FINA 511 Chp 4
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 + .05)1 = $105 in one year.
What is the present value of $100 each year for 20 years at 10 percent per year?
$100{[1 - (1/(1.10)^20)]/0.10}= $851.36
If an annuity pays $50 every 3 years over a 30-year period at 8% per year, then the present value equals ____.
$173.39
From highest to lowest, rank the following compounding periods effective annual rates:
1. continuous 2. weekly 3. semiannual 4. annual
In the formula for continuous compounding, a constant equal to _____ is included.
2.72
What is the formula for the present value of a growing perpetuity?
C/(r - g)
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?
Calculate the payment using the PV of an annuity at 10% for 3 years. $1,000/[(1 - 1/1.103)/.10] = $402.11
Which of the following payment methods amortizes a loan?
Interest plus fixed amount Fixed payments that result in a zero loan balance
How is net present value computed?
NPV = -Cost + PV
How much is $50 at 7% interest at the end of each year forever worth today?
Present Value of a Perpetuity = Annual Payment ÷ Discount Rate = 714.29
One of the most basic principles of finance is that rational individuals prefer to receive a dollar ____ than a dollar ______.
Rational individuals prefer a dollar today to a dollar tomorrow, because they can invest that dollar and have more than a dollar tomorrow.
True or false: The effect of compounding increases exponentially over time.
T: Present value is an exponential function. PV = FV/(1 + r)t
True or false: More money can be earned with compound interest than with simple interest.
T: With compound interest, you earn interest on interest as well as interest on the principal.
Suppose you invest $1,000 and the PV of your future cash flows is $1,100. If the investment becomes riskier, what can happen?
The NPV will decrease and become negative as the discount rate rises with increasing levels of risk.
The present value interest factor for an annuity with an interest rate of 8 percent per year over 20 years is ____.
[1-(1/1.08^20)]/.08 = 9.8181
What will result in a lower present value for a given future cash flow?
a higher interest rate, more time, and more risk
Which compounding interval will result in the lowest future value assuming everything else is held constant?
annual
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
Another term for a partial amortization loan is a(n) ____ loan.
bullet, balloon
When investing in large US 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 idea behind ______ is that interest is earned on interest.
compounding
The limiting case of compounding periods is ____________ compounding.
continuous
If interest rates go up, the present value of a perpetuity will ______.
decrease
Assume interest is compounded monthly. The ______ annual rate will express this rate as though it were compounded annually.
effective
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?
fixed payment
The present value of a growing perpetuity requires the interest rate to be ______ the growth rate.
greater than
The present value of a growing perpetuity will be ______ the present value of a zero-growth perpetuity, all else equal.
greater than
More frequent compounding leads to ____.
higher EARS and EAYS
Which of the following would lower the present value of a future amount?
higher interest rate, longer period of time, higher level of risk. This is because If you have a longer period of time before you need the money, it can accumulate more interest, so you don't need to deposit as much today.
As the compounding frequency increases, the future value will:
increase
When equating the present value of two annuities, one will typically equate the present value of _____________- with the present value of ___________________. An example of this type of problem would be determining how much to save for retirement.
inflows; outflows
For a subsidized Stafford loan:
interest does not accrue until repayment begins
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
The concept of future value implies that a dollar today is worth ______ a dollar in the future, assuming positive interest rates.
more than
The loan balance on partial amortization loans declines so slowly because the ___.
payments are mostly interest
A British consol is an example of a(n):
perpetuity
Which of the following represents an infinite and constant stream of cash flows?
perpetuity
The value of a future cash flow stated in today's dollars is referred to as the _____.
present value
Amortization is the process of paying off loans by regularly reducing the _________.
principal
Interest paid twice a year is known as ______ compounding.
semiannual
The difference between _______ interest and compound interest is that compound interest (increases or decreases) ___________ with time.
simple; increases
Fixed payment loans are typically used for ?
student loans mortgages car loans
The EAR is meaningful for comparisons ____.
without a compounding interval
If you increase the risk level of a project, the discount rate should ______ which will _____ the project's present value.
"increase; decrease": If you increase the risk level of a project, the discount rate should increase, which will decrease the project's present value.
What is the general compounding formula for calculating the annual return on an investment when there is more than one compounding period in a year?
C0(1 + r/m)?^m
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
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
Interest rates and the ___________________ value of a perpetuity have an inverse relationship.
present
The value of a firm can be found by taking the _____ value of all _____ cash flows.
present, future
The interest rate (r) used in the general compounding formula is the ______ interest rate.
quoted
Balloon payments on partial amortization loans are typically quite large because ____.
the loan balance declines slowly
f an annuity pays $100 every 2 years over a 20-year period at 10 percent per year, then the present value equals ____.
Effective 2-year rate = 1.102 - 1 = .21 $100 × [1 - (1/1.2110)]/.21 = $405.41
The principal balance ______ over time of a fixed payment loan.
decreases
If you are promised $100 in one year, $200 in two years, and $300 in 3 years, then 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.
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?
$400 + ($1,200 - 800) × .10 = $440
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?
$6/(.10 - .04)= $100
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
A firm has cash flows of $100 at the end of years 1 - 4. How much will the present value of the firm change if the discount rate rises to 12 percent from 10 percent?
-13.25
If the interest rate is 10% per year and there are 10 years, what is the present value discount factor?
0.3855 by taking 1/(1+0.10)^10
A company plans to pay a $2.50 dividend with annual dividend increases of 4%. If the discount rate is 7%, what is present value of this growing perpetuity?
2.50 / (.07-.04) = 83.33
What are the implications of the time value of money concept?
A dollar today is worth more than a dollar tomorrow and a dollar tomorrow is worth less than a dollar today because you can invest it and have more than a dollar tomorrow.
A dollar tomorrow is worth ______ a dollar today.
A dollar tomorrow is worth less than a dollar today, because if you invest the dollar you have today, you'll have more than a dollar tomorrow.
What will increase wealth?
A positive NPV because it is the same as having that amount of money in your pocket today, so it will increase wealth. A negative NPV is the same as having money taken out of your pocket today.
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?
PV3 = $100[(1 - 1/1.105)/.1] = $379.08 PV0 = $379.08/1.103 = $284.81
What are two to amortize a loan?
Pay principal and interest every period in a fixed payment. Pay the interest each period plus some fixed amount of the principal.
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 (%)
A stream of cash flows that grows at a constant rate for a finite period is called a(n) _____.
growing annuity
PV = C/(r - g) is the formula for the present value of a:
growing perpetuity
Compared to a comparable fixed payment loan, the total interest on a fixed principal loan is ___.
less
In reality, perfect certainty of future cash flows occurs ____.
rarely
When evaluating NPV, the future is typically ______.
uncertain
In a growing perpetuity model, if the growth rate is larger than the interest rate, then the present value will be ____.
undefined
What is the formula for computing future value with continuous compounding?
C0 × e^(rT)
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": Reason: The cash flows for an annuity must happen at regular intervals. These do not (week, month, year).
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?
$100 × [(1 - (1/1.10)4))/.10] - $300 = $16.99
What is the future value of $100 compounded continuously at a stated annual rate of 10 percent for 10 years?
$100 × e.^(10 × 10) = $271.83
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?
$100/(.10 - .06) = $2,500
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
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
How frequently does continuous compounding occur?
Every infinitesimal instant
True or false: Receiving $10 today has the same value as receiving $1 today and $9 one year from now.
F: You could invest nine extra dollars now and have more than nine dollars a year from now.
What are examples of annuities?
Monthly rent payments in a lease Installment loan payments
What is true about the growing perpetuity model assumptions?
The cash flow used is that for next year. The cash flows occur at regular intervals. The interest rate must exceed the growth rate.
The APR is meaningful for comparisons only when the number of ______ per year is given.
compounding periods
If the discount rate increases, the net present value will:
decrease
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 geometric series has a(n) ______ sum.
finite
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
A delayed annuity (or perpetuity) is one that begins ___.
many periods in the future
______ frequent compounding leads to a ______ EAR, all else equal.
more; higher less ; lower