# NOTE: All of the information contained in this file has been collected from the various HELP files found in Excel for each of these functions.

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1 NOTE: All of the information contained in this file has been collected from the various HELP files found in Excel for each of these functions. PV 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. PV(rate,nper,pmt,fv,type) 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 , into the formula as the rate. Nper is the total number of payment periods in an annuity. For example, if you get a four-year car loan and make monthly payments, your loan has 4*12 (or 48) periods. You would enter 48 into the formula for nper. Pmt is the payment made each period and cannot change over the life of the annuity. Typically, pmt includes principal and interest but no other fees or taxes. For example, the monthly payments on a \$10,000, four-year car loan at 12 percent are \$ You would enter into the formula as the pmt. If pmt is omitted, you must include the fv argument. Fv is the future value, or a cash balance you want to attain after the last payment is made. If fv is omitted, it is assumed to be 0 (the future value of a loan, for example, is 0). For example, if you want to save \$50,000 to pay for a special project in 18 years, then \$50,000 is the future value. You could then make a conservative guess at an interest rate and determine how much you must save each month. If fv is omitted, you must include the pmt argument. Type is the number 0 or 1 and indicates when payments are due. Set type equal to If payments are due 0 or omitted At the end of the period 1 At the beginning of the period ACS King s College Page 1

2 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. The following functions apply to annuities: CUMIPMT CUMPRINC FV FVSCHEDULE IPMT PPMT PV RATE XIRR XNPV PMT An annuity is a series of constant cash payments made over a continuous period. For example, a car loan or a mortgage is an annuity. For more information, see the description for each annuity function. In annuity functions, cash you pay out, such as a deposit to savings, is represented by a negative number; cash you receive, such as a dividend check, is represented by a positive number. For example, a \$1,000 deposit to the bank would be represented by the argument if you are the depositor and by the argument 1000 if you are the bank. Example Suppose you're thinking of buying an insurance annuity that pays \$500 at the end of every month for the next 20 years. The cost of the annuity is \$60,000, and the money paid out will earn 8 percent. You want to determine whether this would be a good investment. Using the PV function, you find that the present value of the annuity is: PV(0.08/12, 12*20, 500,, 0) equals -\$59, The result is negative because it represents money that you would pay, an outgoing cash flow. The present value of the annuity (\$59,777.15) is less than what you are asked to pay (\$60,000). Therefore, you determine this would not be a good investment. NPV 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). ACS King s College Page 2

3 NPV(rate,value1,value2,...) Rate is the rate of discount over the length of one period. Value1, value2,... are 1 to 29 arguments representing the payments and income. Value1, value2,... must be equally spaced in time and occur at the end of each period. 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. 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. 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. 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. 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. NPV is also related to the IRR function (internal rate of return). IRR is the rate for which NPV equals zero: NPV(IRR(...),...) = 0. Examples Suppose you're considering an investment in which you pay \$10,000 one year from today and receive an annual income of \$3,000, \$4,200, and \$6,800 in the three years that follow. Assuming an annual discount rate of 10 percent, the net present value of this investment is: NPV(10%, , 3000, 4200, 6800) equals \$1, ACS King s College Page 3

4 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. Consider an investment that starts at the beginning of the first period. Suppose you're interested in buying a shoe store. The cost of the business is \$40,000, and you expect to receive the following income for the first five years of operation: \$8,000, \$9,200, \$10,000, \$12,000, and \$14,500. The annual discount rate is 8 percent. This might represent the rate of inflation or the interest rate of a competing investment. If the cost and income figures from the shoe store are entered in B1 through B6 respectively, then net present value of the shoe store investment is given by: NPV(8%, B2:B6)+B1 equals \$1, In the preceding example, you don't include the initial \$40,000 cost as one of the values, because the payment occurs at the beginning of the first period. Suppose your shoe store's roof collapses during the sixth year and you assume a loss of \$9000 for that year. The net present value of the shoe store investment after six years is given by: NPV(8%, B2:B6, -9000)+B1 equals -\$3, XNPV Returns the net present value for a schedule of cash flows that is not necessarily periodic. To calculate the net present value for a series of cash flows that is periodic, use the NPV function. If this function is not available, run the Setup program to install the Analysis ToolPak. After you install the Analysis ToolPak, you must enable it by using the Add-Ins command on the Tools menu. XNPV(rate,values,dates) Rate is the discount rate to apply to the cash flows. Values is a series of cash flows that corresponds to a schedule of payments in dates. The first payment is optional and corresponds to a cost or payment that occurs at the beginning of the investment. If the first value is a cost or payment, it must be a negative value. All succeeding payments are discounted based on a 365-day year. The series of values must contain at least one positive value and one negative value. ACS King s College Page 4

5 Dates is a schedule of payment dates that corresponds to the cash flow payments. The first payment date indicates the beginning of the schedule of payments. All other dates must be later than this date, but they may occur in any order. Microsoft Excel stores dates as sequential serial numbers so that it can perform calculations on them. Excel stores January 1, 1900, as serial number 1 if your workbook uses the 1900 date system. If your workbook uses the 1904 date system, Excel stores January 1, 1904, as serial number 0 (January 2, 1904, is serial number 1). For example, in the 1900 date system, Excel stores January 1, 1998, as serial number because it is 35,795 days after January 1, Learn more about how Microsoft Excel stores dates and times. Numbers in dates are truncated to integers. If any argument is nonnumeric, XNPV returns the #VALUE! error value. If any number in dates is not a valid date, XNPV returns the #NUM! error value. If any number in dates precedes the starting date, XNPV returns the #NUM! error value. If values and dates contain a different number of values, XNPV returns the #NUM! error value. Example Consider an investment that requires a \$10,000 cash payment on January 1, 1998, and returns: \$2,750 on March 1, 1998; \$4,250 on October 30, 1998; \$3,250 on February 15, 1999; and \$2,750 on April 1, Assume that the cash flows are discounted at 9 percent. The net present value is: XNPV(0.09,{-10000,2750,4250,3250,2750}, {35796,35855,36098,36206,36251}) equals , or \$2, IRR 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 ACS King s College Page 5

6 the interest rate received for an investment consisting of payments (negative values) and income (positive values) that occur at regular periods. IRR(values,guess) Values is an array or a reference to cells that contain numbers for which you want to calculate the internal rate of return. Values must contain at least one positive value and one negative value to calculate the internal rate of return. 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. If an array or reference argument contains text, logical values, or empty cells, those values are ignored. Guess is a number that you guess is close to the result of IRR. Microsoft Excel uses an iterative technique for calculating IRR. Starting with guess, IRR cycles through the calculation until the result is accurate within percent. If IRR can't find a result that works after 20 tries, the #NUM! error value is returned. 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). 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. 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: 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).] Examples Suppose you want to start a restaurant business. You estimate it will cost \$70,000 to start the business and expect to net the following income in the first five years: \$12,000, \$15,000, \$18,000, \$21,000, and \$26,000. B1:B6 contain the following values: \$-70,000, \$12,000, \$15,000, \$18,000, \$21,000 and \$26,000, respectively. ACS King s College Page 6

7 To calculate the investment's internal rate of return after four years: IRR(B1:B5) equals percent To calculate the internal rate of return after five years: IRR(B1:B6) equals 8.66 percent To calculate the internal rate of return after two years, you need to include a guess: IRR(B1:B3,-10%) equals percent MIRR 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. MIRR(values,finance_rate,reinvest_rate) 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. 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. 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. Finance_rate is the interest rate you pay on the money used in the cash flows. Reinvest_rate is the interest rate you receive on the cash flows as you reinvest them. 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). Examples Suppose you're a commercial fisherman just completing your fifth year of operation. Five years ago, you borrowed \$120,000 at 10 percent annual interest to purchase a boat. Your catches have yielded \$39,000, \$30,000, \$21,000, \$37,000, and \$46,000. During these years you reinvested ACS King s College Page 7

8 your profits, earning 12 percent annually. On a worksheet, your loan amount is entered as - \$120,000 in B1, and your five annual profits are entered in B2:B6. To calculate the investment's modified rate of return after five years: MIRR(B1:B6, 10%, 12%) equals percent To calculate the modified rate of return after three years: MIRR(B1:B4, 10%, 12%) equals percent To calculate the five-year modified rate of return based on a reinvest_rate of 14 percent MIRR(B1:B6, 10%, 14%) equals percent XIRR Returns the internal rate of return for a schedule of cash flows that is not necessarily periodic. To calculate the internal rate of return for a series of periodic cash flows, use the IRR function. If this function is not available, run the Setup program to install the Analysis ToolPak. After you install the Analysis ToolPak, you must enable it by using the Add-Ins command on the Tools menu. XIRR(values,dates,guess) Values is a series of cash flows that corresponds to a schedule of payments in dates. The first payment is optional and corresponds to a cost or payment that occurs at the beginning of the investment. If the first value is a cost or payment, it must be a negative value. All succeeding payments are discounted based on a 365-day year. The series of values must contain at least one positive and one negative value. Dates is a schedule of payment dates that corresponds to the cash flow payments. The first payment date indicates the beginning of the schedule of payments. All other dates must be later than this date, but they may occur in any order. Guess is a number that you guess is close to the result of XIRR. Microsoft Excel stores dates as sequential serial numbers so that it can perform calculations on them. Excel stores January 1, 1900, as serial number 1 if your workbook uses the 1900 date system. If your workbook uses the 1904 date system, Excel stores ACS King s College Page 8

9 January 1, 1904, as serial number 0 (January 2, 1904, is serial number 1). For example, in the 1900 date system, Excel stores January 1, 1998, as serial number because it is 35,795 days after January 1, Learn more about how Microsoft Excel stores dates and times. Numbers in dates are truncated to integers. XIRR expects at least one positive cash flow and one negative cash flow; otherwise, XIRR returns the #NUM! error value. If any number in dates is not a valid date, XIRR returns the #NUM! error value. If any number in dates precedes the starting date, XIRR returns the #NUM! error value. If values and dates contain a different number of values, XIRR returns the #NUM! error value. In most cases you do not need to provide guess for the XIRR calculation. If omitted, guess is assumed to be 0.1 (10 percent). XIRR is closely related to XNPV, the net present value function. The rate of return calculated by XIRR is the interest rate corresponding to XNPV = 0. Example Excel uses an iterative technique for calculating XIRR. Using a changing rate (starting with guess), XIRR cycles through the calculation until the result is accurate within percent. If XIRR can't find a result that works after 100 tries, the #NUM! error value is returned. Consider an investment that requires a \$10,000 cash payment on January 1, 1998, and returns \$2,750 on March 1, 1998, \$4,250 on October 30, 1998, \$3,250 on February 15, 1999, and \$2,750 on April 1, The internal rate of return (in the 1900 date system) is: XIRR({-10000,2750,4250,3250,2750}, {"1/1/1998","3/1/1998","10/30/1998","2/15/1999","4/1/1999"},0.1) equals or percent ACS King s College Page 9

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