1.
PV FUNCTION<br />Returns the present value of an investment. The present value is the total amount that a series of future payments is worth now. For example, when you borrow money, the loan amount is the present value to the lender.<br />Syntax<br />PV(rate,nper,pmt,fv,type)<br />Rate is the interest rate per period. For example, if you obtain an automobile loan at a 10 percent annual interest rate and make monthly payments, your interest rate per month is 10%/12, or 0.83%. You would enter 10%/12, or 0.83%, or 0.0083, into the formula as the rate.<br />1234ABDataDescription500Money paid out of an insurance annuity at the end of every month8%Interest rate earned on the money paid out20Years the money will be paid outFormulaDescription (Result)=PV(A3/12, 12*A4, A2, , 0)Present value of an annuity with the terms above (-59,777.15).<br />The result is negative because it represents money that you would pay, an outgoing cash flow. If you are asked to pay (60,000) for the annuity, you would determine this would not be a good investment because the present value of the annuity (59,777.15) is less than what you are asked to pay.<br /> The RATE Function<br />The question to which RATE brings an answer to is:- What is the real interest rate if they ask me for a certain amount each period to pay a loan?<br /> ADescriptions148Number of periods (years, months, weeks..etc)2$550Periodic payment3$24,000Total amount of loan40The balance left to pay at the end of the period. If you omit this argument Excel uses "
0"
.50Payment made at the beginning of the period (1) or at the end of the period (0). If you omit this argument Excel uses "
0"
saying that the payment is made at the end of each period which is usually the reality when you borrow money.65.00%The result with the formula using the RATEfunction.Note: the format of this cell must be "
Percentage"
with any number of decimals. In this example the number of decimals is 2<br />Here is the formula in cell A6:=RATE(A1,-A2,A3,A4,A5)*12<br />Notes on the formula: The payment argument is negative (-A2); If you use months as periods and you want an annual rate you multiply by 12, if you use a years as periods and you want an annual rate you don't multiply......; If you don't use the "
Percentage"
format in cell A6 the result of this example will be 0.05; The formula could also be=RATE(A1,-A2,A3)*12 the arguments in A4 and A5 being optional<br />The PMT Function<br />The question to which PMT brings an answer to is:- If I borrow a certain amount of money and I want it repaid at the end of a certain period of time what will be the periodic payment?<br /> ADescriptions15.00%The annual interest rate.Note: the format of this cell must be "
Percentage"
with any number of decimals. In this example the number of decimals is 2248Number of periodic payments (years, months, weeks)3$24,000Total amount of loan40The balance left to pay at the end of the period. If you omit this argument Excel uses "
0"
.50Payment made at the beginning of the period (1) or at the end of the period (0). If you omit this argument Excel uses "
0"
saying that the payment is made at the end of each period which is usually the reality when you borrow money.6-$550.41The result with the formula using thePMT function.<br />Here is the formula in cell A6:=PMT(A1/12,A2,A3,A4,A5)<br />Notes on the formula: If you don't use the "
Percentage"
format in cell A1 enter 0.05; If you use months as periods the rate must be divided by 12 (A1/12), if you use weeks then you divide by 52 (A1/52), if there are 4 payments per year you will divide the rate by 4 (A1/4)and if the payment is annual you don't divide the rate argument (A1) ; The formula could also be =PMT(A1/12,A2,A3) the arguments in A4 and A5 being optional; If you want the payment to show as a positive value add a minus sign before the equal sign (=-PMT(A1/12,A2,A3,A4,A5))<br />The FV Function (Future value)<br />The question to which FV brings an answer to is:- If I put a certain amount of money in the bank each month how much money will I have saved at the end of a certain period of time?<br /> ADescriptions15.00%The annual interest rate.Note: the format of this cell must be "
Percentage"
with any number of decimals. In this example the number of decimals is 2248Number of periodic deposits (years, months, weeks)3$550Amount of periodic deposits4$0Beginning balance. If you omit this argument Excel uses "
0"
.51Deposits made at the beginning of the period (1) or at the end (0). If you omit this argument Excel uses "
0"
. In the case of the FV function make sure that you enter "
1"
.6-$29,279.68The result with the formula using theFV function.<br />Here is the formula in cell A6:=FV(A1/12,A2,A3,A4,A5)<br />Notes on the formula: If you don't use the "
Percentage"
format in cell A1 enter 0.05; If you use months as periods the rate must be divided by 12 (A1/12), if you use weeks then you divide by 52 (A1/52), if there are 4 payments per year you will divide the rate by 4 (A1/4)and if the payment is annual you don't divide the rate argument (A1) ; The formula could also be =FV(A1/12,A2,A3) the arguments in A4 and A5 being optional; If you want the RESULT to show as a positive value add a minus sign before the equal sign (=-FV(A1/12,A2,A3,A4,A5))<br />The NPER Function<br />The question to which NPER brings an answer to is:- How many months would it take me to repay a certain loan at a certain interest rate if I pay a certain amount each month?<br /> ADescriptions15.0%The annual interest rate.Note: the format of this cell must be "
Percentage"
with any number of decimals. In this example the number of decimals is 22$550Periodic payment3$24,000Total amount of loan40The balance left to pay at the end of the period. If you omit this argument Excel uses "
0"
.50Payment made at the beginning of the period (1) or at the end (0). If you omit this argument Excel uses "
0"
.648.26The result with the formula using the NPERfunction.<br />Here is the formula in cell A6:=NPER(D1/12,-D2,D3,D4,D5)<br />Notes on the formula: If you don't use the "
Percentage"
format in cell A1 enter 0.05; The second argument MUST BE NEGATIVE; If you use months as periods the rate must be divided by 12 (A1/12), if you use weeks then you divide by 52 (A1/52), if there are 4 payments per year you will divide the rate by 4 (A1/4)and if the payment is annual you don't divide the rate argument (A1) ; The formula could also be =NPER(A1/12,A2,A3) the arguments in A4 and A5 being optional;<br /> <br />PPMT FUNCTION<br />Returns the payment on the principal for a given period for an investment based on periodic, constant payments and a constant interest rate<br />Syntax<br />PPMT(rate,per,nper,pv,fv,type)<br />1234ABDataDescription (Result)8%Annual interest rate10Number of years in the loan200,000Amount of loanFormulaDescription (Result)=PPMT(A2, A3, 10, A4)Principal payment for the last year of the loan with the above terms (-27,598.05)<br />IPMT<br />Returns the interest payment for a given period for an investment based on periodic, constant payments and a constant interest rate<br />Remarks<br />Make sure that you are consistent about the units you use for specifying rate and nper. If you make monthly payments on a four-year loan at 12 percent annual interest, use 12%/12 for rate and 4*12 for nper. If you make annual payments on the same loan, use 12% for rate and 4 for nper.<br />For all the arguments, cash you pay out, such as deposits to savings, is represented by negative numbers; cash you receive, such as dividend checks, is represented by positive numbers.<br />12345ABDataDescription10%Annual interest1Period for which you want to find the interest3Years of loan8000Present value of loanFormulaDescription (Result)=IPMT(A2/12, A3*3, A4, A5)Interest due in the first month for a loan with the terms above (-22.41)=IPMT(A2, 3, A4, A5)Interest due in the last year for a loan with the terms above, where payments are made yearly (-292.45)<br />
Note The interest rate is divided by 12 to get a monthly rate. The years the money is paid out is multiplied by 12 to get the number of payments.
NPV<br />Calculates the net present value of an investment by using a discount rate and a series of future payments (negative values) and income (positive values)<br />Syntax<br />NPV(rate,value1,value2, ...)<br />Rate is the rate of discount over the length of one period.<br />Value1, value2, ... are 1 to 29 arguments representing the payments and income.<br />Value1, value2, ... must be equally spaced in time and occur at the end of each period.<br />NPV uses the order of value1, value2, ... to interpret the order of cash flows. Be sure to enter your payment and income values in the correct sequence.<br />Arguments that are numbers, empty cells, logical values, or text representations of numbers are counted; arguments that are error values or text that cannot be translated into numbers are ignored.<br />If an argument is an array or reference, only numbers in that array or reference are counted. Empty cells, logical values, text, or error values in the array or reference are ignored.<br />Remarks<br />The NPV investment begins one period before the date of the value1 cash flow and ends with the last cash flow in the list. The NPV calculation is based on future cash flows. If your first cash flow occurs at the beginning of the first period, the first value must be added to the NPV result, not included in the values arguments. For more information, see the examples below.<br />If n is the number of cash flows in the list of values, the formula for NPV is:<br />NPV is similar to the PV function (present value). The primary difference between PV and NPV is that PV allows cash flows to begin either at the end or at the beginning of the period. Unlike the variable NPV cash flow values, PV cash flows must be constant throughout the investment. For information about annuities and financial functions, see PV.<br />NPV is also related to the IRR function (internal rate of return). IRR is the rate for which NPV equals zero: NPV(IRR(...), ...) = 0.<br />Example 1<br /> 123456ABDataDescription10%Annual discount rate-10,000Initial cost of investment one year from today3,000Return from first year4,200Return from second year6,800Return from third yearFormulaDescription (Result)=NPV(A2, A3, A4, A5, A6)Net present value of this investment (1,188.44)<br />In the preceding example, you include the initial $10,000 cost as one of the values, because the payment occurs at the end of the first period.<br />IRR<br />Returns the internal rate of return for a series of cash flows represented by the numbers in values. These cash flows do not have to be even, as they would be for an annuity. However, the cash flows must occur at regular intervals, such as monthly or annually. The internal rate of return is the interest rate received for an investment consisting of payments (negative values) and income (positive values) that occur at regular periods.<br />Syntax<br />IRR(values,guess)<br />Values is an array or a reference to cells that contain numbers for which you want to calculate the internal rate of return.<br />Values must contain at least one positive value and one negative value to calculate the internal rate of return.<br />IRR uses the order of values to interpret the order of cash flows. Be sure to enter your payment and income values in the sequence you want.<br />If an array or reference argument contains text, logical values, or empty cells, those values are ignored.<br />Guess is a number that you guess is close to the result of IRR.<br />Microsoft Excel uses an iterative technique for calculating IRR. Starting with guess, IRR cycles through the calculation until the result is accurate within 0.00001 percent. If IRR can't find a result that works after 20 tries, the #NUM! error value is returned.<br />In most cases you do not need to provide guess for the IRR calculation. If guess is omitted, it is assumed to be 0.1 (10 percent).<br />If IRR gives the #NUM! error value, or if the result is not close to what you expected, try again with a different value for guess.<br />Remarks<br />IRR is closely related to NPV, the net present value function. The rate of return calculated by IRR is the interest rate corresponding to a 0 (zero) net present value. The following formula demonstrates how NPV and IRR are related:<br />NPV (IRR(B1:B6),B1:B6) equals 3.60E-08 [Within the accuracy of the IRR calculation, the value 3.60E-08 is effectively 0 (zero).]<br />Example<br /> 1234567ABDataDescription-70,000Initial cost of a business12,000Net income for the first year15,000Net income for the second year18,000Net income for the third year21,000Net income for the fourth year26,000Net income for the fifth yearFormulaDescription (Result)=IRR(A2:A6)Investment's internal rate of return after four years (-2%)=IRR(A2:A7)Internal rate of return after five years (9%)=IRR(A2:A4,-10%)To calculate the internal rate of return after two years, you need to include a guess (-44%)<br />MIRR<br />Returns the modified internal rate of return for a series of periodic cash flows. MIRR considers both the cost of the investment and the interest received on reinvestment of cash.<br />Syntax<br />MIRR(values,finance_rate,reinvest_rate)<br />Values is an array or a reference to cells that contain numbers. These numbers represent a series of payments (negative values) and income (positive values) occurring at regular periods.<br />Values must contain at least one positive value and one negative value to calculate the modified internal rate of return. Otherwise, MIRR returns the #DIV/0! error value.<br />If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.<br />Finance_rate is the interest rate you pay on the money used in the cash flows.<br />Reinvest_rate is the interest rate you receive on the cash flows as you reinvest them.<br />Remarks<br />MIRR uses the order of values to interpret the order of cash flows. Be sure to enter your payment and income values in the sequence you want and with the correct signs (positive values for cash received, negative values for cash paid).<br />If n is the number of cash flows in values, frate is the finance_rate, and rrate is the reinvest_rate, then the formula for MIRR is:<br />Example<br /> 123456789ABDataDescription-$120,000Initial cost39,000Return first year30,000Return second year21,000Return third year37,000Return fourth year46,000Return fifth year10.00%Annual interest rate for the 120,000 loan12.00%Annual interest rate for the reinvested profitsFormulaDescription (Result)=MIRR(A2:A7, A8, A9)Investment's modified rate of return after five years (13%)=MIRR(A2:A5, A8, A9)Modified rate of return after three years (-5%)=MIRR(A2:A7, A8, 14%)Five-year modified rate of return based on a reinvest_rate of 14 percent (13%)<br />
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