Question 1
Consider the following mutually exclusive investments
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T=0
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1
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2
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Investment A:
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-100
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20
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120
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Investment B:
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-100
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100
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30
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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
Assume semi-annual coupon payments. Find missing values in the table above.
Please show details of your solution.
Question 3
The MintcoinInc has just paid an annual dividend of 40 cents per share. You forecast that dividends of MintcoinInc will grow at the rate of 25% a year over the next four-year period. From year five on, you expect the subsequent growth rate of dividends to decrease to 8%, the industry average
a. Construct the time line, showing dividends of the company.
b. If the required rate of return for the stock is 12%, calculate its price.
Question 4
Given that the risk-free rate is 2%, the expected return on the market portfolio is 15%, and the standard deviation of returns to the market portfolio is 20%, answer the following questions:
a. You have $500,000 to invest. How should you allocate your wealth between the risk free asset and the market portfolio in order to have a 10% expected return?
b. What is the standard deviation of your portfolio in (a)?
c. What proportions (weights) of your money do you need to invest in the market portfolio and the risk free asset to achieve 20% return?
d. What does the weight on the risk free asset in the portfolio in part (c) mean?
e. What is the standard deviation of your portfolio in part (c)?
f. Are your portfolios in parts (a) and (c) efficient? Why or why not?
g. Comment on the connection between the return on your portfolios in parts (a) and (c) and their risk.
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 of the current machine today is $50,000. Your company's tax rate is 25% and the opportunity cost of capital is 10%. Should your company replace its year-old machine?
Question 7
a. Your credit card quotes annual rate of 22%. What is the effective annual rate on your credit card if you make monthly payments?
b. By law, financial institutions are required to report the simple rate (no effects of compounding included). This rate is called Annual Percentage Rate (or APR). Suppose that you have a mortgage on your house and you calculate that with monthly payments, your effective annual rate is 7%. What APR should your bank quote?
Question 8
- How long will it take to triple your money with an interest rate of 10 percent?
- 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?
- 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%?
- 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 9
Suppose that an analyst has noticed that the return on equity of the XYZ Company has declined from 2016 to 2017.
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(millions)
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2016
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2017
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Sales
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$1,000
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$900
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Earnings before interest and taxes
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$400
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$380
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Interest expense
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$50
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$50
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Taxes
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$70
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$66
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Total assets
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$2,000
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$2,000
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Shareholders' equity
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$1,250
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$1,000
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a. Fill in the following table (please show detailed calculations for each ratio, including the formula used, below that table):
2016 2017
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.