Discounted cash flows and valuation Flashcards
Explain why cash flows occurring at different times must be adjusted to reflect their
value as of a common date before they can be compared, and calculate the present
value and future value for multiple cash flows.
When making decisions involving cash flows over time, we should first identify the
magnitude and timing of the cash flows and then adjust each individual cash flow to
reflect its value as of a common date. For example, the process of discounting
(compounding) the cash flows adjusts them for the time value of money because today’s
dollars are not equal in value to dollars in the future. Once all of the cash flows are in
present (future) value terms, they can be compared to make decisions. Section 6.1
discusses the calculation of present values and future values of multiple cash flows.
Describe how to calculate the present value and the future value of an ordinary
annuity and how an ordinary annuity differs from an annuity due.
An ordinary annuity is a series of equally spaced, level cash flows over time. The cash
flows for an ordinary annuity are assumed to take place at the end of each period. To find
the present value of an ordinary annuity, we multiply the present value of an annuity
factor, which is equal to (1 - Present value factor)/ i, by the amount of the constant cash
flow. An annuity due is an annuity in which the cash flows occur at the beginning of each
period. A lease is an example of an annuity due. In this case, we are effectively prepaying
for the service. To calculate the value of an annuity due, we calculate the present value
(or future value) as though the cash flows were an ordinary annuity. We then multiply the
ordinary annuity value times (1 + i). Section 6.2 discusses the calculation of present
value of an ordinary annuity and an annuity due.
Explain what perpetuities are, where we see them in business, and calculate the
present values of perpetuities.
A perpetuity is like an annuity except that the cash flows are perpetual — they never end.
British Treasury bonds, called consols, were the first widely used securities of this kind.
The most common example of a perpetuity today is preference shares. The issuer of
preference shares promises to pay fixed -rate dividends forever. The cash flows from
companies can also look like perpetuities. To calculate the present value of a perpetuity,
we simply divide the promised constant payment (CF) by the interest rate ( i).
Discuss growing annuities and perpetuities, as well as their application in business,
and calculate their present values.
Financial managers often need to value cash flow streams that increase at a constant rate
over time. These cash flow streams are called growing annuities or growing perpetuities.
An example of a growing annuity is a 10 -year lease contract with an annual adjustment
for the expected rate of inflation over the life of the contract. If the cash flows continue to
grow at a constant rate indefinitely, this cash flow stream is called a growing perpetuity.
Application and calculation of cash flows that grow at a constant rate are discussed in
section 6.4.
Discuss why the effective annual interest rate (EAR) is the appropriate way to
annualise interest rates, and calculate EAR.
The EAR is the annual growth rate that takes compounding into account. Thus, the EAR
is the true cost of borrowing or lending money. When we need to compare interest rates,
we must make sure that the rates to be compared have the same time and compounding
periods. If interest rates are not comparable, they must be converted into common terms.
The easiest way to convert rates to common terms is to calculate the EAR for each
interest rate. The use and calculations of EAR are discussed in section 6.5.
Explain how to calculate the future value of a stream of cash flows.
It would helpful to first construct a time line so that we can identify the timing of each
cash flow. Then you would calculate the future value of each individual cash flow.
Finally, you would add up the future values of all the individual cash flows to determine
the future value of the cash flow stream.
Explain how to calculate the present value of a stream of cash flows.
To calculate the present value of a stream of cash flows, you should first draw a time line
so that you can see that each cash flow is placed in its correct time period. Then you
simply calculate the present value of each cash flow for its time period, and finally you
add up all the present values.
Why is it important to adjust all cash flows to a common date?
When making economic decisions, we need to compare “apples to apples.” This is
possible only when we bring all the cash flows to a common date, which can either be a
present time or some future date. The reason is the time value of money: a dollar today is
worth more than a dollar in the future. Thus, when cash flows are converted to the same
time period, the time value of money concept holds true, and we can concentrate on the
economic aspects of the decision.
How do an ordinary annuity, an annuity due, and a perpetuity differ?
Ordinary annuity assumes that the cash flows occur at the end of a period. Most types of
loans are ordinary annuities. On the other hand, annuity due is an annuity whose payment
is to be made immediately (or at the beginning of a period) instead of at the end of the
period. For example, in many leases the first payment is due immediately, and each
successive payment must be made at the beginning of the month. Perpetuity is a special
case of annuity, and it refers to a constant stream of identical cash flows with no end.
Give two examples of perpetuities.
The text gives the example of British government bonds called consols that have no
maturity and have been traded in the markets since the end of the Napoleonic wars.
Another example could be preference shares of a company that has no maturity and will
pay a constant dividend forever.
What is the annuity transformation method?
The annuity transformation method refers to the conversion of an ordinary annuity to
annuity due. In this process, you first plot all the cash flows on a time line as if the cash
flows were an ordinary annuity. Then you calculate the present or future value factor as
you would with an ordinary annuity, and finally, you multiple your answer by (1 + i).
Conveniently, this relationship works for both present and future value calculations.
What is the difference between a growing annuity and a growing perpetuity?
A stream of cash flows that is growing at a constant rate over time can be called a
growing annuity or growing perpetuity. If the cash flows extend over a finite length of
time, then we call it a growing annuity and can use Equation 6.5 to calculate the present
value. If the growth will continue for a very long time period and perhaps, forever, we
refer to it as the growing perpetuity. We would then use Equation 6.6 to estimate the
present value of this cash flow stream.
What is the APR, and why are lending institutions required to disclose this rate?
APR, or the annual percentage rate, is the annualised interest rate using simple interest. It
is defined as the simple interest charged per period multiplied by the number of
compounding periods per year. Lending institutions are mandated by Consumer Credit
Protection regulations to disclose this rate to essentially make it easier for consumers to
be exposed to the same kind of rate by all businesses.
What is the correct way to annualise an interest rate in financial decision making?
The correct way to annualise interest rates is by calculating the effective annual interest
rate (EAR). This is the annual growth rate that allows for compounding, which means
you earn interest on interest. To calculate the EAR, take the quoted rate and divide it by
the number of compounding periods (quoted rate/m). Then take the resulting interest rate,
add 1 to it, and raise it to the power equal to m. Finally, subtract 1 and the result is EAR.
Distinguish between quoted interest rate, interest rate per period, and effective annual
interest rate.
Quoted interest rate, such as APR, is the interest rate that has been annualised by
multiplying the rate per period by the number of compounding periods. Interest rate per
period is the quoted rate per period. It can be stated in the form of an APR—in that case,
just divide it by the number of compounding periods to obtain the interest rate per period.
Finally, EAR is the annual rate of interest that accounts for the effects of compounding.
