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York SOS: Students Offering Support

FINE 2000 Final Exam-AID Review Package

Tutor: Felix Thai & Saima Kazi Email: [email protected]; [email protected]

Students Offering Support sponsors:

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York SOS: Students Offering Support Preface This document is directed to FINE 2000 students at the Schulich School of Business York University whom are looking for an additional resource to aid them with studying for the course midterm exam. It has been created with regard to the Winter 2009 course and is subject to change for future courses. The focus is primarily on information after the second midterm, Chapter 7-12, 14 References 1. Fundamentals of Corporate Finance: Third Edition 2. Sample questions were provided by Professor Ming Dong

Contents General Study Tips……………………………………………………………………………..3 Chapter 7 Overview……………………………………………………………………............4 Chapter 8 Overview…………………………………………………………………………….5 Chapter 9 Overview.……………………………………………………………………………6 Chapter 10 Overview…………………………………………………………………………...7 Chapter 11 Overview…………………………………………………………………………...8 Chapter 12 Overview…………………………………………………………………………...9 Chapter 14 Overview………………………………………………………………………….10 Sample Problems……………………………………………………………………………...11

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York SOS: Students Offering Support

General Study Tips Your exam format will be similar to your midterm in terms of organization. As usual, the best thing you can do is practice. You’ll have all your formulas, so don’t waste time trying to learn them by heart; just make sure you know how to use them. And need we mention the banal tips – manage your time wisely, don’t stress, come prepared with a calculator, get lots of sleep…?

Format of your final exam: Part 1: Multiple Choice Questions (40 marks) Part 2: Problems/short answers (60 marks)

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York SOS: Students Offering Support Chapter 7 Overview – NPV and Other Investment Criteria The following are ways firms determine how to evaluate investment opportunities: NPV Formula: NPV = PV – Required Investment (C0) Take into consideration the opportunity cost of capital, as it is the return you give up by investing in the project. IRR IRR is the rate of return that makes the NPV equal to 0 Formula: NPV = PV of Anticipated Cash Flows – Cost of Asset = 0 o You can determine IRR by trial and error followed by a graph o You can determine IRR by using finance calculator Payback Period Rule Payback period is the time needed to recover the initial investment. Discounted Payback Discounted payback is the time period it takes for the discounted cash flows generated by the project to cover the initial investment in the project. Book Rate of Return Book rate of return equals the company’s accounting income divided by its assets. Formula: Book rate of return = Book Income/Book Assets Profitability Index Pick the projects that generate the highest NPV per dollar of investment. Formula: NPV/Initial Investment (C0) Some points to note: o NPV has proven to be the only reliable measure of a project’s acceptability o The NPV rule can be adapted to deal with the following situations: o Mutually exclusive projects o The investment timing decision o Long vs short-lived equipment (unequal lives) o Replacing an old machine o Rules for project selection – a firm maximizes its value by accepting all positive NPV projects. With capital rationing, you need to select a group of projects which o Is within the company’s resources o Gives the highest NPV o When capital rationing is in place, NPV by itself cannot lead you to the correct decision: o You must combine NPV with Profitability Index *Take a look at Page 228, Table 7.3 to understand each investment decision rules

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York SOS: Students Offering Support Chapter 8 Overview – Using DCF Analysis to Make Investment Decisions When analyzing a project, first determine whether it is worth undertaking (using NPV) and then determine how to finance it. Incremental Cash flow = Cash flow with the Project – Cash flow without the project Aspects of incremental cash flow: o Sunk costs (do not include) o Opportunity costs (include) o Indirect Effects (beware, as it may not reflect incremental costs of the project) o Net working capital (CHANGE in net working capital; do not forget to recover the working capital at the end fo the project) o Financing costs Tax Shield (CCA) Formula: (Cdtc/r+d)(1+0.5r/1+r) – (Sdtc/r+d)(1/(1+r)t) o When computing NPV, we calculate the PV of operating cash flow separately from the PV of the CCA tax shields o CCA tax shields have an infinite life while projects have a fixed life Some points to note: o Discounting accounting income, rather than cash flow, will lead to erroneous decision o Projects are attractive because of the cash flow they generate, not for the profits o Look for incremental benefits: would this cash flow exist if the project did not exist? Thus, evaluate project on the basis of its incremental cash flow. o All cash flows should be after-tax o Do NOT forget to include working capital in your calculations and make sure to include CHANGE in working capital o Know the 3 methods of calculating CFO

*Definitely know how to calculate the CCA because it will definitely be on the exam (from personal experience) and do ALL the world problems related to CCA – especially the hard ones.

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York SOS: Students Offering Support Chapter 9 Overview – Project Analysis

The following are the different forms of analysis to determine if the project is right for the company: o Sensitivity Analysis – calculates the consequences of incorrectly estimating the variable in your NPV analysis o You develop the optimistic and pessimistic estimates for the underlying variables o Scenario Analysis – changing several variables at once in your NPV forecast o Simulation Analysis – uses a computer to generate hundreds, or even thousands, of possible scenarios. A probability distribution is assigned to each combination of variables to create an entire range of potential outcomes. o Break even Analysis – shows the level of sales at which a company breaks even o Accounting Break-even: Break even revenues = (Fixed Costs + Depreciation)/Profits per $1 of sales  A project which simply breaks even on an accounting basis will always have a negative NPV o NPV Break-even: More useful to focus on a point at which NPV switches from negative to positive o Decision Tree – to diagram the options in a project (sequential decisions and their possible outcomes) Some points to note: o A desirable characteristic in a project is flexibility – always remember that it plays a role in making the decision o Most firms use multiple capital budgeting methods to assess projects such as NPV, IRR and payback rules o For purposes of cash-flow forecasting, firms use quantitative methods, such as sensitivity analysis, as well as qualitative methods such as management’s subjective estimates

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York SOS: Students Offering Support Chapter 10 Overview – Risk, Return and Opportunity Cost of Capital

Formulas: Percentage Return = (capital gain + dividend)/initial share price Dividend Yield = dividend/initial share price Percentage Capital gain = capital gain/initial share price Rate of return on any security = Interest rate on t-bills + Market risk premium Expected market return = Interest rate on t-bills + Normal risk premium Portfolio Rate of Return = (fraction of portfolio in 1st asset x rate of return on 1st asset) + (fraction of portfolio on 2nd asset x rate of return on 2nd asset) Determine Portfolio Risk = σ 2p = w x2σ 2x + w y2σ 2y + 2w x w y σ x σ y ρxy

Risk of each portfolio: o The t-bill portfolio is a safe holding (safest) – government holding o Long-term bonds fall between t-bill portfolio and common stock one in its level of risk o Common stock portfolio is the riskiest option of the three portfolios

Some points to note: o For an investment with a risk that matches the risk on a market portfolio of common stocks, the project’s opportunity cost of capital would be the market rate of return o Diversification is important in reducing risk of investment because stocks do not move in exact lock step meaning poor performance of one stock is offset by strong performance of another o Know the difference between market risk and unique risk o Unique risk can be minimized by creating a diversified portfolio o Market risks are macro risks (cannot be eliminated by diversification) that are affected by change in interest rates, industrial production, inflation, exchange rates, and energy costs o A project with 0 risk must be discounted at t-bill rate o You can measure the risk, or volatility of a security by measuring the standard deviation, or variance, of its price over a period of time.

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York SOS: Students Offering Support Chapter 11 Overview – Risk, Return and Capital Budgeting Systematic risk/non diversifiable risk – common to the whole economy and known as market risk Nonsystematic risk/diversifiable risk – can be eliminated by diversification and known as unique risk Beta coefficient is a measure of how much systematic risk an asset has relative to an average risk asset Beta of a portfolio is the weighted average of the betas of the individual assets CAPM shows the relationship between the expected return on a security and its risk level, or beta Formula: CAPM = rj = rf + β (rm - rf) Expected Return = risk free rate + risk premium Beta of stock = β j = ρ jmσ j/σ σm Beta of stock = β j = cov(rj, rm)/σ σ m2; ρ jm = cov(rj, rm ) / σ j σ m Portfolio Beta = (fraction of portfolio in 1st asset x beta of 1st asset) + (fraction of portfolio in 2nd asset x beta of 2nd asset) Measuring Beta in practice: o Collecting data on the returns on the market portfolio over a specified time period o Collecting data on the returns on a stock over the same time period o Graphing the returns on the stock against the returns on the market o Drawing a regression line through the points and measuring its slope o The slope of the regression line is the stock’s beta Some points to note: o You can use CAPM to estimate the discount rates for new capital projects o A project’s required rate of return depends on the project’s risk o By definition, 1.0 is the average beta of a market portfolio of common stocks o More than 1.0 is sensitive to market fluctuations o Less than 1.0 is not so sensitive to market fluctuations

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York SOS: Students Offering Support Chapter 12 Overview – The Cost of Capital Formulas: Return on Debt: rD = (YTM)(1 – T) Expected Return = risk free rate + risk premium rE = rf + β (rm - rf) Expected Return = dividend yield + growth rE = DIV1/P0 + g Preferred Stock = rP = DivP/P0 D  P  E  WACC =  × (1− TC )rdebt  +  × rpref  +  × requity  V  V  V  Return on Assets: rassets = [D/V x (1-Tc)rdebt] + (E/V x requity) Vocabulary: The following all mean the same thing: o Required rate of return o Cost of capital o Appropriate discount rate Steps for calculating WACC: o Calculate the market value of each of the firm’s securities o Calculate the market weight of each security as a proportion of the firm’s total financing o Determine the required rate of return on each security o Calculate the weighted average of these required returns (do not forget to adjust the cost of debt for taxes) When you can and can’t use WACC: o Measure cost of capital for companies that issue different types of securities o Adjusts the cost of capital for tax-deductibility of interest payments o Use is restricted to certain types of projects o Sometimes used as a company-wide benchmark discount rate o Firms use it because they need a standard discount rate for average risk projects o If a project is not a carbon copy of the firm, then WACC can be used as a benchmark Some points to note: o What can companies do with excess cash? o Invest in project o Pay dividends to shareholders so they can reinvest $ o Beware of false precision – do not expect estimates of the cost of equity to be precise o Remember that the constant growth formula in the DDM will give you poor results if it is applied to firms with unsustainably high current growth rates o Even though higher debt increases WACC, there is implicit cost of using more debt o Flotation costs do not affect WACC

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York SOS: Students Offering Support Chapter 14 Overview – How Corporations Issue Security Venture capital is provided by venture capital firms, financial and investment institutions, such as banks and pension funds, and by government institutions Angel investor is a wealthy individual who invests in early-stage ventures Initial Public Offering (IPO): o Once a firm decides to go public, the first task is to select the underwriters o Obtain approval from the Board of Directors o File preliminary prospectus (red herring) with OSC o Revise prospectus to meet OSC approval, determine price o Sell securities to the public Some points to note: o IPO’s rise in value on first day of issue o Private placement is the sale of securities to a limited number of investors without public offering

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York SOS: Students Offering Support Sample Problems 1. Page 270 #35 – Chapter 8 Note: 1. The 1 year feasibility study is a sunk cost and should not be considered. 2. Price/volume increase factor = (1+ inflation)*(1+ unit sales increase) = (1.015)*(1.04)= 1.0556 For example to find sale revenue in year 2, we multiply year 1 revenue by the price/volume factor. T1

T2

T3

T4

T5

T6

Sales Revenue

255,000

269,178

284,144

299,942

316,619

334,223

Less: Variable cost Fixed cost

16,000 40,000

16,889.6 40,000

17,828.7 40,000

18,819.9 40,000

19,866.3 40,000

20,970.9 40,000

EBIT Less: Taxes35 %

199,000 69,650

212,288.4 74,300.9

226,315.3 79,210.4

241,122.1 84,392.7

256,758.7 89,865.5

273,252.1 95,638.2

Net Income

129,350

137,987.5

147,104.9

156,729.4

166,893.2

177,613.9

Net Working Capital

T0 40,000

T1 44,000

T2 48,400

T3 53,240

T4 58,564

T5 64,420

T6 70,862

4,000

4,400

4,840

5,324

5,856

6,442

Change in NWC

Investment: Land Building Equipment Net working Capital

T0 150,000 350,000 250,000 40,000 (790,000)

T1

T2

T3

T4

T5

T6

(4,000)

(4,400)

(4,840)

(5,324)

(5,856)

(6,442)

129,350

137,987.5

147,104.9

156,729.4

166,893.2

177,613.9 300,000 125,000

T0

T1

T2

T3

T4

T5

T6

(790,000)

125,350

133,587.5

142,264.9

151,405.4

161,037.2

596,171.9

1.000

.8929

.7972

.7118

.6355

.5674

.5066

(790,000)

111,925

106,495.9

101,264.1

96,218.13

91,372.5

302,020.7

∆ NWC Net Income (Excluding CCA tax shield) Salvage Value: Building Equipment

Total Cash flow (excluding CCA tax shield) Discount Factor (12%) PV excluding CCA tax shield

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York SOS: Students Offering Support Total PV (excluding CCA tax shields)

19,296.33

PV of CCA tax shield: Building =

= = 15,685.34 Manufacturing Equipment =

= = (59,121.62 x .94643) – 14,976.39 = 40,978.08 NPV = 19,296.33 + 15,685.34 + 40,978.08 = $ 75,959.75 Since the project has a positive net present value we should go ahead with it. 2. Page 362 #26 – Chapter 11 a.

False. The stock’s risk premium, not its expected rate of return, is twice as high as the market’s.

b.

True. The stock’s unique risk does not affect its contribution to portfolio risk but its market risk does.

c.

False. A stock plotting below the SML offers too low an expected return relative to the expected return indicated by the CAPM. The stock is overpriced. Investors will not want to pay that price to receive the stock’s cash flows. The price must fall to increase the stock’s rate of return.

d.

True. If the portfolio is diversified to such an extent that it has negligible unique risk, then the only source of volatility is its market exposure. A beta of 2 then implies twice the volatility of the market portfolio.

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York SOS: Students Offering Support e.

False. An undiversified portfolio has more than twice the volatility of the market. In addition to the fact that it has double the sensitivity to market risk, it also has volatility due to unique risk.

3. Page 387 #18 – Chapter 12 a.

r = rf + β(rm – rf) = 4% + 1.5 × 7% = 14.5%

b.

Total market value of Muskoka Real Estate is $6 million and the market value of the debt is $2 million. Thus the market value of its equity is $6 - $2, or $4 million. The current capital structure is 1/3 debt, 2/3 equity. Weighted average beta =

c.

×0

WACC =

(1 – Tc) × rdebt +

=

× (1 – .4) × 4% +

+

× 1.5

= 1.0

× requity × 14.5% = 10.47%

d.

If the company wishes to expand its present business then the WACC is a reasonable estimate of the discount rate since the risk of the proposed project is similar to the risk of the existing projects. Use a discount rate of 10.47%.

e.

The WACC of optical projects should be based on the risk of those projects. Using a beta of 1.2, the discount rate for the new venture is r = 4 + 1.2 × 7 = 12.4%

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