Cash Flow and Asset Based Interest Calculation in Cost Accounting

Münchener betriebswirtschaftliche Beiträge Munich Business Research &DVK )ORZ DQG $VVHW %DVHG ,QWHUHVW &DOFXODWLRQ LQ &RVW $FFRXQWLQJ Hans-Ulrich Küpper Ludwig-Maximilians-Universität München Fakultät für Betriebswirtschaft frie Hans-Ulrich Küpper1 Cash Flow and Asset Based Interest Calculation in Cost Accounting 2000-03 Juli 2000 1 Universität München, Fakultät für Betriebswirtschaft, Institut für Produktionswirtschaft und Controlling, Ludwigstraße 28 RG, D-80539 München, Tel. +49 89 2180 2093, email: kuepper@bwl.uni-muenchen.de. Cash Flow and Asset Based Interest Calculation in Cost Accounting Abstract Interest is an important issue in investment and finance theory. Despite this fact it is seldom analyzed in cost accounting. There the calculation of interest costs follows practical rules. Normally, interest costs are calculated on the basis of average capital and current assets, including inventories, work in progress, finished goods and accounts receivable. This paper first discusses a new proposition of Kloock and Maltry. It says that traditional interest calculation could be based on the Preinreich/Lücke-theorem. Using an easy example of a production process, we show that this thesis does not hold as the Preinreich/Lücke-theorem can be applied to different residual incomes. The amount of periodical interest depends on the realization principles which must be given in order to use this theorem and not conversely. Secondly, we show that interest calculation in cost accounting can be based on cash flows. Comparing this method of interest calculation with asset based interest calculation indicates two errors of the traditional interest calculation, the lack of interest yields for gain on sale and the interest on accounts receivable. To avoid these errors the traditional method of interest calculation has to be modified. Then asset based interest calculation can correctly be used in cost accounting. The analysis of interest calculation in cost accounting is an example for the application of investment theory to cost accounting. It shows that it is useful to connect cost accounting with investment and finance theory. By this way decision oriented cost accounting gets a theoretical fundament which allows to derive practical relevant results. Cash Flow and Asset Based Interest Calculation in Cost Accounting 1 1. Preface Calculating interest costs on the basis of assets2 is quite different from the calculation out of cash flows. An important question in theory and practice is, if both methods get the same results, and which of them can be founded by theory. At first sight the asset based method seems to follow thumb rules instead of a theoretical concept. On the contrary Kloock and Maltry3 claim, that the theorem of Preinreich/Lücke, which is used to calculate the residual income, gives a theoretical foundation of the traditional method. Furthermore, their thesis is in contrast to the thesis, that calculation of interest in cost accounting has to be based on cash flows. Therefore, the first issue in chapter 2 is to show the meaning of the Preinreich/Lücke-theorem (2.1). It does not give a foundation of traditional interest calculation, as this theorem presumes a profit realization principle and not conversely (2.2). In chapter 3 cash flow and asset based interest calculations are compared (3.1 and 3.2). Traditional calculation does not equal the cash flow based method, unless it is modified in two aspects. The modified method of asset based interest calculation is based on present or future value. Therefore it is an element to connect cost accounting with investment theory. The asset based method holds for full and direct costing (3.3). The results of this paper show, that decision oriented cost accounting has to be developed as a part of investment theory. This concept is a way to connect short-term (cost and revenue) planning with long-term (investment) planning. 2. Theoretical Foundation of Interest Costs by the Preinreich-Lücke-Theorem? 2.1. Conditions and Proposition of the Preinreich-Lücke-Theorem In a recent paper, Kloock and Maltry4 justify the calculation method of traditional cost accounting by the theorem of Preinreich/Lücke5. This theorem shows the calculation of the residual income. It says ”that the present value of future cash flows equals to the present value of future residual incomes”6 if two conditions are fullfilled7: (1) The sum of cash flows CFt equals the sum of gross incomes before interest costs G t T T ∑ G = ∑ CF t =0 t t =0 s (2) The capital stocks at the beginning of each period equal the difference between the accumulated gross incomes and the accumulated cash flows: t −1 t −1 Vt −1 = ∑ G s − ∑ CFs where V −1 = 0 and VT = 0 . s =0 s =0 2 Kilger (1988); Kloock/Sieben/Schildbach (1993); Schweitzer/Küpper (1998); Hummel/Männel (1986); Franz (1984). 3 Kloock/Maltry (1998). 4 Kloock/Maltry (1998). 5 Preinreich (1937); Lücke (1955). 6 Reichelstein (1997), p. 178. 7 Lücke (1955), pp. 313-317.; Lücke (1965); Kloock (1981). Cash Flow and Asset Based Interest Calculation in Cost Accounting 2 This implies, that the capital stock Vt −1 at the end of each period must be identical to the capital stock Vt at the beginning of the next period. Therefore this prerequisite corresponds to a condition of balance sheet identity:8 Vt = Gt − CFt + Vt −1 To get the residual incomes G t* , gross incomes Gt have to be diminished by interest costs on the capital stock Vt −1 at the beginning of each period. Then the present and the future value K T of residual incomes equals the present and the future value of cash flows: T T T K 0 = ∑ CFt (1 + i ) = ∑ (G t − iV t −1 )(1 + i ) = ∑ Gt* (1 + i ) −t −t −t t =0 t =0 t =0 T T T K T = ∑ CFt (1 + i ) = ∑ (Gt − iVt −1 )(1 + i ) = ∑ Gt* (1 + i ) T −t T −t T −t t =0 t =0 t =0 2.2. Interest Calculation in Traditional Cost Accounting and Influence of Income Realization on Periodical Interest In contrast to investment theory, interest costs in cost accounting are usually calculated on the basis of assets instead of cash flows, e. g. on the basis of average capital and current assets, Time 0 1 2 3 4 5 Cash flows Outflows for material 2400 Inflows from sold products 1700 1700 Assets Material 2400 1200 Products (finished goods) 1200 1200 Sales 1700 1700 Fig. 1: Example of a production process including inventories, work in progress, finished goods and accounts receivable. It is said that cost accounting looks at the input of the different input factors as material, labour and maschines as well as the production process of goods. Traditional Asset Based Asset Interest Calculation Material (2400+1200)/2*2*0,01 = 36 Products 1200*2*0,01 = 24 Accounts receivable 1700*2*2*0,01 = 68 Capital items deducted from total (-2400)*1*0,01 = -24 Sum of interest 104 Fig. 2: Traditional asset based interest calculation 8 Laux (1995), pp164-166.