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How Time and Interest Affect Money Ir. Haery Sihombing MT. Pensyarah Pelawat Fakulti Kejuruteraan Pembuatan Universiti Teknologi Malaysia Melaka BASIC OF A COUNTING RELATED TO COST INTRODUCTION COST ACCOUNTING Accounting is the collection and aggregation of information for decision maker- including managers, investor, regulators, lenders, and the public. Accounting system affect behavior and management and have affects across departments, organizations, and even countries. Information contained within an accounting system has the power to influence actions. Accounting information systems are particularly strong behavioral drivers within the context of a corporation – where profits and the bottom line are daily concerns. COST ACCOUNTING There are three type of accounting systems 1. NATIONAL ACCOUNTING SYSTEMS National accounts are national income and production accounts, such Gross National Product (GNP) and Gross Domestic Product (GDP) which aim to measure and track an economy’s contribution to the well-being of its inhabitants. National income accounts show the national demand or goods and services and are used to track and measure economic growth. Conventional economic thinking has assumed that the increases in goods and services produced domestically (GDP) and national income (GNP) are adequate yardstick to economic health Example: The world bank uses per capita GNP as a major criterion for classifying national economies COST ACCOUNTING 1. NATIONAL ACCOUNTING SYSTEMS COST ACCOUNTING 2. FINANCIAL ACCOUNTING SYSTEMS Financial accounts, such as balance sheets and income statements are used to keep track of business incomes and outflows. These financial reports are for use by persons outside the firm – for example: lenders or investors. There are relevant to the enterprise as a whole and are generally subject to strict government rules The most common financial accounting reports are for external use by are the financial statements in a firm’s annual report to shareholders. In the United States and most developed countries, these reports conform to generally accepted accounting principles developed predominantly by the Financial Accounting Standards Board (FASB) and the Securities and Exchange Commission (SEC) COST ACCOUNTING The overall objective of a firm’s financial accounting statements 1. The overall objective of a fir’s financial accounting statements are: 2. To provide information useful for making rational investment and credit decisions 3. To allow investors and creditors to assess the amount, timing, and uncertainty of cash flows 4. To provide information about the economic resources of a firm and the claims on those resources 5. To provide information about a firm’s operating performance during period 6. To provide information on how a firm obtains and uses money and other financial resources. 7. To provide information on how management ha discharges its stewardship responsibility to owners and the public. COST ACCOUNTING Type of Financial Accounting Statements COST ACCOUNTING 3. MANAGEMENT or COST ACCOUNTING SYSTEMS and CAPITAL BUDGETING Management or cost accounting systems are part of an enterprise’s information system and refer to the internal cost tracking and allocation systems to track costs and expenditures. These are internal rather than external accounting systems. There are no fixed rules governing how an entity should keep track of cash flows internally, although there are many formal methods available for users. Capital budgeting is basically a form of predictive cost accounting over a set time frame which is used to analyze the costs of alternative projects or expenditures over the specified period of time COST ACCOUNTING The main objectives of managerial/cost accounting are (Hilton, 1998): Providing managers with information for decision making and planning. Assisting managers in directing and controlling operations. Motivating managers towards the organization’s goals. Measuring the performance of managers and sub-units within the organization. COST ACCOUNTING INTRODUCTION TIME VALUE OF MONEY : THE ECONOMIC VALUE OF A SUM DEPENDS ON WHEN IT IS RECEIVED. Because money has both EARNING as well as PURCHASING POWER over time (it can be put to work, earning more money for its owner) A Ringgit received today has a greater value than Ringgit received at some future time 1. Foundations: Overview 1. F/P and P/F Factors 2. P/A and A/P Factors 3. F/A and A/F Factors 4. Interpolate Factor Values 5. Calculate i 6. Calculate “n” 7. Spreadsheets F/P and P/F Factors Section 1 1 Basic Derivations: F/P factor F/P Factor To find F given P Fn To Find F given P …………. n Compound forward in time P0 1 Basic Derivations: F/P factor = P(1+i) F1 = F1(1+i)…..but: F2 = P(1+i)(1+i) = P(1+i)2 F2 =F2(1+i) =P(1+i)2 (1+i) F3 = P(1+i)3 In general: Fn = P(1+i)n Fn = P(F/P,i%,n) 1 Present Worth Factor from F/P Since Fn = P(1+i)n We solve for P in terms of FN P = F{ 1/ (1+i)n} = F(1+i)-n Thus: P = F(P/F,i%,n) where (P/F,i%,n) = (1+i)-n Thus, the two factors are: 1. F = P(1+i)n finds the future worth of P; 2. P = F(1+i)-n finds the present worth from F 1 P/F factor –Discounting back in time Discounting back from the future Fn …………. n P/F factor brings a single future sum back to a specific P point in time. P/A and A/P Factors Section 2 2 Example- F/P Analysis Example: P= $1,000;n=3;i=10% What is the future value, F? F = ?? 0 1 2 3 P=$1,000 i=10%/year F3 = $1,000[F/P,10%,3] = $1,000[1.10]3 = $1,000[1.3310] = $1,331.00 2 Example – P/F Analysis Assume F = $100,000, 9 years from now. What is the present worth of this amount now if i =15%? F9 = $100,000 i = 15%/yr 0 1 2 3 ………… 8 9 P= ?? P0 = $100,000(P/F, 15%,9) = $100,000(1/(1.15)9) = $100,000(0.2843) = $28,430 at time t = 0 2 Uniform Series Present Worth and Capital Recovery Factors Annuity Cash Flow P = ?? 1 2 3 ………….. .. .. n-1 n 0 $A per period 2 Uniform Series Present Worth and Capital Recovery Factors Desire an expression for the present worth – P of a stream of equal, end of period cash flows - A P = ?? 0 1 2 3 n-1 n A = given 2 Uniform Series Present Worth and Capital Recovery Factors Write a Present worth expression 1 1 1 1 [1] P A .. (1 i) (1 i) 1 2 (1 i) n 1 (1 i) n Term inside the brackets is a geometric progression. Mult. This equation by 1/(1+i) to yield a second equation 2 Uniform Series Present Worth and Capital Recovery Factors The second equation P 1 1 1 1 A .. n 1 1 i (1 i) (1 i) 2 3 (1 i) (1 i) n [2] To isolate an expression for P in terms of A, subtract Eq [1] from Eq. [2]. Note that numerous terms will drop out. 2 Uniform Series Present Worth and Capital Recovery Factors Setting up the subtraction P 1 1 1 1 1 A ... [2] (1 i) (1 i) (1 i) (1 i) 2 3 4 (1 i) n (1 i) n1 1 1 1 1 - P A (1 i)1 (1 i)2 .. (1 i)n1 (1 i)n [1] i 1 1 = P A n 1 [3] 1 i (1 i) (1 i) 2 Uniform Series Present Worth and Capital Recovery Factors Simplifying Eq. [3] further i 1 1 P A n 1 1 i (1 i) (1 i) A 1 (1 i)n 1 P n 1 1 P A n for i 0 i (1 i) i(1 i) F/A and A/F Factors Section 3 3 F/A and A/F Derivations $F Annuity Cash Flow ………….. N 0 Find $A given the $A per period Future amt. - $F 3 Sinking Fund and Series Compound amount factors (A/F and F/A) Take advantage of what we already have Recall: 1 Substitute “P” and Also: PF n simplify! (1 i) i(1 i)n A P (1 i) 1 n 3 F/A and A/F Derivations $F Annuity Cash Flow ………….. N 0 Find $F given the $A $A per period amounts 3 Example -1 Formosa Plastics has major fabrication plants in Texas and Hong Kong. It is desired to know the future worth of $1,000,000 invested at the end of each year for 8 years, starting one year from now. The interest rate is assumed to be 14% per year. 3 Example-1 •A = $1,000,000/yr; n = 8 yrs, i = 14%/yr •F8 = ?? 3 Example-1 Solution: The cash flow diagram shows the annual payments starting at the end of year 1 and ending in the year the future worth is desired. Cash flows are indicated in $1000 units. The F value in 8 years is F = l000(F/A,14%,8) = 1000( 13.23218) = $13,232.80 = 13.232 million 8 years from now. 3 Example-1 How much money must Carol deposit every year starting, l year from now at 5.5% per year in order to accumulate $6000 seven years from now? 3 Example -2 Solution The cash How diagram from Carol's perspective fits the A/F factor. A= $6000 (A/F,5.5%,7) = 6000(0.12096) = $725.76 per year The A/F factor Value 0f 0.12096 was computed using the A/F factor formula Interpolation in Interest Tables Section 4 4 Interpolation of Factors • All texts on Engineering economy will provide tabulated values of the various interest factors usually at the end of the text in an appendix • Refer to the back of your text for those tables. 4 Interpolation of Factors • Typical Format for Tabulated Interest Tables 4 Interpolation (Estimation Process) • At times, a set of interest tables may not have the exact interest factor needed for an analysis • One may be forced to interpolate between two tabulated values • Linear Interpolation is not exact because: • The functional relationships of the interest factors are non-linear functions • Hence from 2-5% error may be present with interpolation. 4 An Example • Assume you need the value of the A/P factor for i = 7.3% and n = 10 years. • 7.3% is most likely not a tabulated value in most interest tables • So, one must work with i = 7% and i = 8% for n fixed at 10 • Proceed as follows: 4 Basic Setup for Interpolation •Work with the following basic relationships 4 i = 7.3% using the A/P factor • For 7% we would observe: COMPOUND PRESENT SINKING COMPOUND CAPITAL N AMT. FACTOR WORTH FUND AMOUNT RECOVERY F/P P/F A/F F/A A/P 10 1.9672 0.5083 0.0724 13.8164 0.14238 A/P,7%,10) = 0.14238 4 i = 7.3% using the A/P factor • For i = 8% we observe: COMPOUND PRESENT SINKING COMPOUND CAPITAL N AMT. FACTOR WORTH FUND AMOUNT RECOVERY F/P P/F A/F F/A A/P 10 2.1589 0.4632 0.0690 14.4866 0.14903 (A/P,8%,10) = 0.14903 4 Estimating for i = 7.3% • Form the following relationships 4 Final Estimated Factor Value • Observe for i increasing from 7% to 8% the A/P factors also increases. • One then adds the estimated increment to the 7% known value to yield: 4. The Exact Value for 7.3% • Using a previously programmed spreadsheet model the exact value for 7.3% is: Determination of Unknown Number of Interest Section 5 5 When the i – rate is unknown • A class of problems may deal with all of the parameters know except the interest rate. •For many application-type problems, this can become a difficult task •Termed, “rate of return analysis” •In some cases: •i can easily be determined •In others, trial and error must be used 5 Example: i unknown • Assume on can invest $3000 now in a venture in anticipation of gaining $5,000 in five (5) years. •If these amounts are accurate, what interest rate equates these two cash flows? 5 Example: i unknown • The Cash Flow Diagram is… $5,000 0 1 2 3 4 5 $3,000 •F = P(1+i)n •5,000 = 3,000(1+i)5 •(1+i)5 = 5,000/3000 = 1.6667 5 Example: i unknown • Solution: $5,000 0 1 2 3 4 5 •(1+i)5 = 5,000/3000 = $3,000 1.6667 •(1+i) = 1.66670.20 •i = 1.1076 – 1 = 0.1076 = 10.76% 5 For “i” unknown • In general, solving for “i” in a time value formulation is not straight forward. •More often, one will have to resort to some form of trial and error approach as will be shown in future sections. •A sample spreadsheet model for this problem follows. 5 Example of the IRR function =IRR($D7:$D12) Determination of Unknown Number of Years Section 6 6 Unknown Number of Years • Some problems require knowing the number of time periods required given the other parameters •Example: •How long will it take for $1,000 to double in value if the discount rate is 5% per year? •Draw the cash flow diagram as…. 6 Unknown Number of Years Fn = $2000 0 1 2 ... . . . ……. n P = $1,000 i = 5%/year; n is unknown! 56 6 Unknown Number of Years • Solving we have….. Fn = $2000 0 1 2 ... . . . ……. n P = $1,000 •Fn=? = 1000(F/P,5%,x): 2000 = 1000(1.05)x •Solve for “x” in closed form…… 6 Unknown Number of Years • Solving we have….. •(1.05)x = 2000/1000 •Xln(1.05) =ln(2.000) •X = ln(1.05)/ln(2.000) •X = 0.6931/0.0488 = 14.2057 yrs •With discrete compounding it will take 15 years to amass $2,000 (have a little more that $2,000) 6 No. of Years – NPER function • From Excel one can formulate as: =NPER(C23,C22,C20,C21) Spreadsheet Application – Basic Sensitivity Analysis Section 7 7 Basic Sensitivity Analysis • Sensitivity analysis is a procedure applied to a formulated problem whereby one can assess the impact of each input parameter relating to the output variable. •Sensitivity analysis is best performed using a spreadsheet model. •The procedure is to vary the input parameters within certain ranges and observe the change on the output variable. 7 Basic Sensitivity Analysis • By proper modeling, one can perform “what-if” analysis on one or more of the input parameters and observe any changes in a targeted output (response) variable •Commercial add-in packages are available that can be linked to Excel to perform such an analysis •Specifically: Palisade Corporation’s TopRank Excel add-in is most appropriate. 7 Basic Sensitivity Analysis • When you build your own models, devise an approach to permit varying at least one of the input parameters and store the results of each change in the output variable…then plot the results. •If a small change in one of the input parameters represents a significant change in the output variable then… •That input variable is “sensitive” 7 Basic Sensitivity Analysis • If an input parameter is deemed “sensitive” then some effort should go into the estimation of that parameter •Because it does influence the response (output) variable. •Less sensitive input parameters may not have as much effort required to estimate as those input parameters do not have that much impact on the targeted response variable. 7 Basic Sensitivity Analysis • When you build your own models, devise an approach to permit varying at least one of the input parameters and store the results of each change in the output variable…then plot the results. •If a small change in one of the input parameters represents a significant change in the output variable then… •That input variable is “sensitive” Summary • This chapter presents the fundamental time value of money relationships common to most engineering economic analysis calculations •Derivations have been presented for: •Present and Future Worth- P/F and F/P •Annuity Cash flows – P/A, A/P, F/A and A/F Summary • One must master these basic time value of money relationships in order to proceed with more meaningful analysis that can impact decision making. •These relationships are important to you professionally and in your personal lives. •Master these concepts!!!