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### ch04

Course: ECON ECON111, Spring 2009
School: Punjab Engineering...
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Word Count: 1651

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4 UTILITY CHAPTER MAXIMIZATION AND CHOICE The problems in this chapter focus mainly on the utility maximization assumption. Relatively simple computational problems (mainly based on CobbDouglas and CES utility functions) are included. Comparative statics exercises are included in a few problems, but for the most part, introduction of this material is delayed until Chapters 5 and 6. Comments on Problems 4.1 This is...

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4 UTILITY CHAPTER MAXIMIZATION AND CHOICE The problems in this chapter focus mainly on the utility maximization assumption. Relatively simple computational problems (mainly based on CobbDouglas and CES utility functions) are included. Comparative statics exercises are included in a few problems, but for the most part, introduction of this material is delayed until Chapters 5 and 6. Comments on Problems 4.1 This is a simple CobbDouglas example. Part (b) asks students to compute income compensation for a price rise and may prove difficult for them. As a hint they might be told to find the correct bundle on the original indifference curve first, then compute its cost. This uses the Cobb-Douglas utility function to solve for quantity demanded at two different prices. Instructors may wish to introduce the expenditure shares interpretation of the function's exponents (these are covered extensively in the Extensions to Chapter 4 and in a variety of numerical examples in Chapter 5). This starts as an unconstrained maximization problemthere is no income constraint in part (a) on the assumption that this constraint is not limiting. In part (b) there is a total quantity constraint. Students should be asked to interpret what Lagrangian Multiplier means in this case. This problem shows that with concave indifference curves first order conditions do not ensure a local maximum. This is an example of a fixed proportion utility function. The problem might be used to illustrate the notion of perfect complements and the absence of relative price effects for them. Students may need some help with the min ( ) functional notation by using illustrative numerical values for v and g and showing what it means to have excess v or g. This problem introduces a third good for which optimal consumption is zero until income reaches a certain level. This problem provides more practice with the Cobb-Douglas function by asking students to compute the indirect utility function and expenditure function in this case. The manipulations here are often quite difficult for students, primarily because they do not keep an eye on what the final goal is. This problem repeats the lessons of the lump sum principle for the case of a subsidy. Numerical examples are based on the Cobb-Douglas expenditure function. 4.2 4.3 4.4 4.5 4.6 4.7 4.8 10 11 y Solutions Manual 4.9 This problem looks in detail at the first order conditions for a utility maximum with the CES function. Part c of the problem focuses on how relative expenditure shares are determined with the CES function. This problem shows utility maximization in the linear expenditure system (see also the Extensions to Chapter 4). 4.10 Solutions 4.1 a. Set up Lagrangian = ts + (1.00 .10t .25s ) . = ( s / t )0.5 .10 t = (t / s )0.5 .25 s = 1.00 .10t .25s = 0 Ratio of first two equations implies t = 2.5 s Hence 1.00 = .10t + .25s = .50s. s=2 t=5 Utility = 10 b. New utility 10 or ts = 10 and t= t .25 5 = = s .40 8 t = 2.5s 5s 8 Substituting into indifference curve: 5s 2 = 10 8 s2 = 16 s = 4 t = 2.5 Cost of this bundle is 2.00, so Paul needs another dollar. Chapter 4/Utility Maximization and Choicey 12 4.2 Use a simpler notation for this solution: U ( f , c) = f 2 / 3 c1/ 3 a. = f 2 / 3 c1/ 3 + (300 20 f 4c ) = 2 / 3(c / f )1/ 3 20 f = 1/ 3( f / c) 2 / 3 4 c Hence, 5=2 c , 2c = 5 f f I = 300 Substitution into budget constraint yields f = 10, c = 25. b. With the new constraint: f = 20, c = 25 Note: This person always spends 2/3 of income on f and 1/3 on c. Consumption of California wine does not change when price of French wine changes. c. In part a, U ( f , c) = f 2 3c1 3 = 102 3 251 3 = 13.5 . In part b, U ( f , c) = 202 3251 3 = 21.5 . To achieve the part b utility with part a prices, this person will need more income. 23 13 2 3 1 3 23 2 3 1 3 Indirect utility is 21.5 = (2 3) (1 3) Ip f pc = (2 3) I 20 4 . Solving this equation for the required income gives I = 482. With such an income, this person would purchase f = 16.1, c = 40.1, U = 21.5. 4.3 U (c, b) = 20c c 2 + 18b 3b 2 a. U = 20 2c = 0, c U = 18 6b = 0, b So, U = 127. b. Constraint: b + c = 5 = 20c c 2 + 18b 3b 2 + (5 c b) = 20 2c = 0 c = 18 6b = 0 b = 5 c b= 0 c = 3b + 1 so b + 3b + 1 = 5, b = 1, c = 4, U = 79 c = 10 | b= 3 13 y Solutions Manual 4.4 U ( x, y ) = ( x 2 + y 2 )0.5 Maximizing U2 in will also maximize U. a. = x 2 + y 2 + (50 3x 4 y ) = 2x 3 = 0 x = 2y 4 = 0 y = 2x 3 = y 2 = 50 3x 4y = 0 two First equations give y = 4 x 3 . Substituting in budget constraint gives x = 6, y = 8 , U = 10. b. This is not a local maximum because the indifference curves do not have a diminishing MRS (they are in fact concentric circles). Hence, we have necessary but not sufficient conditions for a maximum. In fact the calculated allocation is a minimum utility. If Mr. Ball spends all income on x, say, U = 50/3. 4.5 U (m) = U ( g , v) = Min[ g 2, v] a. No matter what the relative price are (i.e., the slope of the budget constraint) the maximum utility intersection will always be at the vertex of an indifference curve where g = 2v. b. Substituting g = 2v into the budget constraint yields: 2 pg v + pv v = I or v = Similarly, g = I . 2pg + pv 2I 2pg + pv It is easy to show that these two demand functions are homogeneous of degree zero in PG , PV , and I. c. U = g 2 = v so, Indirect Utility is V ( pg , pv , I ) = I 2pg + pv d. The expenditure function is found by interchanging I (= E) and V, E ( pg , pv ,V ) = (2 pg + pv )V . Chapter 4/Utility Maximization and Choicey 14 4.6 a. If x = 4 y = 1 U (z = 0) = 2. If z = 1 U = 0 since x = y = 0. If z = 0.1 (say) x = .9/.25 = 3.6, y = .9. U = (3.6).5 (.9).5 (1.1).5 = 1.89 which is less than U(z = 0) b. At x = 4 y = 1 z =0 MU x / px = MU y / p y = 1 M U z / p z = 1/2 So, even at z = 0, the marginal utility from z is "not worth" the good's price. Notice here that the 1 in the utility function causes this individual to incur some diminishing marginal utility for z before any is bought. Good z illustrates the principle of complementary slackness discussed in Chapter 2. c. If I = 10, optimal choices are x = 16, y = 4, z = 1. A higher income makes it possible to consume z as part of a utility maximum. To find the minimal income at which any (fractional) z would be bought, use the fact that with the Cobb-Douglas this person will spend equal amounts on x, y, and (1+z). That is: px x = p y y = pz (1 + z ) Substituting this into the budget constraint yields: 2 pz (1 + z ) + pz z = I or 3 pz z = I 2 pz Hence, for z > 0 it must be the case that I > 2 pz or I > 4 . 4.7 U ( x, y ) = x y1 a. The demand functions in this case are x = I px , y = (1 ) I p y . Substituting these (1 ) into the utility function gives V ( px , p y , I ) = [ I px ] [(1 ) I p y ] = BIpx p y where B = (1 )(1 ) . 1 (1 ) b. Interchanging I and V yields E ( px , p y ,V ) = B px p y V . c. The elasticity of expenditures with respect to px is given by the exponent . That is, the more important x is in the utility function the greater the proportion that expenditures must be increased to compensate for a proportional rise in the price of x. 15 y Solutions Manual 4.8 a. 0.5 0.5 b. E ( px , p y , U ) = 2 px p y U . With px = 1, p y = 4, U = 2, E = 8 . To raise utility to 3 would require E = 12 that is, an income subsidy of 4. 0.5 0.5 0.5 c. Now we require E = 8 = 2 px 4 3 or px = 8 12 = 2 3 . So px = 4 9 -- that is, each unit must be subsidized by 5/9. at the subsidized price this person chooses to buy x = 9. So total subsidy is 5 one dollar greater than in part c. 0.3 0.7 d. E ( px , p y , U ) = 1.84 px p y U . With px = 1, p y = 4, U = 2, E = 9.71 . Raising U to 3 would require extra expenditures of 4.86. Subsidizing good x alone would require a price of px = 0.26 . That is, a subsidy of 0.74 per unit. With this low price, this person would choose x = 11.2, so total subsidy would be 8.29. 4.9 a. MRS = U/ x 1 = ( x y ) = px /p y for utility maximization. U/ y where = 1 (1 ) . 1 ( 1) = ( px p y ) Hence, x/y = ( px p y ) b. If = 0, x y = p y px so px x = p y y . 1 c. Part a shows px x p y y = ( px p y ) Hence, for < 1 the relative share of income devoted to good x is positively correlated with its relative price. This is a sign of low substitutability. For > 1 the relative share of income devoted to good x is negatively correlated with its relative price a sign of high substitutability. d. The algebra here is very messy. For a solution see the Sydsaeter, Strom, and Berck reference at the end of Chapter 5. 4.10 a. For x < x0 utility is negative so will spend px x0 first. With I- px x0 extra income, this is a standard Cobb-Douglas problem: px ( x x0 ) = ( I px x0 ), p y y = ( I px x0 ) Chapter 4/Utility Maximization and Choicey 16 b. Calculating budget shares from part a yields p xx (1 ) px x0 = + , I I lim( I ) py y I = px x0 I py p xx = , lim( I ) y = . I I 17
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Punjab Engineering College - ECON - ECON111
CHAPTER 5INCOME AND SUBSTITUTION EFFECTSProblems in this chapter focus on comparative statics analyses of income and own-price changes. Many of the problems are fairly easy so that students can approach the ideas involved in shifting budget constraints
Punjab Engineering College - ECON - ECON111
CHAPTER 6DEMAND RELATIONSHIPS AMONG GOODSTwo types of demand relationships are stressed in the problems to Chapter 6: cross-price effects and composite commodity results. The general goal of these problems is to illustrate how the demand for one particu
Punjab Engineering College - ECON - ECON111
CHAPTER 7PRODUCTION FUNCTIONSBecause the problems in this chapter do not involve optimization (cost minimization principles are not presented until Chapter 8), they tend to have a rather uninteresting focus on functional form. Computation of marginal an
Punjab Engineering College - ECON - ECON111
CHAPTER 8COST FUNCTIONSThe problems in this chapter focus mainly on the relationship between production and cost functions. Most of the examples developed are based on the Cobb-Douglas function (or its CES generalization) although a few of the easier on
Punjab Engineering College - ECON - ECON111
Chapter 8Strategy and Game TheoryGame Theory Game theory studies strategic interactions Game theory models portray complex strategic situations in a highly simplified and stylized setting abstract from personal and institutional details to get a mathem
Punjab Engineering College - ECON - ECON111
Chapter 8Strategy and Game TheoryGame Theory Game theory studies strategic interactions Game theory models portray complex strategic situations in a highly simplified and stylized setting abstract from personal and institutional details to get a mathem
Punjab Engineering College - ECON - ECON111
CHAPTER 9PROFIT MAXIMIZATIONProblems in this chapter consist mainly of applications of the P = MC rule for profit maximization by a price-taking firm. A few of the problems (9.29.5) ask students to derive marginal revenue concepts, but this concept is n
Punjab Engineering College - ECON - ECON111
Chapter 9Production FunctionsProduction Function The firms production function for a particular good (q) shows the maximum amount of the good that can be produced using alternative combinations of capital (k) and labor (l)q = f(k,l)Marginal Physical
Punjab Engineering College - ECON - ECON111
CHAPTER 10THE PARTIAL EQUILIBRIUM COMPETITIVE MODELThe problems in this chapter focus on competitive supply behavior in both the short and long runs. For short-run analysis, students are usually asked to construct the industry supply curve (by summing f
Punjab Engineering College - ECON - ECON111
Chapter 10Cost FunctionsDefinitions of Costs Accounting and economic costs are different Accountants stress out-of-pocket expenses, depreciation, and other bookkeeping entries economists focus more on opportunity cost Labor Costs to accountants, labor
Punjab Engineering College - ECON - ECON111
CHAPTER 11APPLYING THE COMPETITIVE MODELThe problems in this chapter are intended to illustrate the types of calculations made using simple competitive models for applied welfare analysis. Usually the problems start from a supply-demand framework much l
Punjab Engineering College - ECON - ECON111
Chapter 11Profit MaximizationThe Nature of Firms A firm is an association of individuals who have organized themselves for the purpose of turning inputs into outputs Different individuals will provide different types of inputs the nature of the contrac
Punjab Engineering College - ECON - ECON111
CHAPTER 12GENERAL EQUILIBRIUM AND WELFAREThe problems in this chapter focus primarily on the simple two-good general equilibrium model in which supply is represented by the production possibility frontier and demand by a set of indifference curves. Beca
Punjab Engineering College - ECON - ECON111
Chapter 12The Partial Equilibrium Competitive ModelMarket Demand Assume that there are only two goods (x and y) An individuals demand for x isMarket demand for X = x i ( px , py , I i )i =1nMarket DemandXpxIndividual 1s demand curvepxIndividu
Punjab Engineering College - ECON - ECON111
CHAPTER 13MONOPOLYThe problems in this chapter deal primarily with marginal revenue-marginal cost calculations in different contexts. For such problems, students primary difficulty is to remember that the marginal revenue concept requires differentiatio
Punjab Engineering College - ECON - ECON111
Chapter 13General Equilibrium and WelfarePerfectly Competitive Price System We assume all markets are perfectly competitive a large number of homogeneous goods both consumption goods and factors of production each good has an equilibrium price there
Punjab Engineering College - ECON - ECON111
CHAPTER 14TRADITIONAL MODELS OF IMPERFECT COMPETITIONThe problems in this chapter are of two types: analytical and essay. The analytical problems look at a few special cases of imperfectly competitive markets for which tractable results can be derived.
Punjab Engineering College - ECON - ECON111
Chapter 14MonopolyMonopoly A monopoly is a single supplier to a market This firm may choose to produce at any point on the market demand curve A monopoly exists because other firms find it unprofitable or impossible to enter the market Barriers to entr
Punjab Engineering College - ECON - ECON111
CHAPTER 15GAME THEORY MODELS OF PRICINGThe first six problems for this chapter are intended to illustrate the concept of Nash equilibrium in a variety of contexts. Many of them have only modest economic content, but are traditional game theory problems.
Punjab Engineering College - ECON - ECON111
Chapter 15Imperfect CompetitionShort-Run Decisions: Pricing &amp; Output When there are only a few firms in a market, predicting output and price can be difficult how aggressively do firms compete? how much information do firms have about rivals? how ofte
Punjab Engineering College - ECON - ECON111
CHAPTER 16LABOR MARKETSBecause the subject of labor demand was treated extensively in Chapter 9, the problems in this chapter focus primarily on labor supply and on equilibrium in the labor market. Most of the labor supply problems (16.116.6) start with
Punjab Engineering College - ECON - ECON111
CHAPTER 17CAPITAL MARKETSThe problems in this chapter are of two general types: (1) those that focus on intertemporal utility maximization and (2) those that ask students to make present discounted value calculations. Before undertaking the PDV problems
Punjab Engineering College - ECON - ECON111
CHAPTER 18UNCERTAINTY AND RISK AVERSIONMost of the problems in this chapter focus on illustrating the concept of risk aversion. That is, they assume that individuals have concave utility of wealth functions and therefore dislike variance in their wealth
Punjab Engineering College - ECON - ECON111
CHAPTER 19THE ECONOMICS OF INFORMATIONThe problems in this chapter stress the economic value of information and illustrate some of the consequences of imperfect information. Only a few of the problems involve complex calculations or utilize calculus max
Punjab Engineering College - ECON - ECON111
CHAPTER 20EXTERNALITIES AND PUBLIC GOODSThe problems in this chapter illustrate how externalities in consumption or production can affect the optimal allocation of resources and, in some cases, describe the remedial action that may be appropriate. Many
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Week 1 Lecture 1 An overview Introduction: Parametric Estimation vs. Nonparametric Estimation I: Parametric density estimation : Let Y1 , Y2 , . . . , Yn i.i.d. with density f (x), 2 R (or R2 , or R10 ). For instance, &quot; # 2 (x ) 1 exp ; 2 R; &gt; 0. f ; (x)
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Week 13 Lecture 24 Adaptive Wavelet Estimation Donoho and Johnstone (1995, JASA). Sketch of the proof. Consider the sequence model where yi = i + zi , i = 1; :; d and zi are independent normal N (0; 1) variables. Set r( ) = d 1 Pk^ k2 . The stein s 2 unbi
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Week 2 Lecture 3 General m . n Model: Let 2 Y1 ; Y2 , o. . , Yn i.i.d. R f; f (m) (x) dx M b Goal: Find f such that Z b f (x) f sup Ef 2Fon [0; 1] with density f 2 F, F =2CM n2m=(2m+1)(Note that K may not be nonnegative). The bias part is Z b Efn (x
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Week 3 Lecture 4 . n Model : Let Y1 ; Y2 , o. . , Yn i.i.d. on [ 1; 1] with density f 2 F , F = R 2 f; f (m) (x) dx M . b We have shown there is a kernel estimator fn such that supf 2FZb E fn (x)2f (x)Cn2m=(2m+1).Because it is hard to analyze the
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Week 4 Lecture 7 Optimal rate of convergence in the sup-norm Model : Let Y1 ; Y2 , . . . , Yn i.i.d. on [0; 1] with density f 2 F (M ), Hlder ball of order . Minimax rate : It can be shown that b inf sup E f^ f F (M ) 2f1Cn log n2 =(2 +1).For simp
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Week 7 Lecture 12 Fourier estimation and Linear Minimaxity An orthonormal basis for L2 ([0; 1]) is1 2k(x) (x)= =1 p2 cos (2 kt) ;2k(x) =p2 sin (2 kx) ; k1.f The periodic Sobolev class W2 (M ) is dened as F= f:jZ1f (m)2M ; f (j ) (0) = f (
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Week 8 Lecture 15 Model: yi = whereM i+ zi , zii:i:d:N (0; 1) , )2Mis an ellipsoid in l2 (N): ( =:Xia2 2 ii P a2 iM2 i. and ai ! 1, thenPinsker Theorem: Let s RN ( ; )=:MRL ( ; ) as! 0.We will only prove this result for the following
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Week 9 Lecture 16 Quadratic functional estimation Model: Observe the sequence model: yi =i:i:d: i+n1=2ziwhere zi N (0; 1). The model comes from the white noise model (or many other models): dy (t) = f (t) dt + n 1=2 dB (t) , t 2 [0; 1] . Let f i (t)
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Week 10 Lecture 18 Linear or nonlinear estimation The sparsity of the coe cients may be possibly quantied using lp norms k kp , which track sparsity for p &lt; 2, with smaller p giving more stringent measures. For instance, p when = 1= n, but apparently (1;
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Week 11 Lecture 20 An Introduction to Wavelet regression Denition: Wavelet is a function such that f2j=2 2j k ; j; k 2 Z gis an orthonormal basis for L2 (R). This function is called mother wavelet which can be often constructed , from father wavelet '. T
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Week 12 Lecture 22 A group of students present Donoho and Johnstone (PTRF, 1994)?1Lecture 23 Review from the presentation Suppose we observe yi = wherei+ zi ; i = 1; :; n,=1is constrained to lie in a ball of radius C dened by lp norm, n o = ; k kp C
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B-54 SOLUTIONSCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEYAnswers to Concepts Review and Critical Thinking Questions 1. 2. The four parts are the present value (PV), the future value (FV), the discount rate (r), and the life of the inves
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B-64 SOLUTIONSCHAPTER 6 DISCOUNTED CASH FLOW VALUATIONAnswers to Concepts Review and Critical Thinking Questions 1. 2. 3. 4. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and the number of payments, or th
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B-110 SOLUTIONSCHAPTER 7 INTEREST RATES AND BOND VALUATIONAnswers to Concepts Review and Critical Thinking Questions 1. 2. 3. No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Long-term Treasury securities have substantia
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B-130 SOLUTIONSCHAPTER 8 STOCK VALUATIONAnswers to Concepts Review and Critical Thinking Questions 1. 2. 3. The value of any investment depends on its cash flows; i.e., what investors will actually receive. The cash flows from a share of stock are the d
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CHAPTER 9 B-139CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIAAnswers to Concepts Review and Critical Thinking Questions 1. A payback period less than the projects life means that the NPV is positive for a zero discount rate, but nothing more
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B-158 SOLUTIONSCHAPTER 10 MAKING CAPITAL INVESTMENT DECISIONSAnswers to Concepts Review and Critical Thinking Questions 1. In this context, an opportunity cost refers to the value of an asset or other input that will be used in a project. The relevant c
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B-178 SOLUTIONSCHAPTER 11 PROJECT ANALYSIS AND EVALUATIONAnswers to Concepts Review and Critical Thinking Questions 1. 2. 3. Forecasting risk is the risk that a poor decision is made because of errors in projected cash flows. The danger is greatest with
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B-198 SOLUTIONSCHAPTER 12 SOME LESSONS FROM CAPITAL MARKET HISTORYAnswers to Concepts Review and Critical Thinking Questions 1. They all wish they had! Since they didnt, it must have been the case that the stellar performance was not foreseeable, at lea
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CHAPTER 13 B-207CHAPTER 13 RISK, RETURN, AND THE SECURITY MARKET LINEAnswers to Concepts Review and Critical Thinking Questions 1. Some of the risk in holding any asset is unique to the asset in question. By investing in a variety of assets, this unique
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CHAPTER 15 B-235CHAPTER 15 COST OF CAPITALAnswers to Concepts Review and Critical Thinking Questions 1. It is the minimum rate of return the firm must earn overall on its existing assets. If it earns more than this, value is created. Book values for deb
HKU - FINA - FINA1003
CHAPTER 1 INTRODUCTION TO CORPORATE FINANCEAnswers to Concepts Review and Critical Thinking Questions 1. Capital budgeting (deciding whether to expand a manufacturing plant), capital structure (deciding whether to issue new equity and use the proceeds to
HKU - FINA - FINA1003
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEYAnswers to Concepts Review and Critical Thinking Questions 1. 2. The four parts are the present value (PV), the future value (FV), the discount rate (r), and the life of the investment (t). Comp
HKU - FINA - FINA1003
CHAPTER 6 DISCOUNTED CASH FLOW VALUATIONAnswers to Concepts Review and Critical Thinking Questions 1. 2. 3. 4. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and the number of payments, or the life of the a
HKU - FINA - FINA1003
CHAPTER 7 INTEREST RATES AND BOND VALUATIONAnswers to Concepts Review and Critical Thinking Questions 1. 2. 3. No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Long-term Treasury securities have substantial interest rate
HKU - FINA - FINA1003
CHAPTER 8 STOCK VALUATIONAnswers to Concepts Review and Critical Thinking Questions 1. 2. 3. The value of any investment depends on its cash flows; i.e., what investors will actually receive. The cash flows from a share of stock are the dividends. Invest
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CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIAAnswers to Concepts Review and Critical Thinking Questions 1. A payback period less than the projects life means that the NPV is positive for a zero discount rate, but nothing more definitive can b
HKU - FINA - FINA1003
CHAPTER 10 MAKING CAPITAL INVESTMENT DECISIONSAnswers to Concepts Review and Critical Thinking Questions 1. In this context, an opportunity cost refers to the value of an asset or other input that will be used in a project. The relevant cost is what the
HKU - FINA - FINA1003
CHAPTER 11 PROJECT ANALYSIS AND EVALUATIONAnswers to Concepts Review and Critical Thinking Questions 1. 2. 3. Forecasting risk is the risk that a poor decision is made because of errors in projected cash flows. The danger is greatest with a new product b
HKU - FINA - FINA1003
CHAPTER 12 SOME LESSONS FROM CAPITAL MARKET HISTORYAnswers to Concepts Review and Critical Thinking Questions 1. 2. 3. 4. They all wish they had! Since they didnt, it must have been the case that the stellar performance was not foreseeable, at least not
HKU - FINA - FINA1003
CHAPTER 13 RISK, RETURN, AND THE SECURITY MARKET LINEAnswers to Concepts Review and Critical Thinking Questions 1. Some of the risk in holding any asset is unique to the asset in question. By investing in a variety of assets, this unique portion of the t
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CHAPTER 15 COST OF CAPITALAnswers to Concepts Review and Critical Thinking Questions 1. 2. 3. 4. 5. It is the minimum rate of return the firm must earn overall on its existing assets. If it earns more than this, value is created. Book values for debt are
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08/09 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT0302 Business Statistics Assignment 1(Do all. Hand in solutions to the ve starred questions on or before 4.2.09.) 1. (a) Give two examples of graphical presentation of d