities sales values;non-interest-bearing securities mw added two entries

PRICEDISC

Calculates the price per 100 currency units of par value of a non-interest- bearing security.

PRICEDISC(Settlement; Maturity; Discount; Redemption [; Basis]) Settlement is the date of purchase of the security. Maturity is the date on which the security matures (expires). Discount is the discount of a security as a percentage. Redemption is the redemption value per 100 currency units of par value.

A security is purchased on 1999-02-15; the maturity date is 1999-03-01. Discount in per cent is 5.25%. The redemption value is 100. When calculating on basis 2 the price discount is as follows: =PRICEDISC("1999-02-15"; "1999-03-01"; 0.0525; 100; 2) returns 99.79583.

PRICEMAT function prices;interest-bearing securities mw added one entry

PRICEMAT

Calculates the price per 100 currency units of par value of a security, that pays interest on the maturity date.

PRICEMAT(Settlement; Maturity; Issue; Rate; Yield [; Basis]) Settlement is the date of purchase of the security. Maturity is the date on which the security matures (expires). Issue is the date of issue of the security. Rate is the interest rate of the security on the issue date. Yield is the annual yield of the security.

Settlement date: February 15 1999, maturity date: April 13 1999, issue date: November 11 1998. Interest rate: 6.1 per cent, yield: 6.1 per cent, basis: 30/360 = 0. The price is calculated as follows: =PRICEMAT("1999-02-15";"1999-04-13";"1998-11-11"; 0.061; 0.061;0) returns 99.98449888.

calculating; durations durations;calculating PDURATION function

PDURATION

Calculates the number of periods required by an investment to attain the desired value.

PDURATION(Rate; PV; FV) Rate is a constant. The interest rate is to be calculated for the entire duration (duration period). The interest rate per period is calculated by dividing the interest rate by the calculated duration. The internal rate for an annuity is to be entered as Rate/12. PV is the present (current) value. The cash value is the deposit of cash or the current cash value of an allowance in kind. As a deposit value a positive value must be entered; the deposit must not be 0 or <0. FV is the expected value. The future value determines the desired (future) value of the deposit.

At an interest rate of 4.75%, a cash value of 25,000 currency units and a future value of 1,000,000 currency units, a duration of 79.49 payment periods is returned. The periodic payment is the resulting quotient from the future value and the duration, in this case 1,000,000/79.49=12,850.20.

calculating;linear depreciations depreciations;linear linear depreciations straight-line depreciations SLN function mw added one entry

SLN

Returns the straight-line depreciation of an asset for one period. The amount of the depreciation is constant during the depreciation period.

SLN(Cost; Salvage; Life) Cost is the initial cost of an asset. Salvage is the value of an asset at the end of the depreciation. Life is the depreciation period determining the number of periods in the depreciation of the asset.

Office equipment with an initial cost of 50,000 currency units is to be depreciated over 7 years. The value at the end of the depreciation is to be 3,500 currency units. =SLN(50000;3,500;84) = 553.57 currency units. The periodic monthly depreciation of the office equipment is 553.57 currency units.

MDURATION function Macauley duration mw added one entry

MDURATION

Calculates the modified Macauley duration of a fixed interest security in years.

MDURATION(Settlement; Maturity; Coupon; Yield; Frequency [; Basis]) Settlement is the date of purchase of the security. Maturity is the date on which the security matures (expires). Coupon is the annual nominal rate of interest (coupon interest rate) Yield is the annual yield of the security. Frequency is the number of interest payments per year (1, 2 or 4).

A security is purchased on 2001-01-01; the maturity date is 2006-01-01. The nominal rate of interest is 8%. The yield is 9.0%. Interest is paid half-yearly (frequency is 2). Using daily balance interest calculation (basis 3) how long is the modified duration? =MDURATION("2001-01-01"; "2006-01-01"; 0.08; 0.09; 2; 3) returns 4.02 years.

calculating;net present values net present values NPV function

NPV

Returns the present value of an investment based on a series of periodic cash flows and a discount rate. To get the net present value, subtract the cost of the project (the initial cash flow at time zero) from the returned value. If the payments take place at irregular intervals, use the XNPV function.

NPV(Rate; ) Rate is the discount rate for a period.

What is the net present value of periodic payments of 10, 20 and 30 currency units with a discount rate of 8.75%. At time zero the costs were paid as -40 currency units. =NPV(8.75%;10;20;30) = 49.43 currency units. The net present value is the returned value minus the initial costs of 40 currency units, therefore 9.43 currency units.

calculating;nominal interest rates nominal interest rates NOMINAL function mw made "nominal interest rates;..." a one level entry

NOMINAL

Calculates the yearly nominal interest rate, given the effective rate and the number of compounding periods per year.

NOMINAL(EffectiveRate; NPerY) EffectiveRate is the effective interest rate NPerY is the number of periodic interest payments per year.

What is the nominal interest per year for an effective interest rate of 13.5% if twelve payments are made per year. =NOMINAL(13.5%;12) = 12.73%. The nominal interest rate per year is 12.73%.

NOMINAL_ADD function

NOMINAL_ADD

Calculates the annual nominal rate of interest on the basis of the effective rate and the number of interest payments per annum.

NOMINAL_ADD(EffectiveRate; NPerY) EffectiveRate is the effective annual rate of interest. NPerY the number of interest payments per year.

What is the nominal rate of interest for a 5.3543% effective rate of interest and quarterly payment. =NOMINAL_ADD(5.3543%;4) returns 0.0525 or 5.25%.

DOLLARFR function converting;decimal fractions, into mixed decimal fractions mw added one entry

DOLLARFR

Converts a quotation that has been given as a decimal number into a mixed decimal fraction.

DOLLARFR(DecimalDollar; Fraction) DecimalDollar is a decimal number. Fraction is a whole number that is used as the denominator of the decimal fraction.

=DOLLARFR(1.125;16) converts into sixteenths. The result is 1.02 for 1 plus 2/16. =DOLLARFR(1.125;8) converts into eighths. The result is 1.1 for 1 plus 1/8.

fractions; converting converting;decimal fractions, into decimal numbers DOLLARDE function mw added one entry

DOLLARDE

Converts a quotation that has been given as a decimal fraction into a decimal number.

DOLLARDE(FractionalDollar; Fraction) FractionalDollar is a number given as a decimal fraction. Fraction is a whole number that is used as the denominator of the decimal fraction.

=DOLLARDE(1.02;16) stands for 1 and 2/16. This returns 1.125. =DOLLARDE(1.1;8) stands for 1 and 1/8. This returns 1.125.

calculating;modified internal rates of return modified internal rates of return MIRR function internal rates of return;modified mw added "internal rates of return;..."

MIRR

Calculates the modified internal rate of return of a series of investments.

MIRR(Values; Investment; ReinvestRate) Values corresponds to the array or the cell reference for cells whose content corresponds to the payments. Investment is the rate of interest of the investments (the negative values of the array) ReinvestRate:the rate of interest of the reinvestment (the positive values of the array)

Assuming a cell content of A1 = -5, A2 = 10, A3 = 15, and A4 = 8, and an investment value of 0.5 and a reinvestment value of 0.1, the result is 94.16%.

YIELD function rates of return;securities yields, see also rates of return mw added two entries

YIELD

Calculates the yield of a security.

YIELD(Settlement; Maturity; Rate; Price; Redemption; Frequency [; Basis]) Settlement is the date of purchase of the security. Maturity is the date on which the security matures (expires). Rate is the annual rate of interest. Price is the price (purchase price) of the security per 100 currency units of par value. Redemption is the redemption value per 100 currency units of par value. Frequency is the number of interest payments per year (1, 2 or 4).

A security is purchased on 1999-02-15. It matures on 2007-11-15. The rate of interest is 5.75%. The price is 95.04287 currency units per 100 units of par value, the redemption value is 100 units. Interest is paid half-yearly (frequency = 2) and the basis is 0. How high is the yield? =YIELD("1999-02-15"; "2007-11-15"; 0.0575 ;95.04287; 100; 2; 0) returns 0.065 or 6.50 per cent.

YIELDDISC function rates of return;non-interest-bearing securities mw added one entry

YIELDDISC

Calculates the annual yield of a non-interest-bearing security.

YIELDDISC(Settlement; Maturity; Price; Redemption [; Basis]) Settlement is the date of purchase of the security. Maturity is the date on which the security matures (expires). Price is the price (purchase price) of the security per 100 currency units of par value. Redemption is the redemption value per 100 currency units of par value.

A non-interest-bearing security is purchased on 1999-02-15. It matures on 1999-03-01. The price is 99.795 currency units per 100 units of par value, the redemption value is 100 units. The basis is 2. How high is the yield? =YIELDDISC("1999-02-15"; "1999-03-01"; 99.795; 100; 2) returns 0.052823 or 5.2823 per cent.

YIELDMAT function rates of return;securities with interest paid on maturity mw added one entry

YIELDMAT

Calculates the annual yield of a security, the interest of which is paid on the date of maturity.

YIELDMAT(Settlement; Maturity; Issue; Rate; Price [; Basis]) Settlement is the date of purchase of the security. Maturity is the date on which the security matures (expires). Issue is the date of issue of the security. Rate is the interest rate of the security on the issue date. Price is the price (purchase price) of the security per 100 currency units of par value.

A security is purchased on 1999-03-15. It matures on 1999-11-03. The issue date was 1998-11-08. The rate of interest is 6.25%, the price is 100.0123 units. The basis is 0. How high is the yield? =YIELDMAT("1999-03-15"; "1999-11-03"; "1998-11-08"; 0.0625; 100.0123; 0) returns 0.060954 or 6.0954 per cent.

calculating;annuities annuities PMT function

PMT

Returns the periodic payment for an annuity with constant interest rates.

PMT(Rate; NPer; PV [ ; [ FV ] [ ; Type ] ]) Rate is the periodic interest rate. NPer is the number of periods in which annuity is paid. PV is the present value (cash value) in a sequence of payments. FV (optional) is the desired value (future value) to be reached at the end of the periodic payments. Type (optional) is the due date for the periodic payments. Type=1 is payment at the beginning and Type=0 is payment at the end of each period.

What are the periodic payments at a yearly interest rate of 1.99% if the payment time is 3 years and the cash value is 25,000 currency units. There are 36 months as 36 payment periods, and the interest rate per payment period is 1.99%/12. =PMT(1.99%/12;36;25000) = -715.96 currency units. The periodic monthly payment is therefore 715.96 currency units.

TBILLEQ function treasury bills;annual return annual return on treasury bills mw changed "treasury bills;..." and added one entry

TBILLEQ

Calculates the annual return on a treasury bill. A treasury bill is purchased on the settlement date and sold at the full par value on the maturity date, that must fall within the same year. A discount is deducted from the purchase price.

TBILLEQ(Settlement; Maturity; Discount) Settlement is the date of purchase of the security. Maturity is the date on which the security matures (expires). Discount is the percentage discount on acquisition of the security.

Settlement date: March 31 1999, maturity date: June 1 1999, discount: 9.14 per cent. The return on the treasury bill corresponding to a security is worked out as follows: =TBILLEQ("1999-03-31";"1999-06-01"; 0.0914) returns 0.094151 or 9.4151 per cent.

TBILLPRICE function treasury bills;prices prices;treasury bills mw added two entries

TBILLPRICE

Calculates the price of a treasury bill per 100 currency units.

TBILLPRICE(Settlement; Maturity; Discount) Settlement is the date of purchase of the security. Maturity is the date on which the security matures (expires). Discount is the percentage discount upon acquisition of the security.

Settlement date: March 31 1999, maturity date: June 1 1999, discount: 9 per cent. The price of the treasury bill is worked out as follows: =TBILLPRICE("1999-03-31";"1999-06-01"; 0.09) returns 98.45.

TBILLYIELD function treasury bills;rates of return rates of return of treasury bills mw added two entries

TBILLYIELD

Calculates the yield of a treasury bill.

TBILLYIELD(Settlement; Maturity; Price) Settlement is the date of purchase of the security. Maturity is the date on which the security matures (expires). Price is the price (purchase price) of the treasury bill per 100 currency units of par value.

Settlement date: March 31 1999, maturity date: June 1 1999, price: 98.45 currency units. The yield of the treasury bill is worked out as follows: =TBILLYIELD("1999-03-31";"1999-06-01"; 98.45) returns 0.091417 or 9.1417 per cent.