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MANAGERIAL ECONOMICS An Analysis of Business Issues Howard Davies and Pun-Lee Lam Published by FT Prentice Hall 1 Chapter 17: Investment Decisions and the Cost of Capital Objectives: After studying the chapter, you should understand: 1. the concepts of capital budgeting and cost of capital 2. some simple techniques for the appraisal of investments 3. some financial models used to estimate the cost of capital 2 Capital Capital and and Capital Capital Budgeting Budgeting Capital: is the stock of assets that will generate a flow of income in the future. Capital budgeting: is the planning process for allocating all expenditures that will have an expected benefit to the firm for more than one year. 3 Investment Investment Appraisal Appraisal Firms normally place projects in the following categories: 1. Replacement and maintenance of old or damaged equipment. 2. Investments to upgrade or replace existing equipment 3. Marketing investments to expand product lines or distribution facilities. 4. Investments for complying with government or insurance-company safety or environmental requirements. 4 Question Question for for Discussion: Discussion: What What are are the the factors factors you you would would consider consider when when making making aa choice choice among among different different investment investment projects? projects? 1. 1. 2. 2. 3. 3. 4. 4. 5 Simple Technique Technique for for Appraisal Appraisal of of Simple Investment Investment Payback-period Payback-period criterion: criterion: Payback Payback period period isis the the amount amount of of time time sufficient sufficient to to cover cover the the initial initial cost cost of of an an investment investment But But itit ignores ignores any any returns returns accrue accrue after after the the pay-back pay-back period; period; ignores ignores the the pattern pattern of of returns; returns; ignores ignores the the time time value value (time (time cost) cost) of of money. money. 6 Example: Initial investment: Cash flow: $10 million $2 million per year Payback-period? If cash flow : $4 million per year Payback-period? 7 Discounting On the the other other hand, hand, the the process process of of discounting discounting On or capitalization capitalization isis to to turn turn aa future future stream stream of of or services or or income income into into its its equivalent equivalent present present services value. When When an an expected expected future future sum sum isis turned turned value. into its its equivalent equivalent present present value, value, we we say say that that itit into discounted or or capitalized. capitalized. isis discounted 8 The present value of a single future amount In general, present value (PV) refers to the value now of payments to be received in the future (I). The present value of I after n year at r is: I PV= (1+r)n 9 Suppose we try to find the present value of a single future amount of $121, to be received after two years. Since goods available in the future are worth less than the same goods available now, the future amount of $121 is worth less than $121 at present. Given the market rate of interest of 10%, its present value is: $121 (1+0.1)2 = $100 This means that the future amount of $121 (to be received after two years) is equivalent to a value of $100 at present. 10 Simple Technique Technique for for Appraisal Appraisal of of Simple Investment Investment Net-present-value Net-present-value technique: technique: Net Net present present value value (NPV) (NPV) isis the the difference difference between between the the present present value value of of aa future future cash cash flow flow and and the the initial initial cost cost of of the the investment investment project; project; aa firm firm should should adopt adopt aa project project ifif the the expected expected NPV NPV isis positive. positive. 11 I1 I2 In NPV = -P + I0 + +…+ + 2 (1+r) (1+r) (1+r)n or I NPV = -P + r where: P: =capital cost, accruing in full at the beginning of the project I1,2,…n =net cash flows arising from the project in years 1 to n r =the opportunity cost of capital 12 Simple Technique for Appraisal of Investment Internal-rate-of-return Internal-rate-of-return method: method: Internal Internal rate rate of of return return (IRR) (IRR) isis the the rate rate of of return return that that will will equate equate the the present present value value of of aa multi-year multi-year cash cash flow flow with with the the cost cost of of investing investing in in aa project. project. Using Using the the NPV NPV equation: equation: the the IRR IRR isis the the discount discount rate rate that that renders renders the the NPV NPV of of the the project project equal equal to to zero. zero. 13 P, P, nn and and the the expected expected future future cash cash returns returns (I) (I) are are known, known, we we try try to to find find IRR. IRR. If If the the IRR IRR isis greater greater than than the the market market rate rate of of interest interest r,r, itit implies implies that that the the present present value value of of the the capital capital good good (PV) (PV) isis greater greater than than its its purchase purchase price price (P) (P) and and the the firm firm should should invest. invest. Conversely, Conversely, ifif IRR IRR isis smaller smaller than than r,r, itit implies implies that that PV PV isis smaller smaller than than PP and and the the firm firm should should not not invest. invest. What are the differences between NPV technique and IRR method? 14 In In most mostsituations, situations, the the IRR IRR method method will willyield yield the the same same results resultsas asthe the NPV NPV method. method. But: But: ••there theremay maybe bemore morethan thanone onevalue valuefor forthe theIRR IRRthat that satisfies satisfiesthe theNPV NPVequation; equation;ififthe thesign signof ofcash cashflows flows changes changesmore morethan thanonce oncein inthe thelife lifeof ofthe theproject, project, there theremay maybe bemultiple multiplesolutions solutions ••the theNPV NPVrule ruleuses usesactual actualopportunity opportunitycost costof ofcapital capital as asthe thediscount discountrate; rate;the theIRR IRRrule ruleassumes assumesthe the shareholders shareholderscan caninvest investat atthe theIRR IRR ••IRR IRRisisexpressed expressedin interms termsof ofaapercentage percentagerate rateof of return, return,ititignores ignoresthe theproject’s project’sabsolute absoluteeffect effecton onthe the wealth wealthof ofshareholders shareholders 15 The The Cost Cost of of Capital Capital A A firm firm will will invest invest only only ifif the the expected expected rate rate of of return return exceeds exceeds the the cost cost of of capital. capital. For For aa firm firm under under rate-of-return rate-of-return regulation, regulation, ifif the the permitted permitted rate rate of of return return isis set set above above the the cost cost of of capital capital (or (or the the required required rate rate of of return), return), the the firm firm will will over-invest; over-invest; conversely, conversely, ifif the the permitted permitted rate rate isis set set below below the the cost cost of of capital, capital, the the firm firm will will under-invest. under-invest. 16 Weighted Weighted Average Average Cost Cost of of Capital Capital (WACC): (WACC): Cost of debt (rd): interest rate paid to creditors net of taxes Cost of equity (re): rate of return to shareholders in order to induce them to invest in the firm WACC : rd × D (D + E) + re × E (D + E) 17 The The Modigliani-Miller Modigliani-Miller (M-M) (M-M) Proposition Proposition Assumptions: •there are no taxes •the capital market is efficient and competitive •there are no transaction costs •there are no costs associated with bankruptcy •shareholders can borrow on the same terms as corporations •the cost of debt is constant, whatever the level of gearing 18 The The Modigliani-Miller Modigliani-Miller (M-M) (M-M) Proposition Proposition • If the assumptions hold, the total market value of two firms that are identical except for their levels of gearing must be the same, and their WACCs must be the same •If they were not the same, investors could improve their position by “arbitrage”, selling the shares of one and buying shares in the other, which would alter the relative prices of shars until the WACCs become equal •The level of gearing is therefore irrelevant to the WACC and the value of the firm 19 The The Cost Cost of of Equity Equity Capital Capital 1. Dividend valuation approach DVA (or dividend growth/discounted cash flow model): Rate of return = Dividend/Price + Expected growth rate D1 re = +g P0 The DVA relies on the equivalence of the market price of a stock, P0, with the present value of the dividends ( or cash flows) expected from the stock. The discount rate in finding the present value is considered to be the cost of equity capital. 20 Assumptions Assumptions There are few assumptions behind the method: (a) future dividends are expected to grow at a constant rate perpetually; (b) future dividends can be discounted at a constant cost of equity capital; (c) future dividends remain a constant proportion of earnings over time; (d) the firm is an all-equity-financed firm, or it has a constant level of leverage (or a constant 21 debt-equity ratio). DVA: expected dividend D1 D2 D3 PV= (1 + r) + (1 + r)2 + (1 + r)3 + ... discounted rate, cost of equity capital Dt PV= Σ [ ] t (1 + r) Assume D1 grows at constant rate of g: D1 D1(1+g) D1(1+g)2 + + ... PV= (1 + r) + (1 + r)2 (1 + r)3 22 D1 Let A = (1 + r) (1 + g) Let B = (1 + r) PV = A(1 + B + B2 + …) (1) × B on both sides: PV × B = A(B + B2 + B3 + …) (2) - (1): PV(1 - B) = A PV = A (1 - B) D1 (1 + r) PV = (1 + r) × (r - g) Given PV = P0 D1 r= P +g 0 (2) 1-B (1 + g) =1(1 + r) (1+r) -(1 + g) = (1 + r) (r - g) = (1 + r) D1 = D0 (1 + g) 23 The The Cost Cost of of Equity Equity Capital Capital 2. Capital asset pricing model (CAPM): Cost of equity capital = risk-free rate + beta (market rate - riskfree rate) Re = Rf + β (Rm - Rf) Therefore, if we use the CAPM to estimate a firm’s cost of equity capital (Re, or the required rate of return), we have to estimate a firm’s beta, the risk-free rate of return, and the market risk premium (the difference between Rm and Rf). 24 In the CAPM, the measure of market risk is known as beta (β). For example, the returns from an asset with a beta of 0.5 will fluctuate by 5% for each 10% fluctuation in the market’s returns. It has been shown that the required risk premium for an asset is directly proportional to its beta. Therefore, the holder of an asset with a beta of 0.5 will require a risk premium only half as large as that offered by the market as a whole. If the market is efficient, the cost of equity capital will be equal to the expected rate of return. 25 [...]... their levels of gearing must be the same, and their WACCs must be the same •If they were not the same, investors could improve their position by “arbitrage”, selling the shares of one and buying shares in the other, which would alter the relative prices of shars until the WACCs become equal The level of gearing is therefore irrelevant to the WACC and the value of the firm 19 The The Cost Cost of of... termsof ofaapercentage percentagerate rateof of return, return,ititignores ignoresthe theproject’s project’sabsolute absoluteeffect effecton onthe the wealth wealthof ofshareholders shareholders 15 The The Cost Cost of of Capital Capital A A firm firm will will invest invest only only ifif the the expected expected rate rate of of return return exceeds exceeds the the cost cost of of capital capital... rate -of- return rate -of- return regulation, regulation, ifif the the permitted permitted rate rate of of return return isis set set above above the the cost cost of of capital capital (or (or the the required required rate rate of of return), return), the the firm firm will will over-invest; over-invest; conversely, conversely, ifif the the permitted permitted rate rate isis set set below below the the cost. .. morethan thanonce oncein inthe thelife lifeof ofthe theproject, project, there theremay maybe bemultiple multiplesolutions solutions • the theNPV NPVrule ruleuses usesactual actualopportunity opportunitycost costof ofcapital capital as asthe thediscount discountrate; rate ;the theIRR IRRrule ruleassumes assumesthe the shareholders shareholderscan caninvest investat atthe theIRR IRR ••IRR IRRisisexpressed... 23 The The Cost Cost of of Equity Equity Capital Capital 2 Capital asset pricing model (CAPM): Cost of equity capital = risk-free rate + beta (market rate - riskfree rate) Re = Rf + β (Rm - Rf) Therefore, if we use the CAPM to estimate a firm’s cost of equity capital (Re, or the required rate of return), we have to estimate a firm’s beta, the risk-free rate of return, and the market risk premium (the. .. the the cost cost of of capital, capital, the the firm firm will will under-invest under-invest 16 Weighted Weighted Average Average Cost Cost of of Capital Capital (WACC): (WACC): Cost of debt (rd): interest rate paid to creditors net of taxes Cost of equity (re): rate of return to shareholders in order to induce them to invest in the firm WACC : rd × D (D + E) + re × E (D + E) 17 The The Modigliani-Miller... Technique for for Appraisal Appraisal of of Simple Investment Investment Net-present-value Net-present-value technique: technique: Net Net present present value value (NPV) (NPV) isis the the difference difference between between the the present present value value of of aa future future cash cash flow flow and and the the initial initial cost cost of of the the investment investment project; project; aa... Internal Internal rate rate of of return return (IRR) (IRR) isis the the rate rate of of return return that that will will equate equate the the present present value value of of aa multi-year multi-year cash cash flow flow with with the the cost cost of of investing investing in in aa project project Using Using the the NPV NPV equation: equation: the the IRR IRR isis the the discount discount rate... •there are no taxes the capital market is efficient and competitive •there are no transaction costs •there are no costs associated with bankruptcy •shareholders can borrow on the same terms as corporations the cost of debt is constant, whatever the level of gearing 18 The The Modigliani-Miller Modigliani-Miller (M-M) (M-M) Proposition Proposition • If the assumptions hold, the total market value of. .. renders renders the the NPV NPV of of the the project project equal equal to to zero zero 13 P, P, nn and and the the expected expected future future cash cash returns returns (I) (I) are are known, known, we we try try to to find find IRR IRR If If the the IRR IRR isis greater greater than than the the market market rate rate of of interest interest r,r, itit implies implies that that the the present ... 17: Investment Decisions and the Cost of Capital Objectives: After studying the chapter, you should understand: the concepts of capital budgeting and cost of capital some simple techniques for the. .. isis the the difference difference between between the the present present value value of of aa future future cash cash flow flow and and the the initial initial cost cost of of the the investment. .. in the other, which would alter the relative prices of shars until the WACCs become equal The level of gearing is therefore irrelevant to the WACC and the value of the firm 19 The The Cost Cost