1 One year from today you will receive the first of six annu

1) One year from today you will receive the first of six annual $6,000 payments. The current interest rate is 8%. This will continue until the end of year 1. The rate will be 9% from the beginning of year 2 to the end of year 3. At the beginning of year 4 the rate will be 10% and will continue at this rate. What is the value today of these future cash flows?

2). You can borrow $4,000 from the bank a 15% annual rate for a 36 month personal loan. A loan shark has offered you a loan of $4,000. You will repay the loan monthly over three years. He calculates that the payments will be $200 per month. What annual rate is “shark” charging you? Should you take the bank loan or the shark loan?

3). You just won the lottery!! You must select between Option A: $1,500,000 per year for 15 years or Option B: $15,000,000 today. Ignore your friends and taxes. If your opportunity cost is 7.00%, which option would you select and in today’s dollars, approximately how much better off would you be compared to the other alternative?

4). You are considering obtaining a car for personal use, you have two alternatives, one purchase the car using a loan from your bank, or lease the car from the dealer. If you borrow, the bank will require monthly payments and will charge you 6.20% for a 3 year loan. If you lease, the dealer will require payments of $260 at the end of each month for 3 years plus a final payment of $13,700 at the end of the third year if you want to keep the car. For a $20,000 car, what is the cost of leasing and which alternative provides the best financing over the 3 years?

5). Binrui is thinking of purchasing a small real estate project. The listing price (asking price) is $300,000. Binrui’s best estimate of the after tax cash flows is $30,000 in each year 1-5 and $36,000 in each year 6-10. In addition, he plans to sell the property at the end of 10 years for $264,000 after tax. If Binrui requires a 16 rate of return on his real estate investments, what is this project worth (present value) to him in today’s dollars?

Solution

QUESTION 1: SOLUTION

You receive 6 instalments of 6,000

Interest rate in year 1 = 8%

Interest rate in year 2 and year 3 = 9%

Interest rate for years 4,5 and 6 =10%

Present value of a future cash flow = FV/(1+r)^n where FV is the future cash flow, r is the interest rate and n is the year in which that cash flow is received.

The present value of the future cash flows = 6,000/1.08 + 6,000/1.09^2 + 6,000/1.09^3 + 6,000/1.10^4 + 6,000/1.10^5 + 6,000/1.10^6 = 26,449.19

The value today of these future cash flows =$ 26,449.19

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