Analysis of Costs & Benefits Basic Methods of Financial Analysis A hallmark of good Six Sigma deployments is the validation of costs and benefits. Although this validation is normally done by people in finance, it is the Black Belt who will do a great deal of the analysis, with the finance person providing guidance and verification. You need to understand the basic tools of the financial analysis to be able to provide credible justifications for the cost of the changes you are proposing. By the way, there are demonstration videos on each of the excel methods explained in this lesson. 1
Fixed, Variable, and Total Costs Total Costs DOLLARS Total Variable Costs Total Fixed Costs Time or Production Analysis of Costs & Benefits 2 Improvements often cost money to implement. They also save money. You will need to quantify the costs and savings so you can assess the relative risk of spending money on the improvements. There are two categories of costs to consider. VARIABLE COSTS are those costs which are expected to change at the same rate as the firm s level of sales. As more units are sold, total variable costs will rise. Examples include sales commissions, shipping costs, hourly wages and raw materials. FIXED COSTS are those costs that are constant, regardless of the quantity produced, over some meaningful range of output. Examples of fixed costs include rent, salaries, depreciation of equipment, etc. TOTAL COSTS are the sum of variable plus fixed costs. 2
Break-even Points Q(P-V) F = EBIT = 0 Where Q is the quantity sold P the price per unit V the variable cost per unit F the total fixed costs Q* is the break-even quantity Analysis of Costs & Benefits 3 One important financial consideration is the level of sales required before interest and taxes (EBIT) to earn sufficient profits to cover fixed + variable costs. HERE IS THE equation. THE TERM Q is the quantity sold, P IS THE price per unit, V IS THE variable cost per unit, AND F IS the fixed cost. 3
Break-even Example A publishing firm is selling books for $30 each. The variable costs are $10 each and fixed costs are $100,000. What is the break-even quantity? F P V Analysis of Costs & Benefits 4 Here s an example of using the breakeven equation. A publishing firm is selling books for $30 each. The variable costs are $10 each and fixed costs are $100,000. What is the break-even quantity? SOLVING FOR Q* we see that THE F TERM is $100,000, THE P TERM is $30, and THE V TERM is $10. The fixed costs will be covered by selling 5,000 books. 4
Quantity Needed to Earn a Target Amount You will often want to know the volume needed to cover the costs of a project, or to earn a specified profit Example: if the publisher in the example wishes to earn a $5,000 profit then the required level of sales is: Analysis of Costs & Benefits 5 It is probably more common that your leaders will want to know when your project will generate a certain amount of savings, rather than just knowing when you ll break even. To find this YOU SIMPLY REPLACE the breakeven value of zero with the target earning before interest and taxes. FOR EXAMPLE, if the publisher in the previous example wanted to know when he would earn $5,000 on his investment, this equation provides the answer: 5,250 units. 5
Time Value of Money Common measures of time value Future value: the value a sum of money will be worth some time in the future Present value: the current value of a sum of money that will be received at some time in the future Net present value: the current value of a future cash flow stream Internal rate of return: the rate of return that equates the present value of future cash flows with costs Analysis of Costs & Benefits 6 Since money can be invested to grow to a larger amount, it is said to have a time value. THERE ARE several common ways to measure the time value of money. FUTURE VALUE is the value a sum of money will have at some future point in time. For example, if you have money in a savings account, it will be worth more in a year by the amount of interest it has earned. PRESENT VALUE is the current value of a sum of money that will be received at some time in the future. For example, you purchase a certificate of deposit for less than it will be worth in one year. NET PRESENT value is similar to present value, except that it is a measure of the current value of a series of future payments. INTERNAL RATE OF return looks at both costs and cash flows and measures the rate of return required to equate the present value of the two cash streams. 6
Future value equation Future Value FV = PV + PV i = PV(1+i) Where FV is the future value, PV is the present value i is the interest rate expressed as a proportion Analysis of Costs & Benefits 7 Here is the equation for future value. In the equation FV IS THE future value being solved for, PV IS THE present value or starting amount, AND i IS the interest rate expressed as a proportion rather than as a percentage 7
PV = $1,000 i = 0.1 FV in 1 year=1000x(1.1)=$1,100. FV in 2 years=1100x(1.1)=$1,210. Future Value Example Compounding Analysis of Costs & Benefits 8 ASSUME THAT you have $1,000 today (Present value PV = $1,000) and that you can invest this sum and earn INTEREST AT the rate of 10% per year (i=0.1). In one year your $1,000 WILL HAVE GROWN by $100 to $1,100. IN TWO YEARS the value will be $1,210. This is the future value (FV) of your $1,000 after two years. THE TABLE illustrates the growth of the investment. OBSERVE THAT in year #2 you earned interest on your original $1,000 and on the $100 interest you earned in year 1. The result is that you earned more interest in year 2 than in year 1. THIS IS KNOWN as compounding. The year time interval is know as the compounding period. ALGEBRAICALLY, HERE S what happened. 8
Future Value Using Excel Analysis of Costs & Benefits 9 It s easy to calculate future value with Microsoft excel. JUST ENTER the known values into a spreadsheet, THEN CLICK the formula bar and look for the FV function. EXCEL FINDS the future value for you. Note that excel will show this as a negative number. If you want a positive result you need to put a minus sign in front of the function in the formula bar. You may wish to view the demo videos showing how to use Excel to solve these problems. 9
Non-annual Compounding N need not be stated in years, it can be any unit of time i must be adjusted if N is not in years E.g., if N is in months, i must be interest-permonth Example: analyze the previous example with quarterly compounding FV = PV i 1+ 4 4 N ( 1 0.025) 8 + Was $1,210.00 = $1,000 = $1,218.40 Analysis of Costs & Benefits 10 The compounding period, N, need not be in years. It can be in any unit of time. IF YOU use non-annual compounding periods be sure to remember to adjust the term i. FOR EXAMPLE, if N is in months instead of years, then i should be divided by 12 so it expresses the interest rate per month. HERE S THE previous example with quarterly compounding periods for two years. WE MULTIPLY the 2 year time period by the number of quarters in a year. AND WE divide the annual interest rate by 4. NOTE THAT the new future value is greater than it was with annual compounding. 10
Non-annual Compounding Using Excel Analysis of Costs & Benefits 11 Once again, Excel can be used to solve these problems. YOU SIMPLY make the required adjustments in the input values. 11
Continuous Compounding When an infinite number of compounding periods are used it is known as continuous compounding because lim n FV = PV n x 1+ 2.71828 n i t e = = where i is the interest rate and t is the number of years Previous example with continuous compounding $1,000 FV 0.1 2 = e = $1, 221.40 x e x Analysis of Costs & Benefits 12 Since the future value increases as the number of compounding periods increases, it makes one curious what would happen if the number of compounding periods increased without limit. THIS IS CALLED continuous compounding, and it is quite commonly used. The equation for continuous compounding uses a constant, e. If you look at our original future value equation you see that it is in the form 1 plus i divided by n, raised to the power n, where n is the number of compounding periods in the time interval. It turns out that if you look at this equation for infinitely large n, you end up with a constant raised to the power i divided by n. The constant has a special name in mathematics, e. To find the future value e is raised to a power equal to the interest rate times the length of the time interval. IF WE LOOK at the previous example with continuous compounding we see that the future value is $1,221.40. 12
Continuous Compounding Using Excel Pert Analysis of Costs & Benefits 13 Excel has a built in function for raising e to some power. It s called exp. This function can be used to solve continuous compounding problems, as shown here. BY THE WAY, I have a little memory aid I use to remember this equation: Pert. P is the present value, e is e, r is the interest rate, and t is the time period. 13
Net Present Value Evaluate cash flow streams of costs and benefits Amounts vary from one period to the next Method: compute the PV for each cash flow and add the results to get the NPV Analysis of Costs & Benefits 14 Net present value is used to evaluate cash flow streams of costs and benefits. THE AMOUNTS can vary from period to period. THE METHOD IS actually very simple. You just compute the present value for each amount in the cash flow and sum the results to get the net present value for the entire stream. 14
Here s a net present value example that we ll analyze with Excel. It shows a 5 year time interval of costs and benefits. MANAGEMENT WANTS a 12% or greater return on investment for any project they fund. 15
Analysis of net present value with Excel is fairly straightforward. But there is a twist which I ll describe to you. You ll need to create a new column showing the difference between the cost and the benefit for each year. Then create a cell showing the rate of return required by management. Ask your finance department for this value. Finally, calculate the net present value using Excel s built-in NPV function. The twist that I mentioned earlier is that you will show the project starting in year zero, then apply the Excel NPV function to the data from year 1 to the last year., in this case the NPV function will use the data shown here. Finally, you must subtract the initial cash outlay from the NPV value returned by Excel. The result for this example shows that the project has a negative value of nearly $1700. Management is not likely to approve this project. 16
Internal Rate of Return Cash flows can be uneven IRR can be used to prioritize projects Analysis of Costs & Benefits 17 The internal rate of return is the yield of an investment in a project given its costs and benefits cash flows. THE CASH flows can be uneven. IRR IS OFTEN used by leaders and Master Black Belts as an important consideration when prioritizing projects. 17
IRR Using Excel Analysis of Costs & Benefits 18 You won t want to calculate IRR by hand. It s an iterative process that requires a computer. EXCEL HAS A built-in IRR function. For the costs and benefits shown, Excel CALCULATES AN IRR of 6%. This value is half of management s 12% funding rate, which is why the NPV is negative. SOMETIMES EXCEL MAY have difficulty finding the IRR. YOU CAN GIVE Excel a hand in these cases by entering different guesses so that Excel will start its search in different places. Usually, however, Excel finds the answer quickly. 18
Tollgate Review DMAIC DMAIC DMAIC Define Measure Analyze Developed Charter ID Team ID Customer VOC CTQ Specs Map Process (SIPOC) Communication plan Financial Estimate Team Kickoff meeting <<<<<<<<<<<<<<<<<<<<<<<<<< Storyboard >>>>>>>>>>>>>>>>>>>>>>>>>> Validate Measurement Opportunity Statement Baseline data Problem Statement Business Case Plot Defects Goal Statement Map to Y s and X s Stratify Process Sigma Detail Process Map Focus Problem Statement ID Potential Causes Categorize/stratify Potential Causes Verify causes with data Quantify cause-effect relationships (Costs) Meet with Finance MBB Sponsor Finance MBB Sponsor Update Documents and Learnings Database Change management tools MBB Sponsor Finance Congratulations, you ve finished the analyze phase of your project! In this phase you have FOCUSED YOUR problem statement with opportunity maps; USED ROOT cause analysis, brainstorming, and cause and effect diagrams to identify potential causes; USED A VARIETY of statistical methods to mine your organization s data warehouse for information on drivers causing the response to vary; USED REGRESSION and correlation analysis to verify your drivers, and DOE to verify the root causes underlying the drivers; AND QUANTIFIED costs and benefits for validation BY FINANCE. You are now ready to proceed to the improve phase of the project. 19
End of Lesson 20