Assignment

1. In Feb 2017, Warren Buffett announced his second March Madness Bracket contest for employees. Any Berkshire Hathaway employee that can pick the Sweet 16 correctly will win $1 million a year for life. You just celebrated your 45th birthday and you expect to live until the age of 85.

a) If you won, and can invest each year's winnings at 5% compounded quarterly, what is the value of the prize today?

b) Now, instead of investing, you spend all of your winnings for 5 years, then you decide to give half of your annual winnings to charity each year, and invest the rest at the same rate as in part a). What would be the value today?

c) If you wanted to establish a scholarship when you die that would provide scholarships payments totaling $100,000 each year growing at 4% per year, how much would you have to invest each month if you could still earn 5% compounded quarterly?

2. The Canada Pension Plan (CPP) is a social insurance program run by the federal government. It is part of Canada's public retirement income system. Every Canadian (or non-citizen working in Canada) above the age of 18 is forced to contribute to the CPP. Only Canadians living in Quebec are exempt from this plan as Quebec has its own public pension plan (QPP). In this problem, we are not concerned about whether CPP delivers a good return on investment, but how to choose when to become a beneficiary.

By default, pension payments start on your 65th birthday, but you can elect to start receiving pensions as early as 5 years before or as late as 5 years after your 65th birthday. For every month for which you elect to start your pension payments earlier than your 65th birthday, your pension payment will be reduced by 0.6% and for every month for which you elect to start your pension payments later your pension payment will be increased by 0.7%. Once you start your pension, your pension payment stays constant until you die. (In reality, you would get inflation adjustments, but we will not consider them here).

Suppose you are approaching your 60th birthday and you have to choose when to start your pension. You expect to live until your 82nd birthday. Assume that if you were to start your pension on your 65th birthday, you would receive a monthly pension of $643.92 (this was the average pension amount for new beneficiaries in March 2017).

a) Should you elect to start your pension on your 60th birthday, your 65th birthday, or your 70th birthday if you require an effective annual rate of return of 7%?(Evaluate all three options on your 60th birthday and compare!)

b) How does your answer to apart a) change, if you are in extraordinary health and expect to live until your 90th birthday.

3. GoProInc has found a piece of land upon which it would like to construct a new production facility. The total cost of the land and new facility is expected to be $12.4 million. The CEO of the firm is quite conservative and will only go ahead with this project once the company has sufficient funds to pay cash for the half of the project's costs. Management feels that they can save $200,000 a month for this purpose. The firm earns 7% compounded monthly on the funds it saves. How long does the company have to wait before building the new facility?

4. Today you decided to buy a new car for $35,000. The dealer is offering you a monthly interest rate of 0.7%. The loan will be paid off over the next 4 years with equal monthly payments.

a) What is your monthly payment amount, if your payments are made at the end of the month?

b) What is your monthly payment amount, if your payments are made at the beginning of the month?

c) Often and especially if your credit history is not ideal, car dealers require you to make a down payment on the price of the car, i.e. a certain amount or percentage of the price has to be paid at the time of purchase. What is your monthly payment amount, if your payments occur at the end of the month, but have to make a down payment of 10% on the price of the car?

d) Loans can have what is called a deferment option. For a specific time period (the deferment period) at the beginning of the loan no payments are made, but the loan will still accumulate interest. What is your monthly payment amount, if the loan includes a deferment period of 1 year and the payments occur at the end of the month?

e) Consider the loan in part c). Suppose that just after you made the 18th payment on the loan, the car dealer allows you to make a one-time payment of $4,000 in addition to all your regular payments. By how much will the remaining 30 (equal size) payments decrease, if you plan to pay off the loan at the same time as in part c)?

5. The MacDonalds are at the bank in order to negotiate a loan to buy a farm where they can raise cows, horses, chickens, sheep, and plant spaghetti trees. They have managed to save $350,000 over the last 10 years that they can use as a down payment. The MacDonalds would like to finance their purchase over 25 years making monthly payments. According to their financial planning schedule, they will clear $7,500 a month and would like their mortgage payments to be at most 30 percent of their monthly earnings. The bank is offering a 25 year amortized mortgage loan at 4.75 percent with a 5-year term.

a) Calculate the maximum price the MacDonalds can pay for their farm.
b) Prepare an amortization table for the first 3 months of the MacDonalds' mortgage.
c) At the end of the 5-year term of their mortgage, how much will the MacDonalds owe on their loan?

6. You are currently 25 years old and have decided to start paying into your registered retirement plan. You will start to deposit $120 at the end of each month starting with this month until you are 65 years old and you retire. Interest rates are expected to be 7.5% compounded monthly from the time you are 25 until you are 45 and then are 6.5% compounded monthly until you retire at 60.

a) How much will be in your retirement account when you retire?
b) According to your family history, you expect to live until you are 85. If interest rates during your retirement are 5% compounded monthly, how much will you be able to withdraw at the end of each month during your retirement?