CH 4: Discounted Cash Flow Valuation

Suppose you paid a $1,200 loan off by paying $400 in principal each year plus 10 percent annual interest. How much is the interest payment in the second year of the loan?

$80 ($1,200 - 400) = 800 $800 × 0.1 = $80

The formula for finding the net present value of a cash outflow now, a positive cash flow in 1 year, a positive cash flow in 2 years, and a positive cash flow in 3 years is

-C0+ C1/(1 + r)^1 + C2/(1 + r)^2+ C3/(1 + r)^3

Which of the following represents an infinite and constant stream of cash flows?

A perpetuity

True or false: Receiving $10 today has the same value as receiving $1 today and $9 one year from now.

False

True or false: The Rule of 72 is a short cut approach to estimate the time needed to double your interest rate.

False

Which of the following payment methods amortizes a loan?

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

True or false: The formula for the present value of an annuity factor is {1-[1/(1+r)^t]} / r

True

Another term for an annuity due is _____.

an annuity in advance

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

annual

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

at the beginning of each period

Another term for a partial amortization loan is a(n) ____ loan.

balloon bullet

When investing in large US stocks, the reinvestment of dividends and capital gains generates

compound interest

The idea behind ______ is that interest is earned on interest.

compounding

The APR is meaningful for comparisons only when the number of ______ per year is given.

compounding periods

When using an annuity table to find the present value of an annuity, you multiply the annuity cash flow by the present value interest ________ for annuities.

factor

A growing annuity has a(n) ____.

finite number of growing cash flows

Cf*{[(1+r)t−1]/r} is the formula for the _______ value of an annuity.

future

Discounting is the process of converting ______ dollars into a ______ value.

future; present

As the compounding frequency increases, the future value will

increase

A perpetuity is a constant stream of cash flows for a(n) ______ period of time.

infinite

Fixed payment loans are typically used for which of the following

mortgages student loans car loans

Payments in a partial amortization loan are based on the amortization period, not the loan period. The remaining balance is then ____.

paid off in a lump sum bullet payment

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

present

The value of a future cash flow stated in today's dollars is referred to as the _____.

present value

Present value represents what an amount of money promised or expected in the future is worth ______.

today

One of the most basic principles of finance is that rational individuals prefer to receive a dollar ____ than a dollar ______.

today; tomorrow

Semiannual compounding means that interest is paid ______ per year.

two times

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 a(n) ______ type of cash flow.

uneven

__ is the process of converting future dollars into a current value.

Discounting

Which of the following are annuities?

Monthly rent payments in a lease Installment loan payments

True or false: The formula for finding the net present value of a cash outflow now, a positive cash flow in 1 year, and a positive cash flow in 2 years is -C0+ C1/(1 + r)^1 + C2/(1 + r)^2.

True

True or false: The spreadsheet (Excel) formula for calculating the present value of $100 at the end of each year for 2 years at 10 percent per year is: PV(.1,2,-100,0).

True

If $100 earns compound interest for 2 years at 10 percent per year, the future value will be ____.

$121.00 FV = $100 × 1.10^2

Which type of amortization is most commonly used in the real world for mortgages and car loans?

Fixed payment

In the formula for the future value of an annuity, the expression in brackets is equal to the

Future value interest factor for an annuity

You invest $100 today. With positive interest rates, the concept of future value implies that the future value of your $100 will be ____ $100.

greater than

A stream of cash flows that grows at a constant rate for a finite period is called a(n) _____.

growing annuity

A loan might be repaid in equal ________ over a specific period of time.

installments

For a positive annual percentage rate (APR) and multiple (more than one) compounding periods per year, the EAR is always ______ the APR.

larger than

A dollar tomorrow is worth ______ a dollar today.

less than

A traditional (non-growing) annuity consists of a(n) ________ stream of cash flows for a fixed period of time.

level

If reinvestment of interest or dividends does not occur, then the future value of an investment will be _____ and the realized yield will be ____ than if reinvestment had occurred.

lower; lower

What is the difference in the future value of $100 at 7 percent interest for 5 years if the interest is compounded semiannually rather than annually?

$0.80

A firm has cash flows of $100 at the end of years 1 - 4. What is the net present value of an investment in this firm if we pay $300 to purchase the firm and the discount rate is 10 percent?

$16.99 $100 × [(1 - (1/1.10)^4))/.10] - $300

To find the future value annuity factor from a time value of money table, read down the rows to find T = 10 and across the columns to find 10 percent. The factor where that column and row intersect is _____.

15.937

To find the future value annuity factor using the time value of money table, read down the rows to find T = 2, then across the columns for an interest rate of 10 percent. The intersection of that row and column will show the factor ____.

2.100

According to the Rule of 72, at 18% per year, it will take ________ years to double your money. Hint: round your answer to the nearest whole number of years.

4 72/18

To find the present value of an annuity of $100 per year for 10 years at 10 percent per year using the tables, look up the present value interest factor which is ______ and multiply that by ______.

6.1446; $100

The present value interest factor for a 30-year annuity with an interest rate of 10 percent per year is ______.

9.4269 [1 - (1/1.10^30)]/.10]

Which of the following is a perpetuity?

A constant stream of cash flows forever

What are the implications of the time value of money concept?

A dollar tomorrow is worth less than a dollar today A dollar today is worth more than a dollar tomorrow

Which of the following is the formula for the present value of a growing perpetuity?

C/(r - g)

Which of the following are ways to amortize a loan?

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

Which of the following are real-world examples of annuities?

Pensions Mortgages

Which of the following is true about a growing annuity?

The cash flows grow for a finite period.

PV = C/(r - g) is the formula for the present value of a

growing perpetuity

Amortization is the process of paying off loans by regularly reducing the _________.

principal

How long will it take to double your money at 10% per year?

7.2% 72/10

From highest to lowest, rank the following compounding periods effective annual rates

Continuous Weekly Semiannual Annual

When finding the present value of an annuity using a spreadsheet (Excel), the interest rate should be entered as a whole number.

False

The concept of future value implies that a dollar today is worth ______ a dollar in the future, assuming positive interest rates.

more than

The value of a firm can be found by taking the _____ value of all _____ cash flows.

present; future

What is the present value of $100 each year for 20 years at 10 percent per year?

$851.36 $100{[1 - (1/(1.10)^20)]/0.10}

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 $100{[1 - (1/(1.10)^3)]/.10}

Suppose you have a car loan that lasts 6 years, a discount rate of 7%, and a loan balance of $15,000 requiring annual payments. What is the annual payment?

$3,146.94

Ralph has $1,000 in an account that pays 10 percent per year. Ralph wants to give this 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 $1,000/[(1 - 1/1.10^3)/.10]

Suppose you paid off a $1,200 loan by paying $400 in principal each year plus 10 percent annual interest over a 3-year period. What is the total payment (interest plus principal) in Year 3?

$440 $400 + ($1,200 - 800) × .10

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 percent per year?

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

If you invest $100 at a stated annual rate of 10 percent compounded quarterly, how much more money will you have in 10 years than if the rate was compounded annually?

$9.13 $100 × (1 + .10/4)^40- $100 × (1.10)^10