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**MANAGERIAL ECONOMICS An Analysis of Business Issues**

Howard Davies and Pun-Lee Lam Published by FT Prentice Hall

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**Investment Decisions and the Cost of Capital**

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

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**Capital and Capital Budgeting**

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.

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Investment 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.

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**Question for Discussion:**

What are the factors you would consider when making a choice among different investment projects? 1. 2. 3. 4.

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**Simple Technique for Appraisal of Investment**

Payback-period criterion: Payback period is the amount of time sufficient to cover the initial cost of an investment But it ignores any returns accrue after the pay-back period; ignores the pattern of returns; ignores the time value (time cost) of money.

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Example: Initial investment: $10 million Cash flow: $2 million per year Payback-period? If cash flow : $4 million per year

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Discounting On the other hand, the process of discounting or capitalization is to turn a future stream of services or income into its equivalent present value. When an expected future sum is turned into its equivalent present value, we say that it is discounted or capitalized.

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**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: PV= I (1+r)n

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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 = $100 (1+0.1)2 This means that the future amount of $121 (to be received after two years) is equivalent to a value of $100 at present.

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**Simple Technique for Appraisal of Investment**

Net-present-value technique: Net present value (NPV) is the difference between the present value of a future cash flow and the initial cost of the investment project; a firm should adopt a project if the expected NPV is positive.

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**or I r I1 I2 In NPV = -P + I0 + + … + + (1+r) (1+r)2 (1+r)n NPV = -P +**

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

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**Simple Technique for Appraisal of Investment**

Internal-rate-of-return method: Internal rate of return (IRR) is the rate of return that will equate the present value of a multi-year cash flow with the cost of investing in a project. Using the NPV equation: the IRR is the discount rate that renders the NPV of the project equal to zero.

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**P, n and the expected future cash returns (I) are known, we try to find IRR.**

If the IRR is greater than the market rate of interest r, it implies that the present value of the capital good (PV) is greater than its purchase price (P) and the firm should invest. Conversely, if IRR is smaller than r, it implies that PV is smaller than P and the firm should not invest. What are the differences between NPV technique and IRR method?

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**In most situations, the IRR method will yield the same results as the NPV method. But:**

there may be more than one value for the IRR that satisfies the NPV equation; if the sign of cash flows changes more than once in the life of the project, there may be multiple solutions the NPV rule uses actual opportunity cost of capital as the discount rate; the IRR rule assumes the shareholders can invest at the IRR IRR is expressed in terms of a percentage rate of return, it ignores the project’s absolute effect on the wealth of shareholders

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The Cost of Capital A firm will invest only if the expected rate of return exceeds the cost of capital. For a firm under rate-of-return regulation, if the permitted rate of return is set above the cost of capital (or the required rate of return), the firm will over-invest; conversely, if the permitted rate is set below the cost of capital, the firm will under-invest.

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**Weighted Average Cost of Capital (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 re D E (D + E) (D + E)

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**The Modigliani-Miller (M-M) 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

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**The Modigliani-Miller (M-M) 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

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**The Cost of Equity 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.

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**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 debt-equity ratio).

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**DVA: expected dividend D1 D2 D3 + + PV= + ... (1 + r) (1 + r)2**

discounted rate, cost of equity capital Dt PV= [ ] (1 + r)t 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

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D1 (1 + g) Let A = Let B = (1 + r) (1 + r) PV = A(1 + B + B2 + …) (1) B on both sides: PV B = A(B + B2 + B3 + …) (2) (2) - (1): PV(1 - B) = A 1 - B = 1 - = (1 + g) (1 + r) A PV = (1+r) -(1 + g) (1 - B) D1 (1 + r) (1 + r) PV = (r - g) (1 + r) (r - g) Given PV = P0 (1 + r) D1 r = + g P0 D1 = D0 (1 + g)

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**The Cost of Equity Capital**

2. Capital asset pricing model (CAPM): Cost of equity capital = risk-free rate beta (market rate - risk- free rate) Re = Rf + (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).

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**In the CAPM, the measure of market risk is known as beta ()**

In the CAPM, the measure of market risk is known as beta () 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.

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