## Investment strategies of SPY and EFA.

- Ten years ago (i.e., in 2011) you obtained a 30-year mortgage for $450,000 with a fixed interest rate of 3.6% APR compounded monthly. The mortgage is a standard fixed rate mortgage with equal monthly payments over the life of the loan.

a. What are the monthly fixed mortgage payments on this mortgage (i.e., the minimum required monthly payments to pay down the mortgage in 30 years)?

b. What is today’s (i.e., in 2021) remaining loan balance immediately after making the 120th monthly payment? Assume that you made all the mortgage payments on time and you made all the minimum required monthly payment over the last 10 years.

c. Today (i.e., in 2021), a mortgage broker contacts you and says that you can reduce your monthly mortgage payments by refinancing the mortgage you obtained 10 years ago. The broker suggests that you refinance your current loan amount into a new 30-year mortgage with a fixed interest rate of 4.2% APR compounded monthly. The mortgage is a standard fixed rate mortgage with equal monthly payments. The mortgage will be fully paid off after 30 years. What are the monthly fixed mortgage payments on this refinanced mortgage?

d. To refinance the loan, you need to pay refinancing costs of $3,500 upfront (i.e, in 2021). Assume you will own your home for an additional 30 years until the new mortgage is fully paid off (i.e., until 2051) and that you do not refinance the mortgage again in the future. Is it beneficial to refinance your current loan from part (a) with the new loan from part (c)? What is the NPV of refinancing your loan?

- You had your first child recently. You would like to set aside some funds so that your child will be able to attend the University of Texas as an undergraduate without taking on any student loans. Total in-state costs of attendance for undergraduate students currently amount to $30,000 per year and are expected to continue to grow at a 3% growth rate per year. Assume that the four-year college expenses for the first year of college need to be paid exactly 18 years from today and that the subsequent costs need to be paid at an annual frequency 19, 20, and 21 years from today. You would like to make 18 equal annual payments starting today to your child’s college savings account to be able to cover the expected college costs. The savings are invested in risk-free Treasury securities that offer a return of 2%. How large are the equal annual contributions to the college savings account over the next 18 years?
- You are considering investing in a standard fixed-rate corporate bond with 25 years remaining to maturity. The bond pays annual coupons of 4% and just made its most recent coupon payment. The face value of the bond is $1000.

a. What is the current price of the coupon bond if its current yield to maturity is 3%?

b. In exactly five years the yield to maturity of the coupon bond will have increased to 5% because the Fed has increased interest rates and because the company has become more risky. What is the price of the coupon bond in five years immediately after it made the coupon payment?

c. What is the Internal Rate of Return (IRR) if you purchase the bond now at the price given in part (a), hold on to the bond for five years, and sell the bond after five years at the price computed in part (b).

- Spot gold market: The current spot gold price for immediate delivery (i.e., gold spot price) is $1840 (bid) and $1850 (ask) per ounce. Besides buying gold you can also short-sell gold. Short-selling gold means that you borrow gold from your broker, sell it immediately on the spot market, and then after some time (e.g., after one year) you buy gold on the market and return it to the broker who lent you the gold.

Forward gold market: Currently, a one-year forward contract of gold trades at a forward price of $1880 (bid) and $1890 (ask) per ounce. If you buy a one-year forward contract of gold, then you will receive delivery of one ounce of gold in one year and you will need to pay $1890 at the time of delivery. Alternatively if you sell a one-year forward contract of gold, you will need to deliver one ounce of gold in one year and you will receive $1880 at the time of delivery.

Assume that gold has no delivery costs, no storage costs, no short-selling costs, and no other transactions costs. You can borrow and lend at a 2% interest rate. You expect that gold prices are going to increase to $2000 over the next year. Are there any arbitrage opportunities here? If yes, explain which transactions you need to perform and quantify the profits you make from this arbitrage. If not, explain why an arbitrage does not exist.

- Uchi is a small restaurant chain specializing in Japanese dishes. Its equity has a market value of $6 million and its debt has a value of $4 million. Its equity beta is 1.3. Investors expect an 8% return on the market portfolio and a 2% risk-free return on Treasury securities per year. The yield-to-maturity of Uchi’s debt is 6% per year and companies with similar credit ratings as Uchi have an annual default probability of 2%. You expect that the debt holders will not receive any payments in case Uchi defaults. Uchi’s marginal corporate tax rate is 20%. What is the Weighted Average Cost of Capital (WACC) of Uchi?
- In early 2010, Morningstar, a Chicago-based financial services company, announced the Morningstar Fund Managers of the Decade. The award was based on the performance of mutual funds from January 2000 to December 2009. The award was not just about returns, though. Morningstar also considered the risks assumed to achieve those results and took into account the strength of the manager, strategy, and firm’s stewardship. They also thought it’s a greater feat to make a lot of money for a lot of people than to earn sky-high returns on a tiny pool of assets, so asset size factored in. The winner for the domestic equity category was Bruce Berkowitz, the manager of the Fairhome (FAIRX) mutual fund. The two runner-up managers were Charlie Dreifus of Royce Special Equity Investment (RYSEX) and Don Yacktman of the Yackman Fund (YACKX).

You want to investigate whether these award-winning managers continued to perform well since then. The Excel file “Mutual Fund Data” includes monthly data for these three award-winning funds, as well as for the Vanguard 500 Index Fund (VFINX) from January 2000 to September 2021. The first tab of the Excel spreadsheet includes the dates (expressed as YYYYMMDD) and the monthly total returns of these funds. The second tab includes the dates (expressed as YYYYMM), the monthly Treasury bill rate, RF (i.e., a monthly rate of return that is not annualized), and the return of the market portfolio, Mkt, which includes all publicly-traded firms in the U.S. For example, a risk-free rate of 0.0041 means that during the corresponding month, you receive a monthly return of 0.41% by investing in Treasury bills.

a. Briefly describe the investment strategies and styles of the four mutual funds. What are the current expense ratios, the current turnover ratios, and the current assets under management of the funds? Check any financial websites (Morningstar, Yahoo, Google, Fund Families) that has information on mutual funds.

b. Compute the following statistics for each of the four funds, for the market, and for Treasury bills over the period from January 2000 to December 2009:

(i) Average arithmetic means of monthly total returns

(ii) Average geometric means of monthly total returns

(iii) Standard deviations of monthly total returns

(iv) Monthly Sharpe ratio

Briefly comment on the performance of the different assets.

c. Compute the following statistics for each of the four funds, for the market, and for Treasury bills over the period from January 2010 to September 2021:

(i) Average arithmetic means of monthly total returns

(ii) Average geometric means of monthly total returns

(iii) Standard deviations of monthly total returns

(iv) Monthly Sharpe ratio

Briefly comment on the performance of the different assets.

d. Estimate the monthly alphas, the market betas, and the R-squared of the regression for each of the four funds using the CAPM model over the period from January 2010 to September 2021. Which fund takes more systematic risk? Which fund has a higher alpha (abnormal return)? What does the R-Squared tell us? What is your conclusion on the persistence of performance for these award-winning funds?

- You invest 60% of your financial assets in the Standard & Poor’s Depository Receipts (SPY) and 40% in the MSCI EAFE Index Fund (EFA). SPY has an expected return of 7% and a standard deviation of 16%. EFA has an expected return of 8% and a standard deviation of 18%. The correlation between the two investments is 80%. The risk-free rate is 2%.

a. Briefly explain the investment strategies of SPY and EFA.

b. What are the expected return, the standard deviation, and the Sharpe ratio of your portfolio? Show the mathematical equations that you use to derive these measures.

c. Which portfolio of SPY and EFA has the highest Sharpe ratio?

- You are analyzing two mutually exclusive projects with the cash flows shown below. The cash flows are in millions. Both projects are equally risky. Your costs of capital are 12%.

Year Project 1 Project 2

0 -$125 -$75

1 $45 $30

2 $36 $25

3 $32 $24

4 $28 $20

5 $24 $16

6 $20 $12

7 $16 $8

8 $12 $4

9 $8 $0

10 $4 $0

a. Compute the NPVs of the two projects

b. Compute the IRRs of the two projects.

c. Compute the simple payback periods of the two projects.

d. Compute the discount rate where you are indifferent between the projects (i.e., incremental IRR).

e. Which project should you execute? Briefly explain why.

- Tito’s Handmade Vodka of Austin is considering expanding its production capacity by purchasing new distilling equipment. The firm has just completed a $10,000 feasibility study to analyze the decision to buy the equipment, resulting in the following estimates:

Capital Expenditures: The cost of the distilling equipment is $100,000 and needs to be paid immediately (i.e., year 0). The equipment will last for ten years. The firm expects to recover a salvage value of $10,000 in year 10 (i.e., 10 years from now).

Marketing: Once the equipment is operating in year 1, the extra capacity is expected to generate $100,000 in additional sales in each of the subsequent ten years (i.e., year 1, year 2, …, year 10).

Operations: The disruption caused by the installation will decrease sales revenues by $20,000 in year 0. The costs of goods (COGS) sold are 60% of their sales revenues. The increased production will require additional inventory on hand of $20,000 to be added in year 0. You will continue to need the inventory of $20,000 until year 9 and it will be fully recovered in year 10 (i.e., the required inventory will be zero in year 10). The firm expects receivables to be 20% of revenues and payables to be 10% of the COGS.

Human Resources: The expansion will require additional sales and administrative costs of $10,000 per year from year 1 through year 10.

Accounting: The equipment will be depreciated equally every year over the 10-year life of the equipment. Thus, the book value after depreciation in year 10 will be zero. Tito’s marginal corporate tax rate is 20% and Tito expects to remain highly profitable in the foreseeable future.

a. Compute the NPV, the IRR, and the SIMPLE PAYBACK of the project. Use a discount rate of 12%

b. In the base case scenario, you assume annual additional sales between year 1 and year 10 to be equal to $100,000. At which annual additional sales does the project just break even (Hint: Use Solver in Excel)?

a. Base-Case Scenario

b. Break-Even Sales

- On Tuesday, November 9th, 2021, GE announced it would split into three public companies, breaking apart the more than century-old company that was once a symbol of American manufacturing might and has struggled in recent years. The company will spin off its main three divisions – aviation, healthcare, and power – into separate publicly traded companies. Discuss in less than 500 words the benefits and costs of this move.