**Problem 1: (15 Points)**

Consider Kathryn, a new student who has just received a loan and started college. She plans to obtain the maximum loan from at the beginning of each year. Although Kathryn does not have to make any payments while she is in school, the 6.8 percent interest owed (compounded monthly) accrues and is added to the balance of the loan. After graduation, Kathryn gets a six-month grace period. This means that monthly payments are still not required, but interest is still accruing. After the grace period, the standard repayment plan is to amortize the debt using monthly payments for 10 years.

Loan Limits:

Freshman |
$6,000 |

Sophomore |
$6,000 |

Junior |
$7,000 |

Senior |
$7,000 |

- Construct cash flows of the loan.
- What will be the loan balance when Kathryn graduates after her fourth year of school?
- What is the loan balance six months after graduation?
- Using the standard repayment plan and a 6.8 percent APR interest rate, compute the monthly payments she owes after the grace period.

**Problem 2: (15 points)**

- You are a financial manager at a soft-drink company. Until today the company bought empty cans from an outside supplier. You are considering whether to purchase a machine and begin manufacturing cans in-house to achieve cost savings.
- The cost of purchasing a can machine is $850,000 and the lifespan of the machine is 8 years. At the end of 8 years, the company expects to sell the machine for $120,000. Assume the machine is depreciated each year at $95,000 per year.
- The cost savings generated by the can machine will be $160,000 per year.
- Assume that the project requires an investment in Net Working Capital (NWC) of $20,000, and none of this is recovered at the end of the project.
- The machine would be purchased at year 0, the NWC investment occurs at year 0, and all subsequent cash flows occur in years 1-8.
- Assume the discount rate is 10% and the corporate tax rate is 21%.
- Determine the NPV of purchasing the can machine. Should you accept or reject the project?

**Problem 3: (20 Points)**

Download 5 years of monthly historical price data for AMZN, GM and the S&P 500 (symbol:

^GSPC) and use adjusted close prices. (You can get historical data from finance.yahoo.com)

- Calculate monthly returns, covariance and correlation between AMZN and GM.
- Consider you have a portfolio with 20 shares of AMZN shares and 1000 shares of GM. (Use adjusted close price from 12/10/2020 for their values) Calculate portfolio return, portfolio variance and standard deviation.
- Calculate Beta for AMZN and GM.
- Calculate expected returns of each stock. (Assume market return is 7% and use 5 year Treasury Bond Yield from 12/10/2020 as your risk free rate)

**Problem 4: (10 Points)**

Consider the following two bonds:

**Bond A **

Term to maturity: 10 years from today

Face value: $1,000

Annual Coupon rate: 6%

Number of payments per year: 2

**Bond B **

Term to maturity: 20 years from today

Face value: $1,000

Annual Coupon rate: 9%

Number of payments per year: 2

Compute the price for each bond. The current YTM for each bond is 8%. Then make a table comparing the bond prices when the YTM varies from 1%, 2% … 17%.

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