I need help doing these 10 problems, please help! Question 1

Consider the following mutually exclusive investments

		1	2
Investment A:	-100	20	120
Investment B:	-100	100	31.25

• Find IRRs for both projects
• Draw a graph, where you will show the NPV of each project as a function of its discount rate (i.e NPV on the vertical axis and r on the horizontal axis). Both NPVs should be on the same graph.
• Find the cross over rate
• Please describe as fully as possible which project is the best.

Question 1 Consider the following mutually exclusive investments T=0 1 Investment A: -100 20 Investment B: -100 100 2 120 31.25 a. Find IRRs for both projects b. Draw a graph, where you will show the NPV of each project as a function of its discount rate (i.e NPV on the vertical axis and r on the horizontal axis). Both NPVs should be on the same graph. c. Find the cross over rate d. Please describe as fully as possible which project is the best. Question 2 Price Coupon YTM Time to maturity ? 0 2% 1 year 890 5% ? 2 years 800 ? 5% 3 years Assume semi-annual coupon payments. Find missing values in the table above. Please show details of your solution. Question 3 (a) The risk-free rate of return is 8 percent, the required rate of return on the market, E[Rm] is 12 percent, and Stock X has a beta coefficient of 1.4. If the dividend expected during the coming year, D 1, is $2.50 and g = 5%, at what price should Stock X sell? (b) Now suppose the following events occur simultaneously: (1) The Federal Reserve Board increases the money supply, causing the riskless rate to drop to 7 percent. 1 (2) Investors' risk aversion declines: this fact, combined with the decline in RF, causes RM to fall to 10 percent. (3) Firm X has a change in management. The new group institutes policies that increase the growth rate to 6 percent. Also, the new management stabilizes sales and profits, and thus causes the beta coefficient to decline from 1.4 to 1.1. After all these changes, what is Stock X's new equilibrium price? (Note: D1 goes to $2.52.) Question 4 Given that the risk-free rate is 5%, the expected return on the market portfolio is 20%, and the standard deviation of returns to the market portfolio is 20%, answer the following questions: a. You have $100,000 to invest. How should you allocate your wealth between the risk free asset and the market portfolio in order to have a 15% expected return? b. What is the standard deviation of your portfolio in (a)? Question 5 Eureka Ltd, is a rapidly growing chain of retail stores. A security analyst's report indicates that debt yielding 8% composes 25% of Eureka's overall capital structure. Furthermore, Eureka's dividends are expected to grow at a rate of 9% per year. Currently, common stock in the company is priced at $30, and it should pay $1.50 per share in dividends during the coming year. The risk free rate is currently equal to 2% and the expected return on the SP 500 index is 10%. The company's estimated beta is 1.5. a. Calculate Eureka's cost of equity using dividend growth model b. Calculate Eureka's cost of equity using the capital asset pricing model c. Assuming a 40% tax rate, calculate Eureka's weighted average cost of capital. Question 6 One year ago your company purchased a machine for $110,000. You have learned that the new, much better machine is available for $150,000. In will be depreciated on a straight line basis and has no salvage value. You expect the machine to produce $60,000 per year in revenue and cost $20,000 per year to operate for the next ten years. The current machine is expected to produce $40,000 per year in revenue and also costs $20,000 per year to operate. The current machine's depreciation expense is $10,000 per for the next 10 years, after which it will be discarded. It will have no salvage value. The market value 2 of the current machine today is $50,000. Your company's tax rate is 45% and the opportunity cost of capital is 10%. Should your company replace its year-old machine? Question 7 The Amazing Video Co. has just paid an annual dividend of 40 cents. You forecast that for the next five years dividends will grow at the rate of 25% a year over the period. From year five on, you expect the growth rate to fall to the industry average of 8% and to remain at this level forever after. a. Draw the time line showing the dividends per share of this stock for years 1 through 6. b. If the expected rate of return for this stock is 15%, calculate its price. Question 8 a. What effective annual rate results from daily compounding of 8%? b. Suppose that you have a mortgage on your house. You make monthly payments. Your bank quotes APR equal 8.5% per year. What is your effective annual rate? Question 9 a. How long will it take to triple your money with an interest rate of 10 percent? b. On the advice of your broker ten years ago, you invested in a $6 stock that is now selling for $30. At what rate has your capital grown? c. Your father is about to retire. His firm has given him the option of retiring with a lump sum of $50,000 or an annuity of $8,000 for ten years. Which is worth more now, if the discount rate is (1) 6%, (2) 18%? d. You are offered a $15,000 life insurance policy requiring thirty annual payments of $195 each. What is the compound value of the payments that you will have made after the policy is paid up, assuming that the discount rate is 10 percent? Question 10 Suppose that an analyst has noticed that the return on equity of the XYZ Company has declined from 2012 to 2013. (millions) 2013 Sales 2012 $1,000 $400 Total assets 3 $90 $2,000 Taxes $30 $100 Interest expense $380 $30 Earnings before interest and taxes $900 $2,000 Shareholders' equity $1,250 a. Fill in the following table (please show detailed calculations for each ratio, including the formula used, below that table): 2013 2012 Return on equity Return on assets Financial leverage ratio Total asset turnover Net profit margin Operating profit margin b. Using the DuPont formula, explain the source of this decline. 4 $1,000 1 A B Year -100 20 120 -100 100 31.25 IRR 20.00% 25.00% Rate A 0% $ 5% $ 10% $ 15% $ 20% $ 25% $ 30% $ 40.00 27.89 17.36 8.13 -7.20 -13.61 B $ $ $ $ $ $ $ 31.25 23.58 16.74 10.59 5.03 -4.59 NPV profile $50.00 $40.00 $30.00 $20.00 $10.00 $- 0% 5% 10% 15% 20% $-10.00 $-20.00 A Cross over rate year A 0 1 2 Cross over rate B -100 20 120 difference -100 0 100 -80 31.25 88.75 10.94% Project B is better because of higher IRR B 25% 30% Price $ 980.30 890 800 Time to maturity 2% 1 5.65% 2 5% 3 Coupon YTM 0 5% 4.7% Used excel formulas to calculate Solution a Rsk free rate Expected return Beta D1 g 8% 12% 1.4 2.5 5% First, calculate the return of the stock Return = Return = Price of the stock = Price of the stock = b Risk free rate + beta * (expected return - risk free rate) 13.60% D1 / (r-g) $ 29.07 Rsk free rate Expected return Beta D1 g 7% 10% 1.1 2.5 5% First, calculate the return of the stock Return = Return = Risk free rate + beta * (expected return - risk free rate) 10.30% Price of the stock = Price of the stock = D1 / (r-g) $ 47.17 Solution Risk free ra Return Stdev 5% 20% 20% Return Investment Weight Weighted return 32880 0.3288 1.64% 67120 0.6712 13.42% 100000 15.07% Risk free Market 5% 20% Risk free Market Weight 1% 0.3288 20% 0.6712 Stdev of portfolio 13.75% Solution Debt yield Debt proportion Growth Price Expected dividend Risk free Return Beta 8% 25% $ $ $ 9% 30.00 2.00 2% 10% 1.50 a Return using DDM 15.67% b Retru using CAPM Return = 14.0% c After tax cost of debt Average cost of equity Weight 4.80% 25% 14.83% 75% Cost of capital 12.33% Solution Cost of old Cost of ne 110000 150000 Revenue Cost 60000 20000 Old revenu Old cost Depreciatio Current pri 40000 20000 10000 50000 Year Initial inve Cash flow Depreciation EBIT Tax Net income Add: Depreciation Cash flow Rate NPV 0 100000 -100000 10% $ 84,337.01 Yes, the new project should be accepted 1 2 3 4 5 6 7 8 9 10 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 Solution Year 0 Dividend 1 0.4 2 0.5 3 0.625 4 0.78125 5 0.976563 6 1.054688 P5 = 15.06696 0 Cash flow 1 0.4 2 0.5 3 0.625 4 0.78125 5 16.04353 P0 = $ 9.56 a Rate Compound 8% 365 EAR = b 8.33% Rate Compound 8.50% 12 EAR = 8.84% Solution a Interest rate triple mon b Nper PV FV 10 6 30 rate 17.46% c 10% 11.5 years Lum sum Annuity Nper 50000 8000 10 Rate 6% PV of annui $ 58,880.70 Annuity amount has higher PV, thus annuity is better Annuity Nper 8000 10 Rate 18% PV of annui $ 35,952.69 Lumpsum is better d PV Pmt Rate Nper FV 15000 195 10% 30 $ 32,076.33 Solution 2013 21.60% 13.50% 1.6 0.5 27.00% 40.00% 2012 26.00% 13.00% 2 0.45 28.89% 42.22% Financial leverage ratio Total asset turnover Net profit margin 1.6 0.5 27.00% 2 0.45 28.89% ROE 21.60% 26.00% ROE ROA Financial leverage ratio Total asset turnover Net profit margin Operating profit margin DuPont 1 A B Year -100 20 120 -100 100 31.25 IRR 20.00% 25.00% Rate A 0% $ 5% $ 10% $ 15% $ 20% $ 25% $ 30% $ 40.00 27.89 17.36 8.13 -7.20 -13.61 B $ $ $ $ $ $ $ 31.25 23.58 16.74 10.59 5.03 -4.59 NPV profile $50.00 $40.00 $30.00 $20.00 $10.00 $- 0% 5% 10% 15% 20% $-10.00 $-20.00 A Cross over rate year A 0 1 2 Cross over rate B -100 20 120 difference -100 0 100 -80 31.25 88.75 10.94% Project B is better because of higher IRR B 25% 30% Price $ 980.30 890 800 Time to maturity 2% 1 5.65% 2 5% 3 Coupon YTM 0 5% 4.7% Used excel formulas to calculate Solution a Rsk free rate Expected return Beta D1 g 8% 12% 1.4 2.5 5% First, calculate the return of the stock Return = Return = Price of the stock = Price of the stock = b Risk free rate + beta * (expected return - risk free rate) 13.60% D1 / (r-g) $ 29.07 Rsk free rate Expected return Beta D1 g 7% 10% 1.1 2.5 5% First, calculate the return of the stock Return = Return = Risk free rate + beta * (expected return - risk free rate) 10.30% Price of the stock = Price of the stock = D1 / (r-g) $ 47.17 Solution Risk free ra Return Stdev 5% 20% 20% Return Investment Weight Weighted return 32880 0.3288 1.64% 67120 0.6712 13.42% 100000 15.07% Risk free Market 5% 20% Risk free Market Weight 1% 0.3288 20% 0.6712 Stdev of portfolio 13.75% Solution Debt yield Debt proportion Growth Price Expected dividend Risk free Return Beta 8% 25% $ $ $ 9% 30.00 2.00 2% 10% 1.50 a Return using DDM 15.67% b Retru using CAPM Return = 14.0% c After tax cost of debt Average cost of equity Weight 4.80% 25% 14.83% 75% Cost of capital 12.33% Solution Cost of old Cost of ne 110000 150000 Revenue Cost 60000 20000 Old revenu Old cost Depreciatio Current pri 40000 20000 10000 50000 Year Initial inve Cash flow Depreciation EBIT Tax Net income Add: Depreciation Cash flow Rate NPV 0 100000 -100000 10% $ 84,337.01 Yes, the new project should be accepted 1 2 3 4 5 6 7 8 9 10 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 40000 15000 25000 10000 15000 15000 30000 Solution Year 0 Dividend 1 0.4 2 0.5 3 0.625 4 0.78125 5 0.976563 6 1.054688 P5 = 15.06696 0 Cash flow 1 0.4 2 0.5 3 0.625 4 0.78125 5 16.04353 P0 = $ 9.56 a Rate Compound 8% 365 EAR = b 8.33% Rate Compound 8.50% 12 EAR = 8.84% Solution a Interest rate triple mon b Nper PV FV 10 6 30 rate 17.46% c 10% 11.5 years Lum sum Annuity Nper 50000 8000 10 Rate 6% PV of annui $ 58,880.70 Annuity amount has higher PV, thus annuity is better Annuity Nper 8000 10 Rate 18% PV of annui $ 35,952.69 Lumpsum is better d PV Pmt Rate Nper FV 15000 195 10% 30 $ 32,076.33 Solution 2013 21.60% 13.50% 1.6 0.5 27.00% 40.00% 2012 26.00% 13.00% 2 0.45 28.89% 42.22% Financial leverage ratio Total asset turnover Net profit margin 1.6 0.5 27.00% 2 0.45 28.89% ROE 21.60% 26.00% ROE ROA Financial leverage ratio Total asset turnover Net profit margin Operating profit margin DuPont