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Problem Set 1, FIN 206

Spring 2024

Problem 1

You have two 8-years old twin children, and you anticipate that when they will turn 18 (exactly 10 years from now) they will need $500,000 to cover living and tuition college expenses. Suppose that the discount rate is 10%.

1. If you want to meet this negative cash flow only with current savings, how much would you need to set aside right now?

2. Suppose, instead, that want to meet this negative cash flow only saving a constant amount at the end of each year, for the next 10 years. What is the amount you should set aside each year?

Problem 2

You are planning the finances for your future retirement. Suppose that you saved $1,500 last year, and you expect your annual savings to grow 5% per year for the next 15 years. Moreover, suppose that you can invest your savings in an asset that pays 8% compounded yearly. How much do you expect to have saved at the end of the fifteenth year?

Problem 3

You have created a new startup and now you need to buy an equipment that costs $20,000. The seller of the equipment offers you to choose between one of the following two deals:

1. The seller would take 10% off the price, and lend you the balance at an annual percentage rate of 9%, compounded yearly

2. The seller would lend you $20,000 at an annual percentage rate of 3%, compounded yearly

Which option do you prefer, and why?

Problem 4

Go to Yahoo Finance (click here) and download the historical adjusted close monthly prices from 02/01/1999 to 01/29/2024 for Amazon (tracker AMZN) and Nvidia (tracker NVDA).

1. Calculate the month-on-month returns for both companies

2. Calculate the average returns and standard deviations of the returns for both companies for the full sample

3. Now, calculate the average returns and standard deviations for Amazon for the period pre 2009, and post 2009 separately. What do you observe? What does it teach us about the hidden assumptions behind the calculations made in part 1?

4. Similarly, calculate the average returns and standard deviations for Nvidia for the period pre 2015, and post 2015 separately. What do you observe? What does it teach us about the hidden assumptions behind the calcula-tions made in part 1?

5. Calculate the covariance between Amazon’s and Nvidia’s returns for the full sample, and comment on what you find.

6. Calculate the return of holding both companies from the beginning to the end of the sample

7. Calculate the returns of holding both companies from the beginning of the sample to march 2020, and compare your finding with those of part 6.