## You have just taken a car loan of \$15,000. The

You have just taken a car loan of \$15,000. The loan is for 48 months at an annual interest rate of 15% (which the bank translates to a monthly rate of 15%/12 = 1.25%). The 48 payments (to be made at the end of each of the next 48 months) are all equal.

a. Calculate the monthly payment on the loan.

b. In a loan table calculate, for each month: the principal remaining on the loan at the beginning of the month and the split of that month’s payment between interest and repayment of principal.

c. Show that the principal at the beginning of each month is the present value of the remaining loan payments at the loan interest rate (use either NPV or the PV functions).

## It is 1 January 1997. Normal America, Inc. (NA) has

It is 1 January 1997. Normal America, Inc. (NA) has paid a year-end dividend in each of the last 10 years, as shown by the table below:

a. Calculate NA’s β with respect to the S&P 500.

b. Suppose that the Treasury bill rate is 5.5% and that the on the market is E(rM) = 13%. If the corporate tax rate TC = 35%, calculate NA ’ s using both the classic CAPM and tax-adjusted model.

c. Assume that NA’s is 8%. If the company is financed by 1/3 equity and 2/3 debt, what is its weighted average using each of the two CAPM models?

## You are considering buying the bonds of a very risky

You are considering buying the bonds of a very risky company. A bond with a \$100 face value, a 1-year maturity, and a rate of 22% is selling for \$95. You consider the probability that the company will actually survive to pay off the bond 80%. With 20% probability, you think that the company will default, in which case you think that you will be able to recover \$40.

a. What is the on the bond?

b. If the company has rE = 25%, tax rate TC = 35%, and 40% of its is equity, what is its weighted average (WACC)?

## You have just turned 35, and you intend to start

You have just turned 35, and you intend to start saving for your retirement. Once you retire in 30 years (when you turn 65), you would like to have an income of \$100,000 per year for the next 20 years. Calculate how much you would have to save between now and age 65 in order to finance your retirement income. Make the following assumptions:

• All savings draw of 10% per year.

• You make the first payment today and the last payment on the day you turn 64 (30 payments).

• You make the first withdrawal when you turn 65 and the last withdrawal when you turn 84 (20 payments).

A mutual fund has been advertising that, had you deposited \$250 per month in the fund for the last 10 years, you would now have accumulated \$85,000. Assuming that these deposits were made at the beginning of each month for a period of 120 months, calculate the effective annual return fund investors got.

The effective annual return can then be calculated in one of two ways:

• (1 + monthly return)12 − 1: This is the compound annual return, which is preferable, since it makes allowance for the reinvestment of each month’s earnings.

• 12* monthly return : This method is often used by banks.

## You currently have \$25,000 in the bank, in a savings

You currently have \$25,000 in the bank, in a savings account that draws 5% interest. Your business needs \$25,000, and you are considering two options: (a) Use the money in your savings account. (b) Borrow the money from the bank at 6%, leaving the money in the savings account.

Your financial analyst suggests that solution (b) above is better. His logic: The sum of the interest paid on the 6% loan is lower than the interest earned at the same time on the \$25,000 deposit. His calculations are illustrated below. Show that this logic is wrong. (If you think about it, it couldn’t be preferable to take a 6% loan when you are getting 5% interest from the bank. However, the explanation for this may not be trivial.)

## You are considering buying a car from a local auto

You are considering buying a car from a local auto The offers you one of two payment options:

• You can pay \$30,000 cash.

• The “deferred payment plan”: You can pay the \$5,000 cash today and a payment of \$1,050 at the end of each of the next 30 months.

As an alternative to the fi nancing, you have approached a local bank, which is willing to give you a car loan of \$25,000 at the rate of 1.25% per month.

a. Assuming that 1.25% is the opportunity cost, calculate the present value of all the payments on the dealer’s deferred payment plan.

b. What is the effective interest rate being charged by the Do this calculation by preparing a spreadsheet like this (only part of the spreadsheet is shown—you have to do this calculation for all 30 months):

Now calculate the IRR of the difference column; this is the monthly effective interest rate on the deferred payment plan.

## In this exercise we solve iteratively for the internal rate

In this exercise we solve iteratively for the Consider an investment which costs 800 and has cash flows of 300, 200, 150, 122, 133 in years 1–5. Setting up the loan table below shows that 10% is greater than the IRR (since the return of principal at the end of year 5 is less than the principal at the beginning of the year):

Setting the IRR? cell equal to 3% shows that 3% is less than the IRR, since the return of principal at the end of year 5 is greater than the principal at the beginning of year 5. By changing the IRR? cell, find the of the investment.