Fin 3200 Chapter 4:Future Value, Present Value and Interest Rates

1. Suppose that Stephen Curry, a basketball player for the Golden State Warriors, will become a free agent at the end of this NBA season. Suppose that Curry is considering two possible contracts from different teams. Note that the salaries are paid at the end of EACH year.

Contract #1 (Boston) Contract #2 (Portland)

Signing bonus (paid today)$1 million $1 million

First-year salary $2 million . $4 million

Second-year salary $4 million $4 million

Third-year salary $5 million $3 million

The interest rate is 10%. Based on this information, which of the following is true?

Curry should take the Portland contract because it has a higher present value.

According to the rule of 72:

72/interest rate is the number of years approximately it will take for an amount to double.

The rule of 72 says that at 6% interest $100 should become $200 in about:

At any fixed interest rate, an increase in time, n, until a payment is made:

reduces the present value.

The "coupon rate" is:

the annual amount of interest payments made on a bond as a percentage of the amount borrowed

Higher savings usually requires higher interest rates because:

saving requires sacrifice and people must be compensated for this sacrifice.

The internal rate of return of an investment is:

the interest rate that equates the present value of an investment with its cost.

If the internal rate of return from an investment is more than the opportunity cost of funds the firm should:

make the investment.

A mortgage, where the monthly payments are the same for the duration of the loan, is an example of a(n):

fixed payment loan

An investment carrying a current cost of $120,000 is going to generate $50,000 of revenue for each of the next three years. To calculate the internal rate of return we need to:

find the interest rate at which the sum of the present values of $50,000 for each of the next three years equals $120,000.

Usually an investment will be profitable if:

The cost of borrowing is less than the internal rate of return

A coupon bond is a bond that:

provides the owner with regular payments

The coupon rate for a coupon bond is equal to the:

annual coupon payment divided by the face value of the bond

If a bond has a face value of $1,000 and a coupon rate of 4.25%, the bond owner will receive annual coupon payments of:

$42.50

If a bond has a face value of $1,000 and the bondholder receives coupon payments of $27.50 semi-annually, the bond's coupon rate is:

5.50%

Which of the following is necessarily true of coupon bonds?

The price is the sum of the present value of coupon payments and the face value.

The price of a coupon bond will increase as the:

term to maturity is shorter.

Suppose the nominal interest rate on a one-year car loan is 8% and the inflation rate is expected to be 3% over the next year. Based on this information, we know:

the ex ante real interest rate is 5%.

The interest rate that equates the price of a bond with the present value of its payments:

will vary inversely with the value of the bond.

As inflation increases, for any fixed nominal interest rate, the real interest rate:

decreases.

Considering the data on real and nominal interest rates for the U.S. from 1979 to 2012, which of the following statements is most accurate?

There have been times when the real interest rate has been negative.

Which of the following statements is most correct?

We can always compute the ex post real interest rate but not the ex ante real rate

From the Fisher equation we see that the nominal interest rate and expected inflation have:

a relationship which is direct and one-to-one.

If a lender wants to earn a real interest rate of 3% and expects inflation to be 3%, he/she should charge a nominal interest rate that:

equals the real rate desired plus expected inflation.

We should expect a country that experiences volatile inflation to also have:

volatile nominal interest rates.

A lender expects to earn a real interest rate of 4.5% over the next 12 months. She charges a 9.25% (annual) nominal rate for a 12-month loan. What inflation rate is she expecting? If the lender is in a 30% marginal tax bracket, the borrower in a 25% marginal tax bracket, and they both have the same inflation expectations, what are the real after-tax rates each expects?

The first part she expected an inflation rate of 4.75%. We obtain this answer using the Fisher equation where i = r + pe. For the second part we need to use a variation of the Fisher equation. The lender receives an after-tax nominal rate of 6.475% from which we subtract the inflation rate of 4.75% and the lender expects a real after-tax rate of 1.725%. The borrower expects to pay an after-tax real rate of 2.188%.

Briefly discuss the relationship between present value and each of the following:

a) future value

b) time

c) interest rate

Holding time and interest rate constant, any percentage change in the future value will cause the same percentage change in the present value. Holding the future value and the interest rate constant, and increase in the time until payment reduces the present value and any decrease in time increases the present value. Holding future value and time constant, an increase in the interest rate reduces the present value and a decrease in the interest rate increases the present value.

You win your state lottery. The lottery officials offer you the following options: you can accept annual payments of $50,000 for 20 years or receive an upfront payment of $700,000. Ignoring issues like mortality tables, taxes, etc.; and assuming the first payment is made immediately, what market interest rate would make it more attractive to take the upfront payment?

Using a financial calculator or a spreadsheet we can equate the $700,000 to the sum of the present value flow of receiving $50,000 a year for the next 20 years, and the internal rate of return is 4.121%. If you are confident that you can earn an average annual return greater than 4.121% a year over the next 20 years, the upfront payment may be the option to select.

You are considering purchasing a home. You find one that you like but you realize that you will need to obtain a mortgage for $100,000. The mortgage company presents you with two options: a 15-year mortgage at a 6.0% annual rate and a 30-year mortgage at a 6.5% annual rate. What will be the fixed annual payment for each mortgage?

Using a financial calculator or a spreadsheet we can determine the 15-year mortgage will require annual payments of $10,296.28; the 30-year mortgage will require annual payments in the amount of $7,657.74.

Explain why countries with high and volatile inflation rates are likely to have volatile nominal interest rates.

Using the Fisher equation (that says the nominal interest rate equals the sum of the real interest rate and the expected rate of inflation), a country where inflation is volatile will have lenders adding a high expected inflation component, thus raising the nominal interest rate. The higher volatility of nominal interest rates is directly the result of the volatility in the inflation rate.