FIN: Ch 6 Discounted Cash Flow Valuation

$100 at the end of each year forever at 10% per year is worth how much today?

$1,000 (100/.1)

The general formula for the EAR Is:

(1+r/m)^m-1

Which of the following are annuities?

Installment loan payments Monthly rent payments in a lease

Most investments involve:

Multiple cash flows

The present value of an annuity due is equal to the present value of a(n) _____ annuity multiplied by (1+r).

Ordinary

The present value formula for a(n) ___________ is PV=C/r, where C is the constant and regularly timed cash flow to infinity, and r is the interest rate.

Perpetuity

APR

The interest rate per period multiplied by the number of periods in the year.

EAR

The interest rate stand as though it were compounded once per year.

What is the present value of an ordinary annuity that pays $100 per year for three years if the interest rate is 10 percent per year?

$248.69

If the interest rate is 10 percent per week, what is the EAR? Assume 52 weeks in a year.

14104%

A credit card charges 18 percent interest per year (APR) (1.5 percent each month). What is the EAR?

19.56% (1.015)^12-1)

You owe $1200 on your credit card, which charges 1.5% per month. If you pay $50 per month starting at the end of this month, how many months will it take to pay off your credit card?

30 months (=NPER(.015,-50,1200,0,0))

At the end of 5 days, you repay your $1,000 loan plus $50 in interest. What is the EAR?

3422.24%

To find the present value of an annuity of $100 per year for 10 years at 10% per year using the tables, find a present value factor of ________ and multiply it by ___________.

6.1446; $100

The present value interest factor for an annuity with an interest rate of 8% per year over 20 years is _________.

9.8181

Which of the following spreadsheet (Excel) functions will calculate the $614.46 present value of an ordinary annuity of $100 per year for 10 years at 10% per year?

=PV(0.10,10,-100,0,0)

An annuity due is a series of payments that are made ________________.

At the beginning of each period

Assume interest is compounded monthly. The ____ annual rate will express this rate as though it were compounded annually.

Effective

Which of the following is the formula for the future value of an annuity?

FV= C(1+r^t-1/r)

Which is greater, the APY or the EAR?

They are the same

You are considering an investment that will earn the following cash flows over the next three years. You expect to earn 6% return on the investment. Match each cash flow with its present value, then match the total amount you should pay for the investment today to the appropriate box. Year 1: $5,000 Year 2: $6,000 Year 3: $5,500 Year 1: Year 2: Year 3: Amount you should pay for the investment:

Year 1: $4,716.98 (5000/1.06) Year 2: $5,339.98 (6000/1.06^2) Year 3: $4,617.91 (5500/1.06^3) Amount you should pay for the investment: $14.674.87

In almost all multiple cash flow calculations, it is implicitly assumed that the cash flows occur at the ______________ of each period.

end

A single cash flow is also known as a:

lump sum

Because of _____________ and ____________, interest rates are often quoted in many different ways.

tradition; legislation

You borrow $100 and agree to pay back your payday loan in 2 weeks for 10% interest over that 2 week period. What is your APR?

260.71%

You have decided to fund an an account that will pay your descendants that inflation-adjusted equivalent of $100 per year forever. You assume inflation will equal 3% per year, and expect the account to earn 7% per year. How much do you need to put in the bank today to ensure your gift will continue forever?

$2,500 (PV= C/(r-g))

Which of the following processes can be used to calculate future value for multiple cash flows?

- Calculate the future value of each cash flow first and then add them up - Compound the accumulated balance forward one year at a time

Ralph has $1000 in an account that pays 10% per year. Ralph wants to give his money to his favorite charity by making three equal donations at the end of the next 3 years. How much will Ralph give to the charity each year?

402.11

Which of the following are true about a partial amortization loan?

-The amortization period is longer than the loan period -The monthly payments do not fully pay off the loan by the end of the loan period -The borrower makes a large balloon payment at the end of the loan period. -The monthly payment is based on a longer amortization period than the maturity of the loan.

What are two ways to calculate a balloon payment?

- Amortize the loan over the loan life to find the ending balance - Find the present value of the payments remaining after the loan term

Interest paid twice a year is known as ______________ compounding.

Semi-annual

Use your financial calculator to find the future value of an annuity of $400 per year for 10 years at 5%.

$5,031.16

Which of the following are ways to amortize a loan?

- Pay principle and interest every period in a fixed payment. - Pay the interest each period plus some fixed amount of principle.

Which of the following should be valued using a perpetuity formula?

- Preferred stock - Cash flows from a product whose sales are expected to remain constant forever - A consol (bond that pays interest only and does not mature)

Which of the following are true about the amortization of a fixed payment loan?

- The amount of interest paid decreases each period - The principal amount paid increases each period

Which of the following methods amortizes a loan?

-Fixed payments that result in zero loan balance -Interest plus fixed amount

Suppose you need $5,000 in one year, $4,3000 in two years, and $5,000 in three years. Match each present value amount to the corresponding cash flow assuming a discount rate of 17%. 1. Present Value of the Year 1 Cash Flow 2. Present Value of the Year 2 Cash Flow 3. Present Value of the Year 3 Cash Flow

1. $4,273.50 ($5,000/1.17) 2. $3,314.21 ($4,300/1.17^2) 3. $3,121.85 ($5,000/1.17^3)

The formula for the ____________ value interest factor of an annuity is {1 - [1/(1 + r)^t]/r}

Present

The original loan amounts is called the:

Principal

With interest-only loans that are NOT perpetuities, the entire principal is:

Repaid at some point in the future

An effective annual rate of 7.12 percent is equal to 7 percent compounded ________________.

Semiannually

You expect to receive bonuses with your job at the end of each year for the next five years. Assume you can invest all of your bonuses at 4.5%, and the bonuses are as shown below, match each amount to its future value at the end of the five years, then match the total to the appropriate box. Year 1: $500 Year 2: $1,200 Year 3: $1,000 Year 4: $2,400 Year 5: $2,200

Year 1: $596.26 Year 2: $1,369.40 Year 3: $1,092.03 Year 4: $2,508.00 Year 5: $2,200.00 Total after 5 years: $7,765.68

Amy took out a mortgage of $100,000 at 4.5% with monthly payments for 30 years. What is her payment to principal and interest each month?

$506.69

Which compounding interval will result in the lowest future value assuming everything else is held constant?

Annual

The first cash flow at the end of week 1 is $100, the second cash flow at the end of month 2 is $100, and the third cash flow at the end of year 3 is $100. This cash flow pattern is an ________ cash flow.

Uneven

Which of the following is true about a growing annuity?

- The cash flows grow at a constant rate. - The cash flows grow for a finite period.

In the Excel setup of a loan amortization problem, which of the following occurs?

- The payment is found using PMT (rate, nper, -pv, fv) - To find the principal payment each month, you subtract the interest payment from the total payment.