Given a sample of 50 observations and 4 explanatory variables, what can you say about autocorrelation if ( a ) d = 1 . 05? ( b ) d = 1 . 40? ( c ) d = 2 . 50? ( d ) d = 3 . 97?
ARBAMINCH UNIVERSITY COLLEGE OF BUSINESS AND ECONOMICS DEPERTMENT OF ACCOUNTING AND FINANCE POST GRADUATE PROGRAM ASSIGNMENT OF Advance Corporate Finance (MSc.) AcFn-612 PREPARED BY: kedir Mohammed sage ID NO, PRBE/066/13 Submitted to: AYENNEWO . (PhD) Arba Minch University 2013e. Answer for advanced corporate finance question Problem 1: You are thinking about a portfolio where you put half your money in stock A (see problem 2) and half your money in the risk free asset (like a Treasury bill). The risk free asset has a return of 5%. a. What is the variance and standard deviation of the risk free asset? b. What is the covariance between stock A and the risk free asset? c. What is the expected return on your portfolio? d. What is the variance on your portfolio? e. What is the standard deviation on your portfolio? ANSWER a) By definition they are both zero (0). b) Again, by definition the answer is zero (0) c) Portfolio weights: WA=0.5 and WF=0.5: E (RP) = 0.5 × 0.0867 + 0.5 × 0.05 = 0.06835 (6.835%) d) VAR(RP) = 0.5 2 × 0.018856 2 = 0.0000889 e) SD (RP) = 0.0000889 0.5 = 0.009428 (0.9428%) Problem 2: Frozen Fruitcakes International Inc. is considering the following project. They want to introduce a new line of pastries and desserts. The sales for this division are expected to be $500,000 per year for each of the next 3 years. For this expansion you are able to use some of your existing machines that are currently not being used. Four years ago you paid $250,000 for these machines and the current market value of the machines is $110,000. You have been using a 5-year straight-line full depreciation on these machines. There is no need to buy any additional equipment. Variable costs for the division are projected at 65% of sales. Fixed costs are 100,000 per year. Total net working capital requirements are $75,000 at the start, $100,000 in year 1, and $50,000 in year 2. Net working capital will be recovered at the end of three years. The tax rate is 34%. a. What is the cash flow from assets for this project in each year? b. What is the NPV of this project if the discount rate is 10%? c. If Frozen Fruitcakes International Inc. is expected to pay a dividend of $1.45 next time, and the dividends are expected to grow at 4.5% forever, what is the cost of equity (or required rate of return on equity) for Frozen Fruitcakes International Inc. if the current stock price is $29. (Hint: you do not need any information from part a. or the previous page for answering this question). d. If Frozen Fruitcakes International Inc. has 10% debt in its capital structure, with a YTM of 6%, what is the weighed cost of capital, RWACC, for Frozen Fruitcakes International Inc.? e. What is the NPV of the new project if it has the same risk as Frozen Fruitcakes International Inc. as a whole? (Use the information in c. and d.) f. Assuming the dividend-growth model you used in part c. is correct, and the return on the market portfolio is 13% and the risk-free rate of return is 2%, what must be the beta of this project? (Hint: use the CAPM or SML) ANSWER a. Cash Flow = Operating Cash Flow - Net Capital Spending - Additions to Net Working Capital Operating Cash Flows for each year are EBIT+ Depreciation - Tax. Given that the firm does not purchase any new equipment, there are no incremental depreciation expenses from operating activities: EBIT = $500,000 - 325,000 - 100,000 = $75,000 Tax = 0.34 × 80,000 = $25,500 Operating Cash Flow = $75,000 - 25,500 = $49,500 per year. Opportunity Cost (in place of Net Capital Spending) = $110,000 - tax Tax = 0.34 × Profit, where Profit = Market Value - Book Value. Book Value = $250,000 - 4 × 50,000 (Depreciation per year) = $50,000 Profit = $110,000 - 50,000 = $60,000 and Tax = 0.34 × $60,000 = $20,400 Opportunity Cost = $110,000 - 20,400 = $89,600 Cash Flows: Year OCF NCS* ) Additions NWC Cash Flow 0 - -89,600 -75,000 -164,600 1 49,500 - -25,000 24,500 2 49,500 - +50,000 99,500 3 49,500 - +50,000** ) 99,500 * ) Opportunity Cost ** ) Recovery of NWC a) NPV = -164,600 + 24,500 / (1.1) + 99,500 / (1.1)2 + 99,500 / (1.1)3 = $14,659.96 b) P0 = D1 / (RE - g), hence we have RE = D1/P0 + g RE = 1.45/29 + 0.045 = 0.095 (9.5%) c) RD = 6% before tax, and hence (1-0.34) × 6% = 3.96% after-tax. RWACC = 0.1 × 3.96 + 0.9 × 9.5 = 8.946% d) If the project has the same risk as the overall firm, we can use the RWACC as the discount rate: NPV = -164,600 + 24,500 / (1.0985) + 99,500 / (1.0895) 2 + 99,500 / (1.0895) 3 = $18,649.51 e) From the CAPM model we have: 0.08946 = 0.02 + project × [0.13 - 0.02] project = 0.63 Problem 3: You are thinking about investing your money in the stock market. You have the following three stocks in mind: stock A, B, and C. You know that the economy is expected to behave according to the following table. You believe the likelihood of each scenario is identical (all states of nature have equal probabilities. You also know the following about your two stocks: State of the Economy RA RB RC Depression -20% 5% –5% Recession 10% 20% 5% Normal 30% -12% 5% Boom 50% 9% -3% a. Calculate the expected returns for stock A, B, and C b. Calculate the total risk for stock A, B, and C c. Calculate the correlation coefficient between stock A and B d. Calculate the correlation coefficient between stock A and C e. Calculate the correlation coefficient between stock B and C f. Based on your previous answers, if you have to form a portfolio consisting of two stocks, which two stocks would you put in your portfolio in terms of risk reduction? g. What is the expected return of a portfolio with equal investments in stock B and C? h. What is the covariance between the returns of the portfolio in part g. and those of stock A? i. Based on your previous answer, does it make sense to add stock A to the portfolio? Why? j. Calculate the expected return of a portfolio with equal investments in stock A and in the portfolio from part g.? k. What is the total risk of this portfolio? l. How can you tell that you have improved your risk-return tradeoff relative to the individual investments in A, B, and C? ANSWER a) E(RA) = 0.25 × -0.20 + 0.25 × 0.10 + 0.25 ×0.30 + 0.25 × 0.50 = 0.175 (17.5%) E(RB) = 0.25 × 0.05 + 0.25 × 0.20 + 0.25 ×-0.12 + 0.25 × 0.09 = 0.055 (5.5%) E(RC) = 0.25 × -0.05 + 0.25 × 0.05 + 0.25 ×0.05 + 0.25 × -0.03 = 0.005 (0.5%) a) SD(RA) = 0.2586 SD(RB) = 0.115 SD(RC) = 0.0456 (All calculations are similar to the previous problems) b) CORR(RA,RB)= –0.1639 c) CORR(RB,RC)= –0.1098 d) CORR(RA,RC)= +0.2441 e) Stocks A and B should give you the biggest diversification benefit because their correlation is the lowest. f) E(RP(B,C)) = 0.5 × 0.055 + 0.5 × 0.005 = 0.03 (3%) g) First find the returns on the portfolio for each state of nature: E(RP(B,C)|Depression) = 0.5 × 0.05 + 0.5 × -0.05 = 0.0 (0%) E(RP(B,C)|Recession) = 0.5 × 0.2 + 0.5 × 0.05 = 0.125 (12.5%) E(RP(B,C)|Normal) = 0.5 × -0.12 + 0.5 × 0.05 = -0.035 (-3.5%) E(RP(B,C)|Boom) = 0.5 × 0.09 + 0.5 × -0.03 = 0.03 (3%) Find the covariance between these returns and the returns for investment A: COV(RA,RP(B,C)) = 0.25 × (-0.2 - 0.175) × (0.0 - 0.03) + 0.25 × (0.1 - 0.175) × (0.125 - 0.03) + 0.25 × (0.3 - 0.175) × (-0.035 - 0.03) + 0.25 × (0.5 - 0.175) × (0.03 - 0.03) = –0.001 h) It only makes no sense to add stock A if the correlation between stock A and the portfolio is equal to +1. Looking at the returns for these two investments, one can easily conclude that this will not be the case. Hence, adding stock A should further diversify the portfolio and should improve the risk-return tradeoff. To calculate the correlation coefficient between the portfolio of B and C and stock A, we need to have the total risk of the portfolio with B and C first: SD (RP(B,C)) = [0.25 × (0.0 - 0.03) 2 + 0.25 × (0.125 - 0.03) 2 + 0.25 × (-0.035 - 0.03) 2