Chapter 6 Discounted Cash Flow Valuation
How frequently does continuous compounding occur?
Every instant
With a fixed payment loan, the amount of interest paid ___ each period.
decreases
Which of the following is a perpetuity?
A constant stream of cash flows forever
Compared to a comparable fixed payment loan, the total interest on a fixed principal loan is ___.
less
Which compounding interval will result in the lowest future value assuming everything else is held constant?
Annual
What are two ways to calculate a balloon payment?
Find the present value of the payments remaining after the loan term. Amortize the loan over the loan life to find the ending balance.
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 payments in a ________ amortization loan are NOT based on the life of the loan.
partial
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
Amortization is the process of paying off loans by regularly reducing the _________.
principal
Interest paid twice a year is known as ______ compounding.
semiannual
What is formula to calculate 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?
$100[(1 − 1/1.10^10)/0.10][1.10]
The APR is always the same as the EAR.
false
A fixed payment loan is most common for consumers.
true
One example of a perpetuity is a British _____.
consol
In terms of time to maturity, U.S. Treasury notes and bonds have initial maturities ranging from ___ years.
2 to 30
Another common term for the effective annual rate (EAR) is the:
APY
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 annuities?
monthly rent payments in a lease and installment loan payments
To find the present value of an annuity of $100 per year for 5 years at 10 percent per year using the tables, look up the present value interest factor which is ______ and multiply that by ______.
3.7908; $100
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.
There is only one way to quote interest rates.
false
The formula for the ______ value interest factor of an annuity is {1-[1/(1+r)t]r}1-[1/(1+r)t]r.
present
A growing annuity has a(n) ____.
finite number of growing cash flows
The _____ rate is used to find the EAR.
quoted
The APR is also called the _____ rate and it differs from the EAR..
stated
The most common way to repay a loan is to pay ____.
interest plus a fixed principal amount every period
___ is the process of paying off loans by regularly reducing the principal.
Amortization
Which of the following payment methods amortizes a loan?
Fixed payments that result in a zero loan balance Interest plus fixed amount
If the term structure of interest rates is upward sloping, then ____.
long-term rates are higher than short-term rates
Which of the following are real-world examples of annuities?
pensions and mortgages
The ______ future value factor is found by taking the future value factor and subtracting one, then dividing this number by the interest rate.
annuity
A lump sum payment to pay off the balance of a partially amortized loan is called a ______, payment.
balloon or bullet
An annuity _______ is an annuity for which the cash flows occur at the beginning of each period.
due
Assuming the same interest rate, the future value of an amount compounded semiannually is ______ the future value of that amount compounded annually.
greater than
In a spreadsheet loan amortization schedule, to find the principal payment each month, you subtract the ___ from the total payment.
interest
Which three of the following are common shapes for the term structure of interest rates?
humped, upward sloping, and downward sloping
When using a financial calculator to determine the number of payments on a loan, you may use the inputs I/Y, PMT, and PV to solve for _____.
N
You owe $1,200 on your credit card, which charges 1.5% per month. If you pay $50 per month starting at the end of this month, which of the following show the steps you will apply using a financial calculator to solve for the number of months will it take to pay off your credit card?
Enter −50 for PMT, 1,200 for PV, and 1.5 for I/Y. Solve for N.
Which of the following show the inputs you would use in a financial calculator to compute the present value of $100 per year for 30 years if the discount rate is 5%?
In your financial calculator, enter 100 for PMT, 30 for N, and 5 for I/Y. Solve for PV.
_____ loans are short-term loans made to consumers which require you to write a check today that is postdated.
Payday
Which of the following are true about a partial amortization loan?
The monthly payments do not fully pay off the loan by the end of the loan period. The monthly payment is based on a longer amortization period than the maturity of the loan. The amortization period is longer than the loan period. The borrower makes a large balloon payment at the end of the loan period.
In the standard present and future value tables, and in all the default settings on a financial calculator, the assumption is that cash flows occur at the ___ of each period.
end
In the standard present and future value tables, and in all the default settings on a financial calculator, the assumption is that cash flows occur at the _______ (beginning/end) of each period.
end
The loan balance on ___ amortization loans declines so slowly because the payments are mostly interest.
partial
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
Another common name for the effective annual rate is the annual percentage ______.
yield
The ___ percentage rate is the interest rate charged per period multiplied by the number of periods in a year.
annual
The ______ percentage rate is the interest rate charged per period multiplied by the number of periods in a year.
annual
A lump sum payment to pay off the balance of a partially amortized loan is called a ___, or bullet, payment.
balloon
The effective annual rate (EAR) takes into account the ______ of interest that occurs within a year.
compounding
The present value of a series of future cash flows is the amount you would need today to _____.
exactly duplicate those future cash flows
Given the same APR, more frequent compounding results in _____.
higher EARs
perpetuity is a constant stream of cash flows for a(n) ______ period of time.
infinite
For a positive stated annual interest rate and multiple (more than one) compounding periods per year, the EAR is always ___ than the APR.
larger
When valuing cash flows, you can either value multiple cash flows or a single sum, also known as a(n) _____ sum.
lump
A single cash flow is also known as a:
lump sum
Most investments involve _____ cash flows.
multiple
One method of calculating future values for multiple cash flows is to compound the accumulated balance forward _____ at a time.
one year
A typical investment has a large cash (inflow/outflow) at the beginning and then a cash (inflows/outflows) for many years.
outflow ; inflows
When the U.S. government wants to borrow money for the long-term (more than one year) it issues:
treasury bonds and treasury notes
Semiannual compounding means that interest is paid ______ per year.
two times
The formula for the present value of an annuity due is _____.
(1 + r) × (PV of an ordinary annuity)
The original loan amount is called the _____.
principal
Because of __________ and _________, interest rates are often quoted in many different ways.
tradition; legislation
When using a financial calculator to find the interest rate, you may use the inputs N, PMT, and PV to find 1/ ___.
y
Which formula shows the present value of an ordinary annuity that pays $100 per year for three years if the interest rate is 10 percent per year?
$100{[1 − (1/(1.10)^3)]/0.10}
Which of the following is the simplest form of loan?
A pure discount loan
You are planning to buy a CD for $1,352. You will receive $1,500 in 2 years. Which inputs will you use in a financial calculator to find the interest rate you will receive on that investment, assuming annual compounding?
Enter −1,352 for PV, 2 for N, and 1,500 for FV. Solve for I/Y.
In the Excel setup of a loan amortization problem, which of the following occurs?
To find the principal payment each month, you subtract the interest payment from the total payment. The payment is found using PMT(rate, nper,-pv, fv).
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
The formula for the annuity present value factor for a 30-year annuity with an interest rate of 10 percent per year is ______.
[1 − (1/1.1030)]/.10]
Which of the following processes can be used to calculate future value for multiple cash flows?
calculate the future value of each cash flow first and then add them up and compound the accumulated balance forward one year at a time
When calculating the future value of multiple cash flows using a spreadsheet, you must:
calculate the future value of each cash flow then add the compounded values together
When calculating the present value of multiple cash flows using a spreadsheet, you must:
calculate the present value of each cash flow then add the discounted values together
The name for a perpetuity in Canada and the United Kingdom is a ___.
consol
The present value of a series of ___ cash flows is the amount you would need today to exactly duplicate those future cash flows.
future
If the interest rate is greater than zero, the value of an annuity due is always ______ an ordinary annuity.
greater than
A perpetuity is a constant stream of cash flows for a(n) ______ period of time.
infinite
For a positive stated annual interest rate and multiple (more than one) compounding periods per year, the EAR is always ______ the APR.
larger than
Versus a similar fixed payment loan, the total interest on a fixed ___ loan is less.
principal
Which of the following is true about a growing annuity?
the cash flows grow at a constant rate and the cash flows grow for a finite period.
Payday loans allow you to ___.
borrow now and repay later
In almost all multiple cash flow calculations, it is implicitly assumed that the cash flows occur at the _____ of each period.
end
The loan balance on partial amortization loans declines so slowly because the ___.
payments are mostly interest
Which of the following is the formula for the EAR?
[1 + (Quoted rate/m)]^m − 1
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. Which of the following formulas show how much Ralph will give to the charity each year?
$1,000/[(1 − 1/1.10^3)/0.10]
What is the formula to calculate the future value of an annuity due of $100 per year for 10 years at 10 percent per year?
$100[(1.10^10 − 1)/0.10][1.10]
You will receive a bonus of $5,000 in one year's time, and would like to take a loan against it now. What is the formula that shows how much you can borrow if you plan to use the entire amount to pay back the loan and your interest rate is 3%?
$5,000/1.03
Which of the following is equal to an effective annual rate of 12.36 percent?
12%, compounded semiannually
Which of the following should be valued using a perpetuity formula?
Cash flows from a product whose sales are expected to remain constant forever A consol (bond that pays interest only and does not mature) Preferred stock
Which shape does the term structure of interest rates usually have?
Upward sloping
Which of the following show the steps you would apply using a financial calculator to find the future value of an annuity of $100 per year for 10 years at 15%?
Enter 100 for PMT, 10 for N, and 15 for I/Y. Solve for FV.
Which of the following is the formula for the future value of an annuity?
FV = C((1+r)t−1r)
True or false: There is only one way to quote interest rates.
False
Which of the following are true about the amortization of a fixed payment loan?
The principal amount paid increases each period. The amount of interest paid decreases each period.
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,)
What is the present value of an ordinary annuity that pays $100 per year for 20 years if the interest rate is 10 percent per year?
$100{[1 - (1/(1.10)^20)]/0.10}
Which of the following show the steps you would apply using a financial calculator to find the future value of an annuity of $400 per year for 10 years at 5%?
Enter 400 for PMT, 10 for N, and 5 for I/Y. Solve for FV.
Which type of amortization is most commonly used in the real world for mortgages and car loans?
Fixed payment
You may use which of the following sets of inputs together to solve for the present value of an annuity using a financial calculator?
N, I/Y, PMT, PV
The ___ future value factor is found by taking the future value factor and subtracting one, then dividing this number by the interest rate.
annuity
An annuity due is a series of payments that are made ____.
at the beginning of each period
Assume interest is compounded monthly. The ______ annual rate will express this rate as though it were compounded annually.
effective
The future value of $100 at 10 percent compounded semiannually is ______ the future value of $100 at 10 percent compounded annually.
greater than
A humped term structure of interest rates indicates that interest rates are expected to _____ as the time to maturity increases.
increase and then decline
The present value of an annuity due is equal to the present value of a(an) ______ annuity multiplied by (1 + r).
ordinary
A typical investment has a large cash ___ at the beginning and then a cash ___ for many years.
outflow; inflows
To use a present value of an annuity table to find the present value of an annuity factor, search the _____ for the number of periods and the _____ for the rate.
row; column
An effective annual rate of 7.12 percent is equal to 7 percent compounded ______.
semiannually EAR= (1+%/t)^t
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
If the interest rate is greater than ___ , the value of an annuity due is always greater than an ordinary annuity.
zero or 0
With interest-only loans that are not perpetuities, the entire principal is _____.
repaid at some point in the future
