Corporate Finance Ch. 2

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

$1,000

The formula for the present value of a perpetuity is ____________.

PV=C/r

Which of the following is the correct formula for the 1-period present value?

PV=FV/(1+r)

The general formula for the effective interest rate is:

[1+(r/m)]^m-1

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

A series of level payments that begins immediately for a specified period of time is called a(n):

annuity due

If you increase the risk level of a project, the discount rate should ______ which will _____ the project's present value.

increase, decrease

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

present value

If the future value is $750 in 1 year and the interest rate is 15 percent, what is the present value?

$652.17

If the interest rate is 10% per year, then what is the present value (PV) of $100 received one year from today?

$90.91

PV = C1/(r - g) is the formula for the present value of a:

growing perpetuity

What is the future value of $100 compounded continuously at a stated annual rate of 10 percent for 10 years?

$271.83

Which of the situations below will increase wealth? (select all that apply) a.) An initial cost of $1,000 and a PV of future cash flows of $1,001. b.) An initial cost of $1,000 and a PV of future cash flows of $999. c.) An initial cost of $1,000 and a PV of future cash flows of $1,101. d.) Cost of $1,000 and a PV of future cash flows of $900.

a, c

The difference between _______ interest and compound interest is that compound interest (increases or decreases) ___________ with time.

simple, increases

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

$248.69 (100[(1/.10)-(1/(.10(1.10)3))] = 248.69)

The future value of $100 at 10 percent compounded semiannually is ______ the future value of $100 at 10 percent compounded annually.

greater than

If you invest $100 at 10 percent per year for 3 years, your future value with annual compounding will be ___.

$133.10

How is net present value (NPV) computed?

NPV=PV-investment

Which of the following is a perpetuity? a.) A constant stream of cash flows forever b.) A growing stream of cash flows for a fixed period c.) An undulating stream of cash flows forever d.) A constant stream of cash flows for a fixed period

a

Which of the following will result in a lower present value for a given future cash flow? (select all that apply) a.) Less risk b.) A lower interest rate c.) More time d.) Less time e.) A higher interest rate f.) More risk

c, e, f

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

compounding

One example of a perpetuity is a British _____.

consol

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

continuous

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

false

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

greater than

The __________ annual interest rate is usually calculated as the total annual payment divided by the number of payments in the year.

quoted

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

semiannually

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

Assume a $100 investment earns a stated interest rate of 10 percent, compounded monthly. What will be the investment value after one year?

$110.47 (100x(1+.0083)^12)

If the interest rate is 9% per year, then what is the present value (PV) of $100 received one year from today?

$91.74

If you invest $1,000 and the present value of the incoming cash flows over the following year is $800, then the NPV is ____.

-$200 (NPV=-1,000+800=-200)

$200 at the end of each year forever at 10% per year is worth how much today?

3,187.49 (rst, find the PV by using the 10 year annuity factor: PV = $200 x 10 year annuity factor = $200 x [1/.1 - 1/.1x(1.1)10]= $1,228.92 To find the future value, multiply $1,228.92 x (1.1)10= $3,187.49.)

Suppose you invest $1,000 and the PV of your future cash flows is $1,100. If the investment becomes riskier, what will happen?

The NPV will decrease

Which of the following are true about the growing perpetuity model assumptions? a. The interest rate must exceed the growth rate. b. The interest and growth rates change at constant rates. c. The cash flows occur at regular intervals. d. The cash flow used is that for next year.

a, c, d

A fixed stream of cash flows that ends after a specified number of years is called a(n):

annuity

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

at the beginning of each period

What are some of the implications of the time value of money concept? a.) A dollar today is worth less than a dollar tomorrow. b.) A dollar today is worth more than a dollar tomorrow. c.) A dollar tomorrow is worth less than a dollar today. d.) A dollar has the same value no matter which day it is.

b, c

e^.09 equals ______.

1.094

What is the future value of $10 compounded for 50 years at 10 percent annual interest? (Use the formula $10 x (1+r)t where r is the annual interest and t is the number of years).

$1,173.91

What is the present value of a perpetuity of $50 per year if the annual interest rate is 10% and the growth rate is 6% per year?

$1,250 (50/(.1-.06))

If you invest $100 at 10 percent per year for 2 years, your future value with annual compounding will be ______.

$121

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

infinite

A company pays a $5 dividend with annual dividend increases of 2 percent. If the discount rate is 12 percent, what is present value of this growing perpetuity?

$50.00 (5/(.12-.02))

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 [($100 × 1.03510) - ($100 × 1..075) = $.80]

What is the future value of $100 compounded for 50 years at 10 percent annual interest? (Use the formula $100 x (1+r)t where r is the annual interest and t is the number of years).

$11,739,09

What is the present value of a perpetuity of $100 per year if the annual interest rate is 10% and the growth rate is 6% per year?

$2,500 (100/(.1-.06))

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

C1/(r-g)

The annual percentage rate is the annual interest rate without consideration of _____.

compounding

The effective annual rate (EAR) takes into account the ______ of interest that occurs within a year.

compounding

A dollar tomorrow is worth ______ a dollar today.

more than

Using the present value of an annuity formula, the present value of $100 received each year for 20 years at 10% per year is:

$851.36 (100[(1/.1)-(1/(.10(1.10)^20))])

Your bank quotes a 9% annual percentage rate on your car loan, which is equal to .75% monthly interest. What is the effective annual rate?

9.38% (1.0075(^12)-1)

Which of the following gives an effective annual yield of 12.36 percent? a.) 12% compounded semiannually b.) 12% compounded quarterly c.) 12% compounded annually d.) 12% compounded monthly

a

True or false: The correct mathematical formula for finding the future value of a $68 investment in 12 years at 9% annual interest is: FV = $68 x 1.129.

false

True or false: The multi-period formula for compounding is FV = (1 + r)t.

false (FV=PV*(1+r)^t)

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

fixed

If the future value is $500 in 1 year and the interest rate is 12 percent per year, what is the present value?

$446.43

Find the future value of an annuity of $100 per year for 10 years at 10 percent per year.

$1,593.75

If you earn 8 percent a year compounded annually for 7 years on a $1,000 present value, your future value will be ____.

$1,713.82

What is the present value of $100 in 10 years at a continuously compounded rate of 10 percent?

$36.79

A company pays a $5 dividend with annual dividend increases of 2 percent. If the discount rate is 12 percent, what is present value of this growing perpetuity?

$55.56 ($5/(.12-.03)=55.56)

Assume 12 percent annual interest is compounded semiannually on a $500 investment. What will that investment be worth after 1 year?

$561.80 (500*(1.06)^2)

Another common name for the stated annual interest rate is _____.

APR

Which term refers to the stated annual interest rate?

APR

Which of the following is the multi-period formula for compounding a present value into a future value?

FV= C0 × (1 + r)τ

Which of the following will increase wealth? a.) a negative NPV b.) a positive NPV c.) a zero NPV

b

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

effective