Financing costs are reflected in the required rate of return which is used to discount after-tax cash flows and investment outlays to estimate net present value NPV i.e.. 2.2 The Intern
Trang 1Reading 7 Discounted Cash Flow Applications
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Capital Budgeting refers to an investment
decision-making process used by an organization to evaluate
and select long-term investment projects
Capital Structure is the mix of debt and equity used to
finance investments and projects
Working capital management refers to the
management of the company’s short-term assets (i.e
inventory) and short-term liabilities (i.e accounts
payable)
Capital budgeting usually uses the following
assumptions:
1 Decisions are based on cash flows; not on accounting
profits (i.e net income):
ignored because it is assumed that if these benefits
or costs are real, they will eventually be reflected in
cash flows
incremental cash flows Sunk costs should be ignored
in the analysis
2 Timing of cash flows is critical i.e cash flows that are
received earlier are more valuable than cash flows
that are received later
3 Cash flows are based on opportunity costs:
Opportunity costs should be included in project costs
These costs refer to the cash flows that could be
generated from an asset if it was not used in the
project
4 Cash flows are analyzed on an after-tax basis Cash
flows on after-tax basis should be incorporated in the
analysis
5 Financing costs are ignored Financing costs are
reflected in the required rate of return which is used to
discount after-tax cash flows and investment outlays
to estimate net present value (NPV) i.e only projects
with expected return > cost of the capital (required
return) will increase the value of the firm
because when financing costs are included in both
cash flows and in the discount rate, it results in
double-counting the financing costs
6 Capital budgeting cash flows are not accounting net
income
For details, refer to Reading 35, Capital Budgeting.s
Independent projects are projects whose cash flows are independent of each other Since projects are
unrelated, each project is evaluated on the basis of its own profitability
Mutually exclusive projects compete directly with each other e.g if Projects A and B are mutually exclusive, you can choose A or B, but you cannot choose both
NPV = Present value of cash inflows − initial investment
1 + −
where,
CFt = After-tax cash flow at time t
r = required rate of return for the investment
CF 0 = investment cash outflow at time zero
Decision Rule:
• Do not Accept a project if NPV< 0 Independent projects: All projects with positive NPV are accepted
Mutually exclusive projects: A project with the highest NPV is accepted
wealth
i.e the higher the opportunity cost of capital, the smaller the NPV
Advantages:
firm
(opportunity cost of capital)
Practice: Example 1, Volume 1, Reading 7
Trang 22.2 The Internal Rate of Return and the Internal Rate of
Return Rule
IRR is the discount rate that makesPresent value of
future cash inflows = initial investment
0
using a financial calculator
As the name implies, internal rate of return (IRR) depends
only on the cash flows of the investment i.e no external
data is needed to calculate it
Example:
IRR is found by solving the following:
Solution:
IRR = 13.45%
Important to Note:
In the equation of calculating IRR, the IRR must be
compatible with the timing of cash flows i.e if cash flows
are semi-annual (quarterly), the IRR will be semi-annual
(quarterly)
When project’s cash flows are a perpetuity, IRR can be
estimated as follows:
= 0 Decision Rule:
•Do not Accept a project if IRR < Cost of Capital
NOTE:
•When IRR> opportunity cost of capital NPV> 0
•When IRR< opportunity cost of capital NPV< 0
both projects ≥ Cost of Capital
•If projects are mutually exclusive and project A IRR >
project B IRR and both IRR ≥ Cost of Capital, accept
Project A because IRRA>IRRB
Advantages of IRR:
2)IRR considers all cash flows
3)IRR involves less subjectivity
4)It is easy to understand
5)It is widely accepted
Limitations of IRR:
reinvested at the IRR; however, this may not always
be realistic
percentages can be misleading and involves difficulty
in ranking projects i.e a firm rather earn 100% on a
$100 investment, or 10% on a $10,000 investment
are or can be multiple IRRs or No IRR at all
No conflict exists between the decision rules for NPV and IRR when:
Conflict exists between the decision rules for NPV and IRR when:
NPV and IRR rank projects differently due to the following reasons:
1) Differences in cash flow patterns
2)Size (scale) differences: Required rate of return favors
small projects because the higher the opportunity cost, the more valuable these funds are Sometimes, the larger, low-rate-of-return project has the better NPV
3)Timing differences: Project with shorter payback
period provides more CF in early years for reinvestment Therefore, when required rate of return
is high, it favors project with early CFs
NPV versus IRR:
discount rate because it assumes reinvestment at r (opportunity cost of capital)
thus, IRR and IRR rankings are not affected by any external interest rate or discount rate
• It is more realistic to assume reinvestment at opportunity cost ‘r’; thus, NPV method is the best
It implies that whenever there is a conflict between NPV and IRR decision rule and to choose between mutually exclusive projects, we should always use NPV rule
Practice: Example 2 & 3, Volume 1, Reading 7
Trang 33 PORTFOLIO RETURN MEASUREMENT
Holding Period Return (HPR): A holding period return
refers to the return earned by an investor from holding
an asset for a specified period of time e.g 1 day, 1
week, 1 month, 5 years etc
Total return = Capital gain (or loss) yield + Dividend yield
=
=+
− 1
where,
P = price
D = dividend
t-1 = beginning of the period
t = end of the period
The money-weighted rate of return (MWR) measures the
compound growth rate in the value of all funds invested
in the account over the entire evaluation period In U.S.,
it is known as “dollar-weighted return” It represents an
internal rate of return (IRR) of an investment Like IRR,
portfolio) are cash outflows for the investor
•All additions to the portfolio are cash outflows for the
investor
investor are cash inflows for the investor
inflow for the investor
It is computed as follows:
where,
IRR represents the MWR
T = number of periods
CF t = cash flow at time t
performance of the portfolio manager when the
manager has discretion over the deposits and
withdrawals made by clients
Advantages of MWR: MWR requires an account to be
valued only at the beginning and end of the evaluation
period
Disadvantages of MWR:
external cash flows to an account
manager has little or no control over the external cash flows to an account
Example:
Assume,
of 1st year = $100
of 2nd year = $950
• Value of investments at the end of 3rd year = $1,270 CF0 = –100
CF1 = –950 CF2 = +350 CF3 = +1,270
−950
Solve for IRR, we have → IRR = 26.11%
The time-weighted rate of return (TWR) measures the compound rate of growth over a stated evaluation period of one unit of money initially invested in the account
an external cash flow occurs
the portfolio manager
of the portfolio manager when the manager has no control over the deposits and withdrawals made by clients
When there are no external cash flows, TWR is computed
as follows:
= r =MV− MV
MV
In order to calculate time weighted return, first of all, holding period return for each sub-period is computed and then these sub-period returns must be linked together (known as chain-linking process) to compute the TWR for the entire evaluation period
Trang 4r twr = (1+r t,1 )×(1+r t,2 ) × … (1+r t,n ) –1
the time-weighted rate of return will not be
expressed as an annual rate
period has a weight = (length of the sub-period /
length of the full evaluation period)
If the investment is for more than one year,
time-weighted return can be annualized by calculating
geometric mean of n annual returns:
Time – weighted return = [(1+R1)(1+R2)…(1+Rn)]1/n – 1
Where,
R it = return for year i
n = total number of annual returns
Method of computing Time-weighted Return for the Year:
days daily returns) using the following formula:
where,
ri = r1, r2, …r365
ii Calculate annual return for the year by linking the
daily holding period returns as follows:
Time – weighted return = [(1+R1)(1+R2)…(1+R365)] – 1
This annual return represents the precise time-weighted
return for the year IF withdrawals and additions to the
portfolio occur only at the end of day Otherwise, it
represents the approximate time-weighted return for the
year
Time-weighted return can be annualized by calculating
geometric mean of n annual returns:
where,
R it = return in period t
n = total number of periods
Advantage of TWR: TWR is not sensitive to any external
cash flows to the account i.e additions and withdrawals
of funds
Disadvantage of TWR:
each time any cash flow occurs
administratively more cumbersome, expensive and potentially more error-prone
Example:
period 1 = $100
The annual return (based on the geometric average) over the entire period is
r = [(1.0150)(1.05800)] –1=0.0739 or 7.39%
TWR versus MWR:
period of strong (positive) performance, MWR > TWR
a period of strong (positive) performance, MWR < TWR
period of weak (negative) performance, MWR < TWR
a period of weak (negative) performance, MWR > TWR
similar results
• When large external cash flows occur (i.e > 10% of account) and during that evaluation period, account’s performance is highly volatile, then MWR and TWR will provide significantly different results
Practice: Example 4 & 5, Volume 1, Reading 7
Trang 54 MONEY MARKET YIELDS
Money market instruments are short-term debt
instruments i.e having maturities of one year or less
These instruments pay par value (face value) at maturity
and are usually discount instruments i.e they do not pay
coupons, but instead are sold below (at discount from)
their par (face) value For example, T-bills are discount
instruments where,
receives face value at maturity
when he/she holds the T-bill to maturity
Other types of money-market instruments include
commercial paper and bankers’ acceptances (which
are discount instruments) and negotiable certificates of
deposit (which are interest bearing instruments that pay
coupons)
discount basis rather than price basis using the bank
discount rate (a 360-day year is commonly used in
pricing money market instruments) The bank discount
rate is defined as:
!=360 − !
! = "1 − !
360# where,
r BD = Annualized yield on a bank discount basis
n = Actual number of days remaining to maturity
Limitations of Yield on a bank discount basis: Bank
discount yield is not a meaningful measure of investors’
return because:
of its purchase price; but returns should be
evaluated relative to the amount invested (i.e
purchase price)
a 365-day year
3 It is annualized based on simple interest; thus, it
ignores the compound interest
•The discount rate for the T-bill can be used to find PV
of other cash flows with risk characteristics similar to
those of the T-bill
of T-bill, the T-bill's yield can be used as a base rate
and a risk premium is added to it to represent higher
risk of cash flows
earned by an investor by holding the instrument to maturity
$ =−+
where,
P 0 = initial purchase price of the instrument
P 1 = Price received for the instrument at its maturity
D 1 = Cash distribution paid by the instrument at its maturity (i.e interest)
For interest-bearing instruments: The purchase and sale prices must include any accrued interest* when the bond is purchased/sold between interest payment dates
*Coupon interest earned by the seller from the last coupon date but not received by the seller as the next coupon date occurs after the date of sale
NOTE:
it is called Full price
is called Clean price
3)Effective annual yield (EAY):
EAY = (I + HPY) 365/t - 1 Rule: The bank discount yield < effective annual yield
market yield can be used to compare the quoted yield on a T-bill to quoted yield on interest-bearing money-market instruments that pay interest on a 360-day basis
annualized holding period yield (assuming a 360-day year) i.e
Money market yield = rMM = (HPY) × (360/ t)
based on purchase price
Practice: Example 6, Volume 1, Reading 7
Trang 6• Thus, money market yield > bank discount yield
Or
360 > !
annualized by multiplying it by 2, it is referred to as the
bond-equivalent yield It ignores compounding of
interest The bond equivalent yield is calculated as
follows:
Practice: Example 7, Volume 1, Reading 7 & End of Chapter Practice Problems for Reading 7
...Disadvantages of MWR:
external cash flows to an account
manager has little or no control over the external cash flows to an account
Example:
Assume,
of 1st... to any external
cash flows to the account i.e additions and withdrawals
of funds
Disadvantage of TWR:
each time any cash flow occurs
administratively... together (known as chain-linking process) to compute the TWR for the entire evaluation period
Trang 4r