Due date: **11 pm on Thursday, February 3rd**

**(via Blackboard)**

The preferred method of submission is an Excel spreadsheet. You need to familiarize yourselves with Excel or financial calculators for the midterm and final exams.

To submit your answers, one person per group (any team member) needs to submit the team homework on Blackboard under Assignments/Group Problem Sets/Group Problem Set 1. The submitted file should list **THE GROUP NUMBER ON THE TITLE**. For example:

Homework1_Group3.xlsx

or

Homework1_Group3.pdf (if you are submitting a pdf file)

# THERE WILL BE A 20% GRADE PENALTY IF THE TITLE IS NOT IN THE ABOVE

**FORMAT.** The list of groups can be found in the Assignments folder on Blackboard. The Excel spreadsheets and YouTube videos, which are posted on Blackboard under Course Documents, can be a great help for this assignment. ** **

## Problem 1

As a financial advisor, you are consulting a client who has won the Florida lottery. The prize for the competition can be paid in 4 different ways described below. The annual discount rate is 11%.

- $1,140,000 now
- A one-time payment of $1,000,000 in 5 years and an additional one-time payment of $1,100,000 in 10 years
- 5 consecutive annual payments of $400,000, with the first payment made at the end of year 3 and the remaining payments made at the end of each of the four following years
- 25 consecutive annual payments, with the first payment of $270,000 made at the end of year 2 and the remaining payments (which occur at year end) declining by 10 % per year
- What is the present value of each alternative and which option would you recommend?
- Suppose that your client would like to replace alternative (1) with a perpetual stream ofconsecutive annual payments (made at year-end), which starts at the end of year 5 and grows by 6% per year forever. What should be the amount of the first payment at the end of year 5 so that you are indifferent between these two alternatives?
- You are comparing alternative (2) to a stream of annual inflows of $160,000 each (paymentsoccur at year-end), with the first payment made at the end of year 1. What is the minimum whole number of payments in this new income stream that would make it more valuable than alternative (2) in present value terms?

## Problem 2

Despite a 9-4 season, UM’s football tickets are in high demand. To help accommodate more fans in the Hard Rock stadium (and earn some extra cash for athletic scholarships), the University is considering a project to increase the capacity of the stadium by building a new VIP section. This will require 3 annual investments of $6 million, the first of which will be made at the end of year 1 (i.e., exactly one year from now), and the second and third investments will be made at the end of years 2 and 3, respectively.

The VIP new section, which will commence operations in year 5, will seat 1,500 people and have infinite life. The stadium will host 8 games per year, and the ticket prices will increase by 3% each year. For simplicity, assume that the stadium will always operate at full capacity, that there are no taxes or additional maintenance expenditures, and that all cash inflows occur at the end of each year (e.g., the first cash inflow from the new section will occur at the end of year 5). The annual discount rate is 11%.

You are asked to compute the minimum price per ticket in the new section that you can charge when the section opens in year 5 to satisfy the University’s financial objective. The University’s objective is to ensure that the present value of all cash inflows from the project over its infinite life exceeds the present value of all cash outflows by at least $1 million.

## Problem 3

After Charlie Harper passed away, his brother Alan and Alan’s son Jake had to move out of Charlie’s beach house in Malibu where they had lived for so many years. Alan has just purchased a new apartment and financed this purchase with a 30-year mortgage that requires a 20% down payment. The rest is to be repaid in equal QUARTERLY installments of $2,200 each. The EAR on this mortgage is 6.5%, and the interest rate is compounded QUARTERLY. For accuracy, please retain three digits after the decimal point in interest rate computations in this problem (for example:

5.123%).

- What was the price of the apartment?
^{[1]} - Suppose that Alan’s lender has to disclose the APR on this mortgage. What APR would thelender quote?
- Based on the APR that you found in (b), which compounding frequency – daily (assuming 365days), monthly, quarterly, semi-annual, or annual – would result in the highest EAR? Please find this EAR.

## Problem 4

Many financial firms and insurance companies, such as Fidelity, New York Life Insurance, Allstate, and others, offer a product called a Life Annuity. Bob and Jane, an elderly couple, are asking for your financial advice regarding one such product that they have been offered. If they purchase a life annuity today, the firm promises to make monthly payments of $3,000 to their household for as long as at least one of the two spouses is alive. Based on lifestyle characteristics of Bob and Jane, the firm estimates that they will each live for exactly 20 years from now. The annual discount rate (stated as an APR) is 6%, compounded monthly. Payments occur at the end of the month, and the first payment will be received at the end of month 1 (i.e., one month from now). For simplicity, assume that Bob and Jane will live for the same number of years from now.

- If all the assumptions are correct, what is the present value of this payment stream?
- Suppose that the firm charges $440,000 today for this contract in order to make a profit on thetransaction. The main risk of the company is that Bob and Jane live longer than anticipated, thus forcing the firm to continue to make payments for more than 20 years. What is the maximum number of months (from today) during which the firm can make payments to Bob and Jane before it starts losing money (i.e. before the PV of contract payments exceeds the price charged by the firm)?
- The spouses would like to make sure that they can keep up with the rising living expenses andrequest that their monthly payments grow at the monthly rate of 0.1%. What is the present value of this growing annuity, if all other assumptions remain the same (first monthly payment is $3,000, life expectancy is 20 years, and the discount rate is an APR of 6% with monthly compounding)?

## Problem 5

As part of the management recruitment process, the board of Google, Inc. (symbol: GOOG) has asked you to make a presentation to the firm’s shareholders on the performance of Google stock in August 2021.

- Please find the closing prices of Google stock on the last trading days of August 2021 and

July 2021 (i.e., the closing prices of Google on Aug 31, 2021 and Jul 30, 2021, respectively).^{[2]}

What is the rate of return of Google for the month of August 2021? ^{[3]}

- If Google continues to deliver the rate of monthly return you found in (a), how many months will it take since August 2021 for the stock price to reach $4,000? Assume that you start with the closing price on August 2021 and that your returns are compounded monthly.
- Convinced by the growth potential of the firm, you bought 50 shares of Google at the closing price on August 31, 2021 as part of your savings plan. You are planning to sell your shares in exactly two years from the time of purchase. You also plan to use all proceeds (i.e., the total amount received from selling your shares) for a down payment on a new home in the city where you will move after graduating from UM. Assuming that Google will continue to generate the same monthly return as in (a) and that your down payment will be 20% of the home price, what is the price of the home that you will be able to afford after you sell your shares?

[1] You are asked to compute the actual selling price of the apartment, i.e. the price that would be quoted in a real estate listing (and which does not depend on how the purchaser decides to pay: with a loan or with cash).

[2] Please retrieve historical prices for Google stock from Yahoo Finance.

[3] The return for a non-dividend-paying stock, such as Google, can be computed from the closing prices based on the following formula: r = (P_{1 }– P_{0})/P_{0}, where P_{1 }and P_{0 }are the closing prices at the end of the period and at the beginning of the period, respectively (i.e., Aug 31 and Jul 30 in our case).

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