Corporate Finance Chapter 9

72 rule

72/interest rate (5%=5) = the number of years for the principal to double

Suppose someone offered you your choice of two equally risky annuities, each paying $5,000 per year for 5 years. One is an annuity due, while the other is a regular (or deferred) annuity. If you are a rational wealth-maximizing investor which annuity would you choose? a. The annuity due. b. The deferred annuity. c. Either one, because as the problem is set up, they have the same present value. d. Without information about the appropriate interest rate, we cannot find the values of the two annuities; hence we cannot tell which is better. e. The annuity due; however, if the payments on both were doubled to $10,000, the deferred annuity would be preferred.

A

What is the present value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate? a. $670.43 b. $842.91 c. $1,169.56 d. $1,348.48 e. $1,522.64

A

Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will a. Be higher. b. Be lower. c. Stay the same. d. Cannot tell. e. Be variable.

B

If a 5-year regular annuity has a present value of $1,000, and if the interest rate is 10 percent, what is the amount of each annuity payment? a. $240.42 b. $263.80 c. $300.20 d. $315.38 e. $346.87

B

If it were evaluated with an interest rate of 0 percent, a 10-year regular annuity would have a present value of $3,755.50. If the future (compounded) value of this annuity, evaluated at Year 10, is $5,440.22, what effective annual interest rate must the analyst be using to find the future value? a. 7% b. 8% c. 9% d. 10% e. 11%

B

Which of the following statements is correct? a. Cash flow time lines are helpful graphical displays for situations involving simple annual interest but are not useful when time periods are more frequent than annual. b. The future value of an annuity due is equal to the future value of an otherwise identical regular annuity with interest compounded on each payment for one additional period. c. There is no precise method of calculating either present values or future values when fractional time periods are involved. We must instead use rough approximations. d. The terminal value of a stream of uneven cash flows is found by simply summing up all the cash flows. e. The annual percentage rate (APR) cannot be equivalent to the effective annual rate (EAR).

B

Which of the following statements is correct? a. The PV of an ordinary annuity will be larger than the PV of an annuity due, other things held constant. b. The effective annual rate will always be greater than the simple rate except in situations where the periodic rate is equal to the simple rate. c. If you were borrowing money from a bank, and the simple interest rate was 10 percent, you would be better off if the bank used daily rather than quarterly compounding. d. If you were borrowing money from a bank, and the simple interest rate was 10 percent, daily compounding, you would be better off if the bank used a 365-day year rather than a 360-day year. e. $100 placed in a bank account which pays 6 percent will double faster if the bank pays interest annually rather than daily.

B

You deposited $1,000 in a savings account that pays 8 percent interest, compounded quarterly, planning to use it to finish your last year in college. Eighteen months later, you decide to go to the Rocky Mountains to become a ski instructor rather than continue in school, so you close out your account. How much money will you receive? a. $1,171 b. $1,126 c. $1,082 d. $1,163 e. $1,008

B

At an effective annual interest rate of 20 percent, how many years will it take a given amount to triple in value? (Round to the closest year.) a. 5 b. 8 c. 6 d. 10 e. 9

C

Gomez Electronics needs to arrange financing for its expansion program. Bank A offers to lend Gomez the required funds on a loan where interest must be paid monthly, and the quoted rate is 8 percent. Bank B will charge 9 percent, with interest due at the end of the year. What is the difference in the effective annual rates charged by the two banks? a. 0.25% b. 0.50% c. 0.70% d. 1.00% e. 1.25%

C

Suppose the present value of a 2-year ordinary annuity is $100. If the discount rate is 10 percent, what must be the annual cash flow? a. $65.45 b. $82.64 c. $57.62 d. $53.78 e. $79.22

C

Which of the following statements is correct? a. Other things held constant, an increase in the number of discounting periods per year increases the present value of a given annual annuity. b. Other things held constant, an increase in the number of discounting periods per year increases the present value of a lump sum to be received in the future. c. The payment made each period under an amortized loan is constant, and it consists of some interest and some principal. The later we are is the loan's life, the smaller the interest portion of the payment. d. There is an inverse relationship between the present value interest factor of an annuity and the future value interest factor of an annuity, (i.e., one is the reciprocal of the other). e. Each of the above statements is true.

C

Which of the following statements is correct? a. Simple rates can't be used in present value or future value calculations because they fail to account for compounding effects. b. The periodic interest rate can be used directly in calculations as long as the number of payments per year is greater than or equal to the number of compounding periods per year. c. In all cases where interest is added or payments are made more frequently than annually, the periodic rate is less than the annual rate. d. Generally, the APR is greater than the EAR as a result of compounding effects. e. If the compounding period is semiannual then the periodic rate will equal the effective annual rate divided by two.

C

If you presently have $6,000 invested at a rate of 15 percent, how many years will it take for your investment to triple? (Round up to obtain a whole number of years if necessary.) a. 2 years b. 4 years c. 6 years d. 8 years e. 10 years

D

Steaks Galore needs to arrange financing for its expansion program. One bank offers to lend the required $1,000,000 on a loan which requires interest to be paid at the end of each quarter. The quoted rate is 10 percent, and the principal must be repaid at the end of the year. A second lender offers 9 percent, daily compounding (365-day year), with interest and principal due at the end of the year. What is the difference in the effective annual rates (EFF%) charged by the two banks? a. 0.31% b. 0.53% c. 0.75% d. 0.96% e. 1.25%

D

Which of the following statements is correct? a. If a bank uses quarterly compounding for saving accounts, the simple rate will be greater than the effective annual rate. b. The present value of a future sum increases as the simple interest rate increases or the number of discount periods per year decreases. c. The present value of a future sum increases as either the simple interest rate or the number of discount periods per year increases. d. The present value of a future sum decreases as either the simple interest rate or the number of discount periods per year increases. e. All of the above statements are false.

D

A $10,000 loan is to be amortized over 5 years, with annual end-of-year payments. Given the following facts, which of these statements is correct? a. The annual payments would be larger if the interest rate were lower. b. If the loan were amortized over 10 years rather than 5 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 5-year amortization plan. c. The last payment would have a higher proportion of interest than the first payment. d. The proportion of interest versus principal repayment would be the same for each of the 5 payments. e. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were higher.

E

What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate? a. $670.44 b. $842.91 c. $1,169.56 d. $1,522.64 e. $1,348.48

E

Which of the following statements is false? a. If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series. b. To increase present consumption beyond present income normally requires either the payment of interest or else an opportunity cost of interest foregone. c. Disregarding risk, if money has time value, it is impossible for the present value of a given sum to be greater than its future value. d. Disregarding risk, if the present value of a sum is equal to its future value, either r = 0 or t = 0. e. Each of the above statements is true.

E

A capital budgeting project is acceptable if the rate of return required for such a project is greater than the project's internal rate of return.

F

Because we usually assume positive interest rates in time value analyses, the present value of a three year annuity will always be less than the future value of a single lump sum, if the annuity payment equals the original lump sum investment.

F

NPV and IRR will always lead to the same accept/reject decision for mutually exclusive projects.

F

Perpetuities represent a series of even cash flows over a finite period of time.

F

The effective annual rate is always greater than the simple rate as a result of compounding effects.

F

The future value of a cash flow is positively related to interest rate and negatively related to the amount of time until maturity.

F

The greater the number of compounding periods within a year, the greater the future value of a lump sum invested initially, and the greater the present value of a given lump sum to be received at maturity.

F

When a loan is amortized, the largest portion of the periodic payment goes to reduce principal in the early years of the loan such that the accumulated interest can be spread out over the life of the loan.

F

All else equal, if a bond's yield to maturity increases, its price will fall.

T

An increase in the discount rate used in computing the NPV of a project will lower the value of the NPV for that project.

T

Disregarding risk, if money has time value, the future value of some amount of money always will be more than the amount originally invested, and the present value of some amount to be received in the future is always less than that future amount to be received

T

If we calculate a periodic interest rate, say a monthly rate, in order to get the simple annual rate, we can multiply the periodic rate by the number of periods within a year.

T

The NPV method implicitly assumes that the rate at which cash flows can be reinvested is the required rate of return, whereas the IRR method implies that the firm has the opportunity to reinvest at the project's IRR.

T

The present value of a future cash flow is the amount of money if invested today at particular interest would turn into the future value at maturity.

T

There exists an IRR solution for each time the direction of cash flows associated with a project is interrupted.

T

time value of money

The principles and computations used to revalue cash payoffs at different times so they are stated in dollars of the same time period; used to convert dollars from one time period to those of another time period.

amortized loan

a loan that requires equal payments over its life

cash outflow

a payment, of cash for expenses, and so forth

cash inflow

a receipt of cash from an investment or other sources

amortization schedule

a schedule showing precisely how a loan will be repaid

annuity

a series of payments of equal amounts at fixed, equal intervals for a specified number of periods

lump-sum amount

a single payment that is made either today or some date in the future

perpetuity

a stream of equal payments expected to continue forever

annuity due

an annuity with payments at the beginning of each period

ordinary annuity

an annuity with payments that occur at the end of each period

annual percentage rate (APR)

another name for the simple interest rate

cash flow (CF)

cash flows in general, including uneven cash flows

payment (PMT)

constant cash flows - the amount of an annuity payment

uneven cash flows

multiple payments of different amounts over a period of time

consols

perpetual bonds issued by the british gov to consolidate past debts

future value (FV)

the amount to which a cash flow or series of cash flows will grow over a given period of time compounded at a given rate

effective annual rate (EAR)

the annual rate of earned considering the compounding rate

present value (PV)

the current value of a future cash flows

terminal value

the future value of a cash flow stream

annual compounding

the process of determining the future value of a cash flow or series of cash flows when interest is paid once a year

discounting

the process of determining the present value in the future; the reverse of compounding

opportunity cost rate

the rate of return best available alternative investments of equal risk

simple (quotes) interest rate

the rate quoted by borrowers and lenders that is used to determine the rate earned per compounding period

cash flow

timeline An important tool used in time value of money analysis; a graphical representation used to show the timing of cash flows.

compound interest

when interest is left in an investment to earn additional interest