Financial Analysis - USCA MBA - CH4 SB

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 + 0.10/4)^40 − $100 × (1.10)^10 = $9.13.

If the interest rate is 10 percent per year, then what is today's value of $100 received one year from today?

$90.91 Present Value = Today's Value / (1 + interest rate) PV = $100/1.10 = $90.91

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

FV = C × (1 + r)^τ

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

False

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 The cash flows for an annuity must happen at regular intervals. These do not (week, month, year).

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

$1,000 C/r for perpetuity equation

What is the future value of an annuity due of $100 per year for 10 years at 10 percent per year?

$1,753.12 Future Value of an Annuity = C(((1+r)^t-1)/r) Future Value of an Annuity Due = C(((1+r)^t-1)/r)(1+r) $100[(1.1010 −1)/0.10][1.10] = $1,753.12. Note you must multiply by 1+r because this is an annuity due

What is the future value of $100 compounded for 50 years at 10 percent annual interest?

$11,739.09 Future Value = Primary x (1 + Interest)^Times Compounded FV = $100 × 1.10^50 = $11,739.09.

What is the future value of $100 at 10 percent simple interest for 2 years?

$120 $100 + 2(0.10 × $100) = $120.

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

$121 FV = $100 × 1.10^2 = $121.

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

False You could invest nine extra dollars now and have more than nine dollars a year from now.

Compared to a comparable fixed payment loan, the total interest on a fixed principal loan is ___.

Less

Which of the following will result in a lower present value for a given future cash flow? - more time - less time - a higher interest rate - more risk - a lower interest rate - less risk

More time A Higher Interest Rate More Risk

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

PV = FV/(1 + r)

Which of the following are ways to amortize a loan? Pay both interest and principal in one lump sum at maturity. Pay principal and interest every period in a fixed payment. Pay the interest each period plus some fixed amount of the principal. Pay only interest every period and pay the principal off at maturity.

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

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

Present Value

Interest paid twice a year is known as ______ compounding.

Semiannual

Which of the following are ways in which a $5,000 fixed principal repayment loan differs from a comparable $5,000 fixed payment loan? The amount of interest paid each period is different. The total payment each period for each type of loan is different. The total principal repaid amount is different. The amount of principal paid each period is different.

The amount of interest paid each period is different. The total payment each period for each type of loan is different. The amount of principal paid each period is different.

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

True or false: A one-period formula for present value is PV = FV/(1 + r).

True PV = C1/(1 + r). Either FV or C1 can be used to designate the cash flow in Year 1.

Which party benefits from delaying interest accrual for a subsidized Stafford loan?

borrower

The real world has moved away from using ______ for calculating future and present values.

time value of money tables

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

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

future; present

The present value of a perpetuity can be found as the limit of a(n) ______ series.

geometric

If the interest rate is greater than zero, the value of an annuity due is always ______ an ordinary annuity.

greater than

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

growing annuity

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

larger

A dollar tomorrow is worth ______ a dollar today.

less than

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

present; future

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

principal

The interest rate (r) used in the general compounding formula is the ______ interest rate.

quoted

Fixed payment loans are typically used for which of the following? credit card loans student loans car loans mortgages

student loans car loans mortgages

If you invest $100 at 10 percent simple interest, how much will you have in 10 years?

$200 Simple Interest = (Primary x Interest Rate) x Number of Years + Primary FV = $100 + 10($100 × 0.10) = $200.

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 Calculate the payment using the PV of an annuity at 10 percent for 3 years. PV = C/((1-1/(1+r)^t)/r) $1,000/[(1 − 1/1.10^3)/0.10] = $402.11.

From highest to lowest, rank the following compounding periods effective annual rates: - semiannual - weekly - continuous - annual

1. Continuous 2. Weekly 3. Semiannual 4. Annual

For a subsidized Stafford loan,

Interest does not accrue until repayment begins

Which of the following is true about a growing annuity? The cash flows grow for an infinite period. The cash flows grow at the rate of inflation. The cash flows grow for a finite period. The cash flows grow at an irregular rate.

The cash flows grow for a finite period.

Which of the following are true about the amortization of a fixed payment loan? The payment amount decreases each period. The principal amount paid increases each period. The amount of interest and principal paid increases each period. The amount of interest paid decreases each period.

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

True or false: The first step in calculating the present value of a delayed annuity is to find the present value of the annuity one period prior to the first payment using the present value of an annuity formula.

True

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 formula for the present value of an annuity factor is C{(1-1/(1 + r)^t)/r}

True

Semiannual compounding means that interest is paid ______ per year.

Twice

The present value of a growing perpetuity will be ______ the present value of a zero-growth perpetuity, all else equal.

greater than

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

infinite

Which of the following payment methods amortizes a loan? interest plus fixed amount fixed payments that result in a zero loan balance single lump sum payment fixed interest payments only

interest plus fixed amount fixed payments that result in a zero loan balance

When using the spreadsheet (Excel) function for finding the PV of an annuity, it's a good idea to enter the ______ as a negative value.

payment

The loan balance on partial amortization loans declines so slowly because the ___.

payments are mostly interest

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

payments or installments

C/r is the formula for the present value of a(n) ____.

perpetuity

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

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

present

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 × 1.035^10) − ($100 × 1.07^5) = $0.80.

If you invest $1,000 and your NPV is $200, then the present value of your future cash flows is ______.

$1,200 NPV = −Cost + PV → PV = NPV + Cost PV = $200 + 1,000 = $1,200.

At an annual interest rate of 10 percent, what is the present value of a perpetuity growing at 4 percent per year if next year's cash flow is $6?

$100 $6/(0.10 − 0.04)= $100.

Which one of the following constitutes an infrequent annuity? $100 in random time periods $100 once every 2 years $100 every month $100 every year

$100 once every 2 years

A 5-year $10,000 loan with a 15-year amortization period paid monthly at 10 percent, compounded monthly, will have monthly payments of ____.

$107.46 C/((1-(1/(1+r)^t)/r) $10,000/[(1 − 1/(1 + 0.10/12)12x15)/(0.10/12)] = $107.46. (Note that the loan is amortized for 15 years, even though a balloon payment will be due in 5 years.)

If you invest $100 at 10 percent compounded annually, how much money will you have at the end of 3 years?

$133.10 Future Value = Primary x (1 + Interest)^Time Compounded FV = $100 × 1.10^3 = $133.10.

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 Net Present Value of an Annuity = CF[(1-1/(1+r)^t)/r] - costs $100 × [(1 − (1/1.10)4))/0.10] − $300 = $16.99.

What is the present value of an annuity of $100 per year that begins at the end of year 4 and lasts for 5 years if the interest rate is 10 percent per year?

$284.81 Present Value of an Annuity = C((1-1/(1+r)^t)/r) PV3 = $100[(1 − 1/1.10^5)/0.1] = $379.08. Present Value of Cash = FV / (1+r)^t PV0= $379.08/1.10^3 = $284.81.

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

$3,146.94 Total Loan Cost = C x ((1-(1/(1+r)^t)/r) C = 15,000/[((1-(1+.07)^6)/.07] $3,146.94 Notice the C had to be moved to the other side

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) × 0.10 = $440.

Which of the following can be used to calculate present value? - a financial calculator - random number generation - a time value of money table - an algebraic formula

- a financial calculator - a time value of money table - an algebraic formula

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 ____.

2.10

In the formula for continuous compounding, a constant equal to _____ is included.

2.72 or e

If the cash flows of an annuity start at the end of year 4, the present value of an annuity formula will discount all of the annuity cash flows back to the end of year _______.

3

Which of the situations below will increase wealth? - An initial cost of $1,000 and a PV of future cash flows of $1,101. - Cost of $1,000 and a PV of future cash flows of $900. - An initial cost of $1,000 and a PV of future cash flows of $999. - An initial cost of $1,000 and a PV of future cash flows of $1,001.

An initial cost of $1,000 and a PV of future cash flows of $1,101. An initial cost of $1,000 and a PV of future cash flows of $1,001.

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

C/(r − g)

What is the formula for computing future value with continuous compounding?

C0 × e^(rT) This is PERT from previous classes

What is the general compounding formula for calculating the annual return on investment when there is more than one compounding period in a year?

C0(1 + r/m)^m

When investing in large U.S. stocks, the reinvestment of dividends and capital gains generates ______.

compound interest

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

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

compounding

The limiting case of compounding periods is ______ compounding.

continuous

The principal balance ______ over time of a fixed payment loan.

decreases

If you are promised $100 in 1 year, $200 in 2 years, and $300 in 3 years, and if you can earn a positive interest rate on your investments, those promises combined equal ______ $600 today.

less than The sum of those cash flows is $600, so if you deposited $600 today at a positive interest rate and withdrew the series of payments described, there would be money left in the account at the end because of accumulated interest. So you would need to deposit less than $600, which means the present value is less than $600.

In an infrequent annuity, the payments occur ____.

less than once a year

Annuity time value of money tables is computed based on an _________ annuity.

ordinary

Annuity time value of money tables are based on _____.

ordinary annuities

The payments in a ________ amortization loan are not based on the life of the loan.

partial

Suppose you are promised $100 at the end of year 1, $200 at the end of year 2, and $300 at the end of year 3. If the interest rate is 10 percent per year, what is the present value of these promises?

$481.59 $100/1.1 + $200/1.1^2 + $300/1.1^3 = $481.59.

A company plans to pay a $5 dividend with annual dividend increases of 3 percent. If the discount rate is 12 percent, what is the present value of this growing perpetuity?

$55.56 $5/(0.12 − 0.03) = $55.56.

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

$652.17 Future Value / (1 + Interest rate) $750/1.15 = $652.17.

What is the present value of an annuity that makes payments of $100 per year for 10 years if the first payment is made immediately and the discount rate is 10 percent per year?

$675.90 Present Value of a Growing Annuity = C((1-1/(1+r)^t)/r)*(1+r) PV = $100[(1 − 1/1.10^10)/0.10][1.10] = $675.90.

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 You are repaying $400 each year. Interest is computed on the principal outstanding for the year, which is ($1,200 − 400) = 800. $800 × 0.1 = $80.

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

4 Rule of 72 72/Interest Percentage = Number of years to double primary

If the cash flows of an annuity start at the end of year 6 (date 6), the present value of an annuity formula will discount all of the annuity cash flows back to the end of year ___.

5

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 (1-(1/(1+r)^number of years))/r

Your bank quotes a 9% APR on your car loan (.75 percent interest each month). What is the EAR?

9.38% 1.0075^12 - 1 = 9.38%

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+r)^number of years))/r [1 − (1/1.1030)]/0.10] = 9.4269.

What are two ways to calculate a balloon payment? Amortize the loan over the loan life to find the ending balance. Find the future value of the payments for the loan term. Find the present value of the payments remaining after the loan term. Amortize the loan over the amortization period to get the balance.

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

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

False Forgot to add primary value FV = PV × (1 + r)^t.

What are two ways to calculate a balloon payment? Amortize the loan over the amortization period to get the balance. Find the present value of the payments remaining after the loan term. Find the future value of the payments for the loan term. Amortize the loan over the loan life to find the ending balance.

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

Which of the following is a perpetuity?

a constant stream of cash flows forever

Which of the following represents an infinite and constant stream of cash flows? a growing annuity an annuity a perpetuity a growing perpetuity

a perpetuity A perpetuity represents an infinite and constant stream of cash flows. A growing perpetuity does not have a constant stream of cash flows.

Another term for an annuity due is _____.

an annuity in advance In Example 4.23, this type of annuity is called an annuity due or annuity in advance.

Which compounding interval will result in the lowest future value assuming everything else is held constant? - annual - quarterly - monthly - continuously

annual

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

at the beginning of each period

A lump sum payment to pay off the balance of a partially amortized loan is called a ______ payment.

balloon or bullet

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

balloon or bullet

A geometric series has a(n) ______ sum.

finite

A growing annuity has a(n) ____.

finite number of growing cash flows

Which type of amortization is most commonly used in the real world for mortgages and car loans? variable period fixed interest fixed principal fixed payment

fixed payment

Balloon payments on partial amortization loans are typically quite large because ____.

the loan balance declines slowly

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

$851.36 C((1-(1/(1+r)^number of years))/r) $100{[1 − (1/(1.10)20)]/0.10} = $851.36.

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

$2,500 $100/(0.10 − 0.06) = $2,500.

What is the present value of an ordinary annuity that pays $100 per year for 3 years if the interest rate is 10 percent per year?

$248.69 C/(1+r) + C/(1+r)^2 + C/(1+r)^3... or C((1-(1/(1+r)^number of years))/r) 100{[1 − (1/(1.10)^3)]/0.10}

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 Future Value / (1 + Interest rate) $500/1.12 = $446.43.

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

$561.80 Primary + (1 + (Interest Rate per Year / Number of Times Compounded per Year))^Number of times compounded $500 × (1.06)2 = $561.80

A perpetuity will pay $5 next year with payments increasing at a rate of 2 percent annually. What is the value of the 2 percent growth if the interest rate is 10 percent?

$62.50 Growing Annuity Equation C/(r-g)

How much is $50 at 7 percent interest at the end of each year forever worth today?

$714.29 = C/r = 100/0.07 = 714.29

A company plans to pay a $2.50 dividend with annual dividend increases of 4 percent. If the discount rate is 7 percent, what is the present value of this growing perpetuity?

$83.33 $2.5/.07-.04 = $83.33

Which of the following would lower the present value of a future amount? - a higher level of risk - a longer period of time - a higher interest rate - a shorter time period

- a higher level of risk - a longer period of time - a higher interest rate

Time value of money tables is not as common as they once were because ______.

- it is easier to use inexpensive financial calculators instead - they are available for only a relatively small number of interest rates

When there are multiple time periods, which of the following would lower the present value of a single future cash flow, all else constant? - higher cash flows - more risk - more time periods - higher interest rates

- more risk - more time periods - higher interest rates

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 Net Present Value = -Cost + Return NPV = −$1,000 + 800 = −$200.

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

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.

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

Discounting

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

A delayed annuity (or perpetuity) is one that begins ______.

many periods in the future

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

more than

The EAR is meaningful by itself, but the ______ is only meaningful when the number of compounding periods per year is given.

annual percentage rate

The ______ is the annual interest rate without consideration of compounding.

annual percentage rate

A _______ annuity begins in the future.

delayed

According to the Rule of 72, to find the amount of time required for a sum of money to double in value, you ______.

divide 72 by the interest rate (%)

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

effective

How frequently does continuous compounding occur?

every infinitesimal instant

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

C(((1+r)^t−1)/r) is the formula for the ________ value of an annuity

future

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 If interest rates are positive, $100 given to you today will be worth more than $100 in the future (for example, if the interest rate is 5%, your $100 will be worth $100 x (1 + 0.05)1 = $105 in 1 year).

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

growing perpetuity

A positive NPV will ______ wealth.

increase

As the compounding frequency increases, the future value will ______.

increase

Which of the following are annuities? tips to a waiter installment loan payments monthly rent payments in a lease monthly grocery bill

installment loan payments monthly rent payments in a lease

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

level

Which of the following are real-world examples of annuities? mortgages common stock dividends pensions preferred stock dividends

mortgages pensions