1. BUSINESS MATHEMATICS & STATISTICS

2. Module 4 Financial Mathematics Applications of Linear Equations ( Lecture 17-18) Break-even Analysis ( Lectures 19-22) Mid-Term Examination

3. LECTURE 17 Review Lecture 16 Financial Mathematics Introduction to Linear Equations

4. PROJECT FINANCIAL ANALYSIS Cost estimates Revenue estimates Forecasts of costs Forecasts of revenues Net cash flows Benefit cost analysis Internal Rate of Return Break-Even Analysis

5. EXCEL FUNCTIONS FINANCIAL ANALYSIS AMORDEGRC Returns the depreciation for each accounting period by using a depreciation coefficient AMORLINC Returns the depreciation for each accounting period

6. AMORDEGRC Depreciation Using Depreciation Coefficient AMORDEGRC(cost,date_purchased,first_period,s alvage,period,rate,basis) Cost cost of the asset. Date_purchased date of the purchase of the asset. First_period date of the end of the first period. Salvage salvage value at the end of the life of the asset. Period period. Rate rate of depreciation. Basis year basis to be used.

7. AMORLINC Depreciation Using Prorated Depreciation AMORLINC(cost,date_purchased,first_period,salvage,perio d,rate,basis) Cost cost of the asset Date_purchased date of the purchase of the asset. First_period date of the end of the first period. Salvage salvage value at the end of the life of the asset. Period period. Rate rate of depreciation. Basis year basis to be used.

8. AMORLINC 1 Data Description 22400 Cost 38/19/2008 Date purchased 412/31/2008End of the first period 5300 Salvagevalue 61 Period 715% Depreciation rate 81 Actual basis (see above) 9(Result)=AMORLINC(A2,A3,A4,A5,A6,A7,A7)First period depreciation (360)

9. EXCEL FUNCTIONS FINANCIAL ANALYSIS CUMIPMT Returns the cumulative interest paid between two periods CUMPRINC Returns the cumulative principal paid on a loan between two periods

10. EXCEL FUNCTIONS FINANCIAL ANALYSIS DB Returns the depreciation of an asset for a specified period using the fixed-declining balance method DDB Returns the depreciation of an asset for a specified period using the double-declining balance method or some other method you specify

11. EXCEL FUNCTIONS FINANCIAL ANALYSIS IRR Returns the internal rate of return for a series of cash flows MIRR Returns the internal rate of return where positive and negative cash flows are financed at different rates

12. INTERNAL RATE OF RETURN IRR 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. Guess is a number that you guess is close to the result of IRR.

13. IRR(values,guess) 1 Data Description 2-70,000Initial cost of a business 312,000Net income for the first year 415,000Net income for the secondyear 518,000Net income for the third year 621,000Net income for the fourth year 726,000Net income for the fifth year Formula Description (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%)

14. BUSINESS MATHEMATICS & STATISTICS

15. EXCEL FUNCTIONS FINANCIAL ANALYSIS PV Returns the present value of an investment NPV Returns the net present value of an investment based on a series of periodic cash flows and a discount rate

16. NPV NPV(rate,value1,value2,...) Rate rate of discount over the length of one period Value1, value2,... 1 to 29 arguments representing the payments and income

17. PV(rate,nper,pmt,fv,type) Rate interest rate per period Nper total number of payment periods in an annuity Pmt payment made each period and cannot change over the life of the annuity Fv future value, or a cash balance you want to attain after the last payment is made Type number 0 or 1 and indicates when payments are due.

18. PV(rate,nper,pmt,fv,type) 1 DataDescription 2 500Money paid out of an insurance annuity at the end of every month 38%Interest rate earned on the money paid out 420Years the money will be paid out 5 FormulaDescription 6=PV(A3/12, 12*A4, A2,, 0) Present value of an annuity with the terms above (-59,777.15).

19. NPV 1 DataDescription 2 10%Annual discount rate 3 -10,000Initial cost of investment one year from today 4 3,000Return from first year 5 4,200Return from second year 6 6,800 Return from third year 7 =NPV(A2, A3, A4, A5, A6) Net present value of this investment (1,188.44)

20. NPV 1 DataDescription 2 10%Annual discount rate 3 -10,000Initial cost of investment one year from today 4 3,000Return from first year 5 4,200Return from second year 6 6,800 Return from third year 7 =NPV(A2, A3, A4, A5, A6) Net present value of this investment (1,188.44)

21. EXCEL FUNCTIONS FINANCIAL ANALYSIS SLN Returns the straight-line depreciation of an asset for one period SYD Returns the sum-of-years' digits depreciation of an asset for a specified period

22. EXCEL FUNCTIONS FINANCIAL ANALYSIS VDB Returns the depreciation of an asset for a specified or partial period using a declining balance method XIRR Returns the internal rate of return for a schedule of cash flows that is not necessarily periodic

23. EXCEL FUNCTIONS FINANCIAL ANALYSIS XNPV Returns the net present value for a schedule of cash flows that is not necessarily periodic

24. BUSINESS MATHEMATICS & STATISTICS