Value of Money Questions:

1. Consider the following payment alternatives:

a. Five equal payments of $6,000 starting 2 years from today.

b. Perpetual annual payment of $2,000 starting seven years from today.

c. Twenty payments starting at the end of the year. The first payment will be $2,000 and each consecutive payment will be 2% higher than the previous one.

d. Eleven equal payments of $3,000. The first payment is today

Which alternative would you prefer to receive, if the annual interest rate is 5%?

2. A company lifecycle usually consists of three stages. Growing stage, mature stage and decaying stage. Rinse Inc. is a new high-tech company. The companys expected cash flow in one year is $10,000 and it is expected to grow by 8% every year for 3 years. Then, the company will reach its mature stage and its cash flows will remain constant for five more years. Then after, on its final and decaying stage, the companys cash flows will shrink by 5% each year forever.

What is the PV of all the cash flows generated by the company if the interest rate is 5%?

Loans Questions

1.Bill and Clarice are both 70 years old. They own a lovely Victorian style house, which was estimated at $700,000. Lately the couple calculated that their monthly expenditures are $5,000, yet their pension is only $2,800. The couple decided to take a 20-year reverse mortgage (bullet loan) to cover the remaining $2,200 they need each month. The loan (principal and interest) will be paid when they (or their children) sell the house in 20 years.

The bank agreed to lend the couple the money with a monthly interest rate of 0.33%.

a. What percent of the house's value TODAY does the loan (present value) represent?

b. What will be the bullet loan payment (the amount the couple will have to pay) at the end of the loan period?

c. Suppose that the Victorian house value is expected to increase by 0.25% each month. How much money will be left to the couple when they sell the house and pay the loan in 20 years?

2. To finance their dream one year around the world trip, Clair and Brian took a 5 year $120,000 regular loan with annual payments (the meaning of a regular loan is that the principal payments are constant). The annual interest rate in the market is 5%.

a. Present the full amortization table

b. Suppose that, right after the second payment, the bank offered the couple a new loan for the rest of the period with an annual interest rate of 3.5%. For this proposed refinancing plan, the bank demands a certain fee from the couple (paid today). What will be the maximum fee that Clair and Brian will agree to pay for refinancing the loan?

3. The Loaner company took a 5 year, $200,000 loan with equal annual payments. The first payment will be made in one year. The annual interest rate is 8%.

a. Calculate the annual payment.

b. Present the full amortization table.

c. What is the principal payment on the 4th payment?

6. You took a 10-year, $100,000 mortgage paid in equal monthly payments. The monthly interest rate is 1%.

a. Calculate the monthly payment

b. What part of the 20th payment is interest and what part of the payments is principle?

c. After 4 years (48 payments), you decide to pay the remaining amount to the bank. Assuming there are no fees, how much would you have to pay back the bank at that point?

Interest Rate Questions

1. For the last several years, Bill and Hilary are considering to sell their house and move to a luxurious retirement home. In order to move to the retirement home, they need to deposit a one-time cash deposit of $600,000 to the retirement home. 15 years ago, Bill and Hilary took a $1,000,000, 25-year mortgage with equal monthly payments. The effective interest rate on the mortgage was 6.168%. Today, right after Bill and Hilary made their monthly mortgage payment, they received an offer to sell their house for $1,150,000. Before selling the house, Bill and Hilary want to know if after the sale they will be able to afford moving into the retirement home. Assume that they do not need to pay any fee for the prepayment of their mortgage. Will they move to the retirement home?

2. You want to take a loan for $50,000. The bank offers you a 6-year loan with an attractive 8% stated interest rate and quarterly installments. In the fine print of the loan contract, you find that the bank asks for a $2,500 handling fee which has to be paid up- front.

What is the effective annual rate for this loan?

a. 12.5% b. 9.83% c. 10.2% d. 2.46%

Show your work.

3. You decide to buy a new car which cost $1,000. The car dealer offers you two payment options: (1) Pay in cash during the upcoming month (you have until the end of the month) and receive a 3% discount. (2) Pay the full price during the next two months. What is the effective annual rate which one can derive from the car dealer's payment options?

Inflation Questions

1. You need a loan. Since you know that your cousin Gilbert has just graduated from his MBA degree and managed to find a very rewarding job, you asked him for a $10,000 loan. Gilbert offered you a 4-years non index-linked loan (nominal loan) with an effective annual rate of 8%. Before taking the loan, you checked the terms in the local bank, which offered you an index-linked loan (Inflation-linked/Real loan) with real annual interest rate of 5% compounded semiannually. You also spoke with your economist friend who told you that the CPI is expected to increase by 3%.

Which loan will you take?

2. David is the owner of a small apple orchard. Due to a few years of drought and a sharp increase in the real-estate prices, David decided to uproot all of the apple trees and build two houses instead. In order to realize his plan he needs $100,000. Since he does not have the necessary funds at the moment and the bank will not lend him any more money, he decided to go and ask for a loan from his old friend Tony Soprano. Tony gave him two options: (1) A 10-year nominal loan with equal annual payments and an annual interest rate of 18%. (2) A ten year index-linked (linked to Tonys index which is determined by Tony) loan with equal annual payments (in real value). You estimate that if there will not be any trouble Tonys index is expected to increase by 10% each year.

a. What is the real interest rate in Tonys second option?

b. Suppose that Tony has decided that his index will actually increase by 7% each year (for the ten year period). Calculate the actual annual payment in the first two years of the loan for each of Tony's offers.

c. Calculate the loan's balance in each of Tony's option after 3 years.

d. Repeat sections b and c, but now, suppose that Tony has decided that his index will actually increase by 3% each year (for the ten year period).

3. You are now 30 years old. After looking at the mirror and discovering a few gray hairs, you realize that you need to think about the future and start saving for your pension for which you will make annual deposits. The deposits will be made at the end of each year starting at the end of this year. You plan to retire at the age of 65. The annual nominal interest rate is 4%:

Suppose that you plan to live until the age of 85 and you want to be able to withdraw $200,000 in real terms each year (from the age of 66). Suppose that the annual expected inflation is 2% (for the entire period).