COMPUTER APPLICATIONS IN BANKING & FINANCE. Salih KATIRCIOGLU

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1 COMPUTER APPLICATIONS IN BANKING & FINANCE Salih KATIRCIOGLU Eastern Mediterranean University Faculty of Business and Economics Department of Banking and Finance Famagusta, Turkish Republic of Northern Cyprus (TRNC) 1

2 PROBLEM 1. Create The Interest Rate Factor Table For Future Value Of $1 In N Periods (F/P, i, N) In Excel Program By Using Following Formula: Future Value (FV) = P(1+i) n Future Value Interest Rate Factor (FVIF) = (1+i) n PROBLEM 2. Create The Interest Factor Table For Present Value Of $1 In N Periods (F/P, i, N) In Excel Program By Using Following Formula: Present Value (PV) = FV / (1+i) n Present Value Interest Rate Factor (PVIF) = 1 FVIF ( 1+ i) n PROBLEM 3. Create The Interest Factor Table For Present Value Of An Annuity Of $1 In N Periods (P/A, i, N) In Excel Program By Using Following Formula: (P/A, i, n) = 1 ( 1+ i) i n PROBLEM 4. Create The Interest Factor Table For Future Value Of An Annuity Of $1 In N Periods (F/A, i, N) In Excel Program By Using Following Formula: (F/A, i, n) = ( 1+ i) n 1 i 2

3 Table 1. Future Value of $ 1 in period N (P/F, i, N) N 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

4 Table 2. Present Value of $ 1 in period N (P/F, i, N) N 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

5 Table 3. Present Value of an Annuity of $ 1 per period (P/A, i, n) N 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

6 Table 4. Future Value Of An Annuity Of $ 1 per period (F/A, i, n) N 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

7 PROBLEM 5. Automotive Computer Systems (ACS) sells electronic components to automobile manufacturers. Its sales, profits and stock price are highly correlated with the economy as a whole. The current price of ACS stock is $20 per share. Your assessment of the possible dollar returns (stock price + dividends) from owning one share of the stock for 1 year and their associated probabilities are as follows: $ Return $14 $18 $20 $22 $24 $26 Probabilit y a. What are the expected rate of return and standard deviation of the rate of return for an investment of $20 in ACS stock? Ans: E (r ) = 5%, σ = 16.28% r = P1 P0 P 0 2 i i σ = i( i x) Er ()= P r Px x = ExpectedValue = P i x i b. Draw a bar-chart of $ returns and their probabilities. PROBLEM 6. You are considering purchasing stock in Massive Manufacturing Company. The current price per share is $40. You have the following expectations regarding the price of the stock 1 year from now (no dividends are expected): Future Price $20 $30 $40 $50 $60 $80 Probability a. What is the price expected to be 1 year from now? Ans: $46 E(X) = ΣP i. X i b. If the price turns out to be $46, what rate of return will you have earned? Ans: 15% P1 P0 r = P0 c. Determine the probability distribution of the rates of return on this stock. What is the expected rate of return as calculated from this probability distribution? d. Using the probability distribution of c, calculate the standard deviation of the rate of return on this stock. Ans: 42.13% 7

8 PROBLEM 7. A firm has two investment opportunities open to it, only one of which the firm can accept. The cash outlays required by the two projects and their resulting net incremental cash returns are shown below (in m.$). End of Year Project A (1000) Project B (1000) Assume that the riskiness of these projects implies a required rate of return of 15%. Are either of the projects financially acceptable (> $0) or should management reject both? Ci Net Present Value (NPV) = - C 0 + ( 1+ ) Ans: NPV A = $307.51, NPV B = $ Both are acceptable but more preferable one is Project B. r n PROBLEM 8. Calculate the annual rates of return for Dynamics International Corporation s (DIC) common stock from the stock price and cash dividend data below. Year Year Closing Prices Annual Cash Dividends Annual Rate of Return 1980 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ price change + cash dividend r = purchase price 8

9 PROBLEM 9. Units Sold (x) TFC TVC TC Sales Pretax Income Net Income 0 $ 200, $ $ 200, $100, $ 200, $200, $ 200, $300, $ 200, $400, $ 200, $500, $ 200, $600, $ 200, $700, Unit Selling $ Price = Unit Variable $ Cost = Tax = 50.00% B.E.P. = B.E.P. ($) = $ 600, Cost And Sales relationships and Break Even Point $1,200, $1,000, Sales and Costs $800, $600, $400, $200, TFC TVC TC $ Sales Units Sold 9

10 PROBLEM 10. Calculate the following income statement by using Excel. Pro Forma Income Statement First Quarter JAN FEB MAR YTD Sales $ ,00 $ ,00 $ ,00 $ ,00 Variable Expenses Material???? Labor???? Contribution???? Fixed Costs Depreciation 500,00 500,00 500, ,00 Advertising 750,00 750,00 750, ,00 Administration 1.000, , , ,00 EBIT???? Interest Expense 500,00 500,00 500, ,00 Profit Before Tax???? Tax (32%)???? Net Income???? Formulas Used: Material = Sales 0.25 Labor = Sales 0.30 Contribution = Sales - Variable Expenses (Variable expenses = Material exp. + Labor exp.) EBIT (earnings before debt interest and income tax) = Contribution - TFC Profit before tax = EBIT - Interest expense Net Income = Profit before tax - tax (32%) 10

11 PROBLEM 11. Find the solutions for income statement, balance sheet and financial ratios of Happy Daze Corporation. HAPPY DAZE CORPORATION Income Statement ($000) Years REVENUES 33,000 35,893 42,555 52,108 62,319 Cost of Sales 22,841 24,407 29,972 38,412 47,719 GROSS MARGIN????? Selling Expenses 3,214 3,975 4,113 4,675 4,896 Administrative Expenses 2,500 2,734 3,041 3,455 3,815 Other ,054 TOTAL EXPENSES????? OPERATING INCOME????? Interest Expense PRE TAX INCOME????? Income Taxes (35%)????? NET PROFIT????? Earnings per Share (EPS)????? (Dividend / share) Note: Number of outstanding shares is 33, % of Net Profit will be Distributed to shareholders. 11

12 HAPPY DAZE CORPORATION Balance Sheet ($000) Years ASSETS CURRENT ASSETS: Cash $ 422 1,481 1,281 1,247 1,532 Accounts Receivable 3,626 3,702 4,783 6,377 7,476 Inventories 5,162 4,460 4,872 5,983 6,913 Other Current Assets ,031 TOTAL CURRENT ASSETS:????? FIXED ASSETS: Plant & Equipment 5,995 6,100 7,900 10,100 13,421 Accumulated Depreciation: Net Plant 5,995 6,100 7,900 10,100 13,421 Other 7,545 8,170 9,834 12,034 15,555 TOTAL FIXED ASSETS????? TOTAL ASSETS????? L & O/E CURRENT LIABILITIES : Accounts Payable 3,654 2,890 3,187 4,671 6,200 Accrued Liabilities 1, ,234 1,538 1,844 Notes Payable Short Term Debt 880 1,031 1, TOTAL CURRENT LIABILITIES????? LONG TERM DEBT Notes Payable , Bonds 2,000 2,500 2,500 2, Bank Debt TOTAL LONG TERM DEBT????? OTHER LIABILITIES: Deferred Income Tax TOTAL LIABILITIES????? EQUITY: Common Stock 1,200 1,200 1,200 1,200 1,200 Capital Surplus 2,150 2,150 2,150 2,150 2,150 Retained Earnings 5,126 7,287 9,666 12,161 14,594 TOTAL EQUITY????? TOTAL LIABILITIES & OWNERS EQUITY????? HAPPY DAZE CORPORATION 12

13 Turnover Ratios Total Assets Fixed Assets Current Assets Receivables Inventory Payables Turnover - Days Total Assets Fixed Assets Current Assets Receivables Inventory Payables Leverage Liability/Assets Liability/Equity LT Debt/Equity Liquidity Working Capital Current Ratio Quick Ratio Coverage Interest FINANCIAL RATIOS YEARS Average Profitability Gross Margin Operating Income Income Before Tax Net Profit Operating Income/Assets Profit/Assets Profit/Equity Dupont Analysis Asset Turnover times ROS = ROI (ROA) times Leverage = ROE 13

14 PROBLEM 12. SOURCES AND USES OF FUNDS Create a Sources and Uses of Funds table for Sparta Hats, Inc. in excel program. SOURCES AND USES OF FUNDS ANALYSIS FOR SPARTA HATS, INC. DEC.31, DEC.31, SOURCE USE ASSETS Cash $ 80,00 $ 180,00?? Marketable Securities 70,00 60,00?? Net Accounts Receivable 300,00 380,00?? Inventories 200,00 360,00?? Gross Fixed Assets 700,00 920,00?? Allowance for Depreciation -250,00-300,00?? Total Assets $ 1.100,00 $ 1.600,00 LIABILITIES & OWNERS' EQUITY Accounts Payable $ 100,00 $ 130,00?? Notes Payable 200,00 150,00?? Accruals 50,00 70,00?? Long-term debt 200,00 250,00?? Common Stock 100,00 500,00?? Retained Earnings 450,00 500,00?? Total Liabilities&Owners' equity $ 1.100,00 $ 1.600,00 TOTAL?? 14

15 DB Returns the depreciation of an asset for a specified period using the fixed-declining balance method. Syntax DB(cost, salvage, life, period, month) Cost is the initial cost of the asset. Salvage is the value at the end of the depreciation (sometimes called the salvage value of the asset). Life is the number of periods over which the asset is being depreciated (sometimes called the useful life of the asset). Period is the period for which you want to calculate the depreciation. Period must use the same units as life. Month 12. is the number of months in the first year. If month is omitted, it is assumed to be Remarks The fixed-declining balance method computes depreciation at a fixed rate. DB uses the following formulas to calculate depreciation for a period: (cost - total depreciation from prior periods) * rate where: rate = 1 - ((salvage / cost) ^ (1 / life)), rounded to three decimal places Depreciation for the first and last periods are special cases. For the first period, DB uses this formula: cost * rate * month / 12 For the last period, DB uses this formula: ((cost - total depreciation from prior periods) * rate * (12 - month)) / 12 Examples 15

16 Suppose a factory purchases a new machine. The machine costs $1,000,000 and has a lifetime of six years. The salvage value of the machine is $100,000. The following examples show depreciation over the life of the machine. The results are rounded to whole numbers. DB( ,100000,6,1,7) equals $186,083 DB( ,100000,6,2,7) equals $259,639 DB( ,100000,6,3,7) equals $176,814 DB( ,100000,6,4,7) equals $120,411 DB( ,100000,6,5,7) equals $82,000 DB( ,100000,6,6,7) equals $55,842 DB( ,100000,6,7,7) equals $15,845 DDB Returns the depreciation of an asset for a spcified period using the double-declining balance method or some other method you specify. Syntax DDB(cost, salvage, life, period, factor) Cost is the initial cost of the asset. Salvage is the value at the end of the depreciation (sometimes called the salvage value of the asset). Life is the number of periods over which the asset is being depreciated (sometimes called the useful life of the asset). Period is the period for which you want to calculate the depreciation. Period must use the same units as life. Factor is the rate at which the balance declines. If factor is omitted, it is assumed to be 2 (the double-declining balance method). All five arguments must be positive numbers. Remarks 16

17 The double-declining balance method computes depreciation at an accelerated rate. Depreciation is highest in the first period and decreases in successive periods. DDB uses the following formula to calculate depreciation for a period: cost - salvage(total depreciation from prior periods) * factor / life Change factor if you do not want to use the double-declining balance method. Examples Suppose a factory purchases a new machine. The machine costs $2400 and has a lifetime of 10 years. The salvage value of the machine is $300. The following examples show depreciation over several periods. The results are rounded to two decimal places. DDB(2400,300,3650,1) equals $1.32, the first day's depreciation. Microsoft Excel automatically assumes that factor is 2. DDB(2400,300,120,1,2) equals $40.00, the first month's depreciation. DDB(2400,300,10,1,2) equals $480.00, the first year's depreciation. DDB(2400,300,10,2,1.5) equals $306.00, the second year's depreciation using a factor of 1.5 instead of the double-declining balance method. DDB(2400,300,10,10) equals $22.12, the 10th year's depreciation. Microsoft Excel automatically assumes that factor is 2. FV Returns the future value of an investment based on periodic, constant payments and a constant interest rate. Syntax FV(rate, nper, pmt, pv, type) For a more complete description of the arguments in FV and for more information on annuity functions, see PV. Rate is the interest rate per period. Nper is the total number of payment periods in an annuity. Pmt is the payment made each period; it cannot change over the life of the annuity. Typically, pmt contains principal and interest but no other fees or taxes. Pv is the present value, or the lump-sum amount that a series of future payments is worth right now. If pv is omitted, it is assumed to be 0. 17

18 Type is the number 0 or 1 and indicates when payments are due. If type is omitted, it is assumed to be 0. Set type equal to If payments are due 0 At the end of the period 1 At the beginning of the period Remarks 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. 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. Examples FV(0.5%, 10, -200, -500, 1) equals $ FV(1%, 12, -1000) equals $12, FV(11%/12, 35, -2000,, 1) equals $82, Suppose you want to save money for a special project occurring a year from now. You deposit $1000 into a savings account that earns 6 percent annual interest compounded monthly (monthly interest of 6%/12, or 0.5%). You plan to deposit $100 at the beginning of every month for the next 12 months. How much money will be in the account at the end of 12 months? FV(0.5%, 12, -100, -1000, 1) equals $

19 IPMT Returns the interest payment for a given period for an investment based on periodic, constant payments and a constant interest rate. For a more complete description of the arguments in IPMT and for more information on annuity functions, see PV. Syntax IPMT(rate, per, nper, pv, fv, type) Rate is the interest rate per period. Per is the period for which you want to find the interest, and must be in the range 1 to nper. Nper is the total number of payment periods in an annuity. Pv is the present value, or the lump-sum amount that a series of future payments is worth right now. 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). Type is the number 0 or 1 and indicates when payments are due. If type is omitted, it is assumed to be 0. Set type equal to If payments are due 0 At the end of the period 1 At the beginning of the period Remarks 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. 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. Examples 19

20 The following formula calculates the interest due in the first month of a three-year $8000 loan at 10 percent annual interest: IPMT(0.1/12, 1, 36, 8000) equals -$66.67 The following formula calculates the interest due in the last year of a three-year $8000 loan at 10 percent annual interest, where payments are made yearly: IPMT(0.1, 3, 3, 8000) equals -$ 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. 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. Syntax 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. 20

21 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. To calculate the investment's internal rate of return after four years: IRR(B1:B5) equals -2.12% To calculate the internal rate of return after five years: IRR(B1:B6) equals 8.66% To calculate the internal rate of return after two years, you need to include a guess: IRR(B1:B3,-10%) equals % Remarks 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 zero net present value. The following macro 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.) 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. Syntax 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. 21

22 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 Reinvest_rate is the interest rate you pay on the money used in the cash flows. is the interest rate you receive on the cash flows as you reinvest them. Remarks 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). 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: Examples MIRR = (, [ ]).( 1 rrate) (, [ ]).( 1+ frate) NPV rrate values positive + NPV frate values negative n 1 n 1 1 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 your profits, earning 12% annually. In 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 12.61% To calculate the modified rate of return after three years: MIRR(B1:B4, 10%, 12%) equals -4.80% To calculate the five-year modified rate of return based on a reinvest_rate of 14% MIRR(B1:B6, 10%, 14%) equals 13.48% 22

23 NPER Returns the number of periods for an investment based on periodic, constant payments and a constant interest rate. Syntax NPER(rate, pmt, pv, fv, type) For a more complete description of the arguments in NPER and for more information about annuity functions, see PV. Rate is the interest rate per period. Pmt is the payment made each period; it cannot change over the life of the annuity. Typically, pmt contains principal and interest but no other fees or taxes. Pv is the present value, or the lump-sum amount that a series of future payments is worth right now. 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). 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 Examples NPER(12%/12, -100, -1000, 10000, 1) equals 60 NPER(1%, -100, -1000, 10000) equals 60 NPER(1%, -100, 1000) equals 11 NPV Returns the net present value of an investment based on a series of periodic cash flows and a discount rate. The net present value of an investment is today's value of a series of future payments (negative values) and income (positive values). Syntax 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. 23

24 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. Remarks 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. If n is the number of cash flows in the list of values, the formula for NPV is: NPV = n Valuesi ( 1 rate) i 1 + i 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 $3000, $4200, and $6800 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 $

25 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: $8000, $9200, $10,000, $12,000, and $14,500. The annual discount rate is 8%. 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 $ 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 $9000 for that year. The net present value of the shoe store investment after six years is given by: NPV(8%, B2:B6, -9000)+B1 equals -$ PMT Returns the periodic payment for an annuity based on constant payments and a constant interest rate. Syntax PMT(rate, nper, pv, fv, type) For a more complete description of the arguments in PMT, see PV. Rate is the interest rate per period. Nper is the total number of payment periods in an annuity. Pv is the present value the total amount that a series of future payments is worth now. 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). 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 25

26 1 At the beginning of the period Remarks The payment returned by PMT includes principal and interest but no taxes, reserve payments, or fees sometimes associated with annuities. 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. Tip To find the total amount paid over the duration of the annuity, multiply the returned PMT value by nper. Examples The following macro formula returns the monthly payment on a $10,000 loan at an annual rate of 8% that you must pay off in 10 months: PMT(8%/12, 10, 10000) equals -$ For the same loan, if payments are due at the beginning of the period, the payment is: PMT(8%/12, 10, 10000, 0), 1) equals -$ The following macro formula returns the amount someone must pay to you each month if you loan that person $5000 at 12% and want to be paid back in five months: PMT(12%/12, 5, -5000) equals $ Suppose you want to save $50,000 in 18 years by saving a constant amount each month. If you assume you'll be able to earn 6% interest on your savings, you can use PMT to determine how much to save each month: PMT(6%/12, 18*12, 0), 50000) equals -$ If you pay $ into a 6% savings account every month for 18 years, you will have $50,

27 PPMT Returns the payment on the principal for a given period for an investment based on periodic, constant payments and a constant interest rate. Syntax PPMT(rate, per, nper, pv, fv, type) For a more complete description of the arguments in PPMT, see PV. Rate is the interest rate per period. Per specifies the period and must be in the range 1 to nper. Nper is the total number of payment periods in an annuity. Pv is the present value the total amount that a series of future payments is worth now. 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). 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 Remarks 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. Examples The following formula returns the principal payment for the first month of a two-year $2000 loan at 10% annual interest: PPMT(10%/12, 1, 24, 2000) equals -$75.62 The following function returns the principal payment for the last year of a 10-year $200,000 loan at 8% annual interest: PPMT(8%, 10, 10, ) equals -$27,

28 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. Syntax PV(rate, nper, pmt, fv, type) Rate is the interest rate per period. For example, if you obtain an automobile loan at a 10% 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% are $ You would enter into the formula as the pmt. 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. 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 Remarks 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% 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. 28

29 The following functions apply to annuities: CUMIPMT PPMT CUMPRINC PV FV RATE FVSCHEDULE IPMT XNPV PMT XIRR 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 $1000 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. Microsoft Excel solves for one financial argument in terms of the others. If rate is not 0, then: nper nper ( 1+ rate) 1 PV ( 1+ rate) + pmt( 1+ rate type) + fv = 0 rate If rate is 0, then: (pmt nper) + pv + fv = 0 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%. 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. 29

30 RATE Returns the interest rate per period of an annuity. RATE is calculated by iteration and can have zero or more solutions. If the successive results of RATE do not converge to within after 20 iterations, RATE returns the #NUM! error value. Syntax RATE(nper, pmt, pv, fv, type, guess) See PV for a complete description of the arguments nper, pmt, pv, fv, and type. Nper is the total number of payment periods in an annuity. 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. Pv is the present value the total amount that a series of future payments is worth now. 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). 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 Guess is your guess for what the rate will be. If you omit guess, it is assumed to be 10%. If RATE does not converge, try different values for guess. RATE usually converges if guess is between 0 and 1. Remarks Make sure that you are consistent about the units you use for specifying guess and nper. If you make monthly payments on a four-year loan at 12% annual interest, use 12%/12 for guess and 4*12 for nper. If you make annual payments on the same loan, use 12% for guess and 4 for nper. Example To calculate the rate of a four-year $8000 loan with monthly payments of $200: RATE(48, -200, 8000) equals 0.77% 30

31 This is the monthly rate, because the period is monthly. The annual rate is 0.77%*12, which equals 9.24%. SLN Returns the straight-line depreciation of an asset for one period. Syntax SLN(cost, salvage, life) Cost is the initial cost of the asset. Salvage is the value at the end of the depreciation (sometimes called the salvage value of the asset). Life is the number of periods over which the asset is being depreciated (sometimes called the useful life of the asset). Example Suppose you've bought a truck for $30,000 that has a useful life of 10 years and a salvage value of $7500. The depreciation allowance for each year is: SLN(30000, 7500, 10) equals $2250 SYD Returns the sum-of-years' digits depreciation of an asset for a specified period. Syntax SYD(cost, salvage, life, per) Cost is the initial cost of the asset. Salvage is the value at the end of the depreciation (sometimes called the salvage value of the asset). Life is the number of periods over which the asset is being depreciated (sometimes called the useful life of the asset). Per is the period and must use the same units as life. Remark 31

32 SYD is calculated as follows: Examples ( Cost Salvage )( Life per + ) SYD = ( Life)( Life + 1) If you've bought a truck for $30,000 that has a useful life of 10 years and a salvage value of $7500, the yearly depreciation allowance for the first year is: SYD(30000,7500,10,1) equals $ The yearly depreciation allowance for the 10th year is: SYD(30000,7500,10,10) equals $ VDB Returns the depreciation of an asset for any period you specify, including partial periods, using the double-declining balance method or some other method you specify. VDB stands for variable declining balance. Syntax VDB(cost, salvage, life, start_period, end_period, factor, no_switch) Cost is the initial cost of the asset. Salvage is the value at the end of the depreciation (sometimes called the salvage value of the asset). Life is the number of periods over which the asset is being depreciated (sometimes called the useful life of the asset). Start_period is the starting period for which you want to calculate the depreciation. Start_period must use the same units as life. End_period is the ending period for which you want to calculate the depreciation. End_period must use the same units as life. Factor is the rate at which the balance declines. If factor is omitted, it is assumed to be 2 (the double-declining balance method). Change factor if you do not want to use the double-declining balance method. For a description of the double-declining balance method, see DDB. 32