# FREE DCF Valuation Question and Answers

#### EAR = [1 + (APR/m]^m -1

Remember that the APR is the quoted rate

Always use the decimal format (12% = .12)

m = number of compounding periods

The formula you provided is indeed the formula for calculating the Effective Annual Rate (EAR). It is used to determine the annual rate of return taking into account compounding.

#### Are excellent examples of pure discount loans.

The principal amount is repaid at some future date, without any periodic interest payments.

Treasury bills are unique among these options as they represent pure discount loans with no periodic interest payments, making them a straightforward example of this type of financial instrument.

#### Infinite series of equal payments

A perpetuity is a type of financial arrangement where a fixed payment is received or made indefinitely. It can be seen as an infinite series of equal payments, where each payment is of the same amount and occurs at regular intervals, such as annually or semi-annually. The formula to calculate the present value (PV) of a perpetuity is:

PV

=

๐ถ

๐

PV=

r

C

โWhere:

๐ถ

C is the fixed payment amount (or coupon payment),

๐

r is the discount rate (or interest rate).

In finance, perpetuities are used to value financial instruments such as preferred stocks, bonds with no maturity date (consols), and certain types of annuities.

#### Multiple Cash Flows - FV Example 4:

Suppose you plan to deposit $100 into an account in one year and $300 into the account in three years. How much will be in the account in five years if the interest rate is 8%?

The future value of the account after five years, considering the $100 deposit in one year and $300 deposit in three years, at an interest rate of 8% per year, will be approximately $485.97. This calculation demonstrates how future values of different cash flows can be determined using compound interest formulas.

#### Annuity - Car Loan:

After carefully going over your budget, you have determined you can afford to pay $350 per month towards a new sports car. You call up your local bank and find out that the going rate is 6.99% for 5 years.
How much can you borrow?

You can borrow approximately $17,679.91 to purchase the sports car, given a monthly payment of $350 at an annual interest rate of 6.99% over a 5-year period. This amount accounts for the present value of the annuity payments over the loan term.

#### Beginning Balance x Interest Rate

The correct choice related to formulas used in an amortization table to calculate specific loan details is Formulas for Amortization Table: Interest Paid, which represents the calculation of the interest portion of a loan payment based on the beginning balance and interest rate for each period.

#### This is the annual rate that is quoted by law

By definition APR = period rate times the number of periods per year

The Annual Percentage Rate (APR) is the annual rate that is quoted by law for financial products such as loans, credit cards, and mortgages. It represents the total cost of borrowing, including interest and certain fees, expressed as an annual percentage. The APR is designed to provide consumers with a standardized way to compare the costs of borrowing across different financial products.

#### Pure Discount Loans - Example 5.12:

If a T-bill promises to repay $10,000 in 12 months and the market interest rate is 7 percent, how much will the bill sell for in the market?

The Treasury bill will sell for approximately $9,345.79 in the market today, considering a market interest rate of 7% per year and the promise of repayment of $10,000 in 12 months. This demonstrates how the present value of a future cash flow is determined using a discount rate, reflecting the concept of pure discount loans in financial markets.

#### Finite series of equal payments that occur at regular intervals

An annuity refers to a finite series of equal payments that occur at regular intervals, such as monthly, quarterly, or annually. These payments are made over a specified period of time. An annuity can be structured to receive payments (an ordinary annuity) or make payments (an annuity due).

#### Formulas for Amortization Table: Principal Payment

The total annual payment is the sum of all payments made in a year towards a loan or mortgage. It includes both the principal repayment and the interest paid during the year.Formula:

Total Annual Payment

=

Principal Payment

+

Interest Paid

Total Annual Payment=Principal Payment+Interest Paid

#### This is the actual rate paid (or received) after accounting for compounding that occurs during the year

If you want to compare two alternative investments with different compounding periods you need to compute the EAR and use that for comparison.

The Effective Annual Rate (EAR) is the correct choice that represents the actual rate paid or received after considering the impact of compounding within a year, making it essential for comparing investments or loans with different compounding periods.