1 Income statement and cash flows

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1 The Chinese University of Hong Kong Department of Systems Engineering & Engineering Management SEG 2510 Course Notes 12 for review and discussion (2009/2010) 1 Income statement and cash flows We went through a detailed example in Course Notes 11 Section 2, and hinted at the construction of an income statement with a standard template for better presentation. Try to go over the following table which summarizes the income statements for the five years. Can you find out which entries are given data and which are derived from calculations based on the MACRS depreciation tables and the US tax tables? Revenues 110, , , , ,000 Sales 35,000 Expenses O & M 40,000 40,000 40,000 40,000 40,000 Depreciation 33,330 44,440 14,810 7,410 0 Taxable income 36,670 25,560 55,190 62, ,000 Taxes 5,500 3,834 8,798 10,647 23,950 Net income 31,170 21,726 46,392 51,943 81,050 Net cash flow 64,500 66,166 61,202 59,353 81,050 A knowledge in understanding the internals of income statements is important for us to look deeper in cash flow statements and the extensive field of financial statement analysis. The task of filling-in-the-blanks for the rows of depreciation, taxable income, taxes, net income, and net cash flows is often not as straightfoward as assuming that those number entries are always provided. An income statement leads to cash flows, both before tax and after tax, referring to as the before-tax cash flow (BTCF) and after-tax cash flow (ATCF), respectively. How should BTCF and ATCF analysis be performed using NPV and IRR methods for choosing among alternatives? Are BTCF and ATCF related with cash flow statements? 1

2 2 BTCF and ATCF analysis: NPV and IRR There is an important missing component for BTCF in the income statement of the previous section: CF0 = 100, 000, which is the initial capital budget for the drill press in Year 0. From the given data in the first three rows of the income statement, we obtain BTCF as the following cash-flow sequence: {CF0, C1, C2,..., C5} BT = { , 70000, 70000,...,105000} Performing an BTCF analysis requires a knowledge of the before-tax discount rate x BT (or commonly referred to as the MARR BT ), giving NPV BT = CF0 + 0 = CF0 + 5 i=1 5 i=1 Ci BT (1 + x BT ) i Ci BT (1 + IRR BT ) i Finding the ATCF from BTCF appears to be straightforward if one omits the details and uses the data from the row on net cash flows, i.e., {CF0, C1, C2,..., C5} AT = { , 64500, 66166,...,81050} Assuming a knowledge of the after-tax discount rate x AT (or the MARR AT ) is available, an ATCF analysis can be readily carried out by using the aftertax cash flows and after-tax MARR in the NPV AT and IRR AT equations. 2.1 Depreciation, Taxable income, and Taxes The transition from BTCF to ATCF involves more complications than that shown in the row of net cash flows of the income statement. Let BTCF k, ATCF k stand for the before-tax and after-tax cash flows in Year k, and R k, E k, d k, X k be the revenues, expenses, depreciation, and taxable income, respectively, for that year. d k has to be determined from the value of k and the MACRS percentage table; and the following expressions then define the transition process: X k = R k E k d k ATCF k = BTCF k tax i (X k ) where i is the tax range index i for the taxable income X k based on a given tax table. When approximation can be taken by assuming a single tax rate r tax, tax i (X k ) can be replaced by r tax X k. Another way to present the transition from BTCF to ATCF is to use a table with additional columns for depreciation, taxable income, and taxes: 2

3 k BTCF Depreciation Taxable income Taxes ATCF 0-100, , ,000 33,330 36,670 5,500 64, ,000 44,440 25,560 3,834 66, ,000 14,810 55,190 8,798 61, ,000 7,410 62,590 10,647 59, , ,000 23,950 81, MARR: before tax and after tax The BTCF and ATCF give adequate information for finding IRR BT and IRR AT. However, the evaluation of NPV BT and NPV AT require knowledge of MARR which may be different before tax and after tax. A common expression to relate the two MARR is MARR BT = MARR AT 1 r tax However, this is not a result which has a sound theoretical basis. With a small (large) tax rate, the after-tax MARR is always less than before-tax MARR with a small (large) difference. 3 Cash flow statement Income statement and cash flow statement are two important components in financial statement analysis. While income statement focuses on the derivation of the net income based on revenues and expenses, cash flow statement has a structural decomposition of cash flows from operation, investing, and financing activities with reference to the net income and net cash flows. However, income statement and cash flow statement are not independent of each other but are related. In order to maintain consistency between the two and often with the latter following the former, some changes in the structure of the income statement described in Section 1 is often necessary. For example, the last row for the net cash flow in the income statement is deleted from the income statement and put at the end of the cash flow statement. Net income is often used to provide a common linkage between the two, as the last row of the former and the first row of the latter. Additional rows for both statements are needed for a broader classification. Referring to the same example used in Section 1, a typical template for 3

4 cash flow statement has the following description which provides a linkage with the income statement: Operating activities Net income 31,170 21,726 46,392 51,943 81,050 Depreciation 33,330 44,440 14,810 7,410 0 Investing activities Investment -100,000 Salvage 35,000 Financing activities Borrowed funds Principal repayment Net cash flow -100,000 64,500 66,166 61,202 59,353 81,050 There is a problem in this direct linkage, as the last column does not add up correctly. Apparently this is due to the inclusion of the salvage value, which has also been taken into consideration in obtaining the net income. Proper accounting procedure, such as adjustments to reconcile net income to net cash, is often required as additional rows under operating activities. 4 Supply and demand: basics of economics Understanding the price/quantity relationships between demand and supply of goods often requires graphical interpretation of the price curves of demand and supply, under the influence of various factors affecting curve shifting and movement along curves. 4.1 Demand curve: movement and shift The law of demand specifies a general relationship between price P and quantity demanded Q in a demand curve, where an increase in Q leads to a fall in P. Typically, P = k/q or a linearly decreasing function with price-intercept P 0 and quantity-intercept Q 0 is used for the demand curve. Movement along the demand curve shows the marginal benefit or the willingness and ability to pay as the quantity falls or rises. Downward price movement implies an increase of quantity demanded; whilst upward price movement indicates a decrease in quantity demanded, ceteris paribus. 4

5 Demand changes in terms of right curve shifting and left curve shifting correspond to demand increases and decreases, respectively. Demand curve shifting depends mainly on 6 factors: 1) prices of related goods (substitutes P s, and complements P c ); 2) expected future price P f ; 3) income I; 4) expected future income I f ; 5) population; 6) preferences Substitution and income effects There are two major effects, namely substitution effect and income effect. Substitution effect relates with the rise of relative price or opportunity cost of the subsitution good and cause an increase in quantity demanded, i.e., the increase/decrease in P s causes a right/left shift of the demand curve. The effect of supplements is just the opposite of substitutes, i.e., the decrease/increase in P c causes a right/left shift of the demand curve. The income effect differentiates between normal goods and inferior goods in their sharply contrasting influence on the demand curve. For normal goods, an increase/decrease in income I causes the demand curve to shift right/left because of increase/decrease in quantity demanded. For inferior goods, the opposite income effect will result Future price and future income Consumers expectation of future price and future income affect the demand curve in a similar way, An expected increase/decrease in future price (or future income) will shift the demand curve to the right/left because of increased/decreased quantity demanded Problem solving using graphical qualitative reasoning Answering questions like What is the effect on the price of a tape and the quantity of tapes sold (i) if the price of the CD rises; (ii) if the consumers incomes increase? requires a qualitative reasoning process based on our knowledge on demand curve. Let us go through the exercise and try to draw appropriate curves to illustrate. As CD is a substitute good for tape and for (i), the increase in price of a substitute (the CD) will right shift the demand curve. Assuming ceteris paribus and no change in the supply curve (discussed later), a new equilibrium will reach for a higher price and a larger quantity demanded for tapes. For (ii) we have the income effect and expect the demand curve to shift right by assuming that tapes are normal goods. Again, an equilibrium will reach for a higher price and a larger quantity demanded for tapes. However, if we assume that tapes are inferior goods 5

6 then a left shift in the demand curve will result in a lower price and smaller quantity demanded for tapes. 4.2 Supply curve: movement and shift The law of supply specifies a general relationship between price P and quantity supplied Q in a supply curve, where an increase in Q leads to a rise in P because of marginal cost increases. Typically, P = P 0 + kf(q) (where P 0 is the minimum supply price and f(q) is an increasing function of Q) or simply a linearly increasing function P = P 0 + kq with k > 0. There are 5 major factors affecting the supply curve: 1) prices of productive resources P p ; 2) prices of related goods produced (substitutes P ps and complements P pc ); 3) expected future prices; 4) number of suppliers; and 5) technology. Comparing with the factors of the demand curve, there are similarities and differences. There are unique supply factors, for example, P p is related with productive resources which directly affect the minimum supply price P 0 and cause an upward lift or downward drop of the supply curve. The technology factor tends to give a right shift to the supply curve due to technology advances. The number of suppliers factor acts in similar way as the population factor in demand. As for the prices of related goods produced, the substitutes P ps in supply act in a way like the complements in demand; while the complements P pc in supply act like the substitutes in demand, for the supply curve shifting. 4.3 Market equilibrium The law of demand and the law of supply interact to give the intersection points due to the various factors affecting demand and supply. These intersection points are called equilibrium points which provide the price and quantity information at market equilibrium after a reasonable settling time. Considering the left/right shift possibilities of both the demand and supply curves, a number of different scenarios may arise to give different predictions of the rise/fall of price and increase/decrease of quantity. Mathematically, if models on the supply and demand curves are available, more quantitative information on the equilibrium point can be derived. For example, for the demand curve P = k d /Q and supply curve P = P 0 + k s Q, the equilibrium point is governed by a quadratic equation k s Q 2 + P 0 Q = k d 6

7 It is often not necessary to use mathematical equations to handle equilibrium. Some typical questions (e.g, from Parkin 1 ) can readily be answered using qualitative reasoning from graphs: [Question 1:] If the number of pizza producers increases, then the equilibrium price of a pizza falls and the equilibrium quantity increases. [Solution:] From the number of suppliers factor, there is a right shift in the supply curve of pizza. The new equilibrim point on the demand curve indicates a price decrease with a corresponding increase in quantity demanded. [Question 2:] Draw necessary diagram to justify the following statement: An increase in demand and an increase in supply bring in an increased quantity but an uncertain price change. [Solution:] Draw two parallel lines to the right of the supply curve: one closer and one further apart, and find the two intersection points with the right-shifted increased demand curve. Both points indicate an increased quantity; but the one closer may indicate a rise in price while the one further apart may indicate a price drop. 5 Price elasticity of demand Elasticity has been an important concept in physics. Hooke s law states that precisely as E L/L = F/A for a spring with length L and area A will have a change in length L under the action of a force F; it is a linear law with the elasticity constant E. In economics, the price elasticity of demand is defined as η = Q Q / P P = Q P P Q where P is the price and Q is the quantity demanded of the good in the market. It expresses a linear relationship in the change of quantity demanded Q under the action of a change P in the market price. More commonly, the price elasticity of demand η is verbally stated as the ratio of the percentage change of quantity demanded over the percentage change of price, ceteris paribus. 1 M. Parkin, Economics, 8th Edition, Pearson International Edition,

8 Depending on the different values of η (usually positive, or taken to be the absolute value of Q P P Q ), we have the classification of elasticity: perfectly inelastic (η = 0); inelastic (0 < η < 1); unit elastic (η = 1); elastic (η > 1); and perfectly elastic (η ). How would the price elasticity of demand affect the demand curve? The demand curve is a vertical line when we have perfectly inelastic demand (because the slope P/ Q, or there is no change in quantity demand despite large change in price). The demand curve is a horizontal line when we have perfectly elastic demand (because the slope P/ Q = 0, or there is no change in price despite large change in quantity demand). [Question 1:] Prove that the demand curve P = k Q elasticity of demand independent of k. will have a unit price [Solution:] Since P = k/q, dp/dq = k/q 2. Therefore, P/ Q = k/q 2, and Q P P Q = 1. [Question 2:](from Parkin) Suppose the price elasticity of demand for pizza is Then if the price of pizza rises by 10 percent, the quantity of pizza demanded decreases by 20.0 percent. [Solution:] Since η = 2 and P/P = 10%, we have Q P 2 10% = 20%. 5.1 Assignment 5 problem P Q = 2 implies that Q/Q = Consider a straight-line demand curve with quantity-intercept Q 0 and priceintercept P 0 ; and (Q, P) is a general point on this demand curve with Q = kq 0 (where 0 k 1). Show that the price elasticity of demand at (Q, P) is given by 1 k k. Discuss the possibilities for having unit elastic, perfectly elastic, and perfectly inelastic demands. 8