• “Average” performance is not necessarily good. Use the leader’s.
• Seasonal factors can distort ratios.
• Window dressing techniques can make statements and ratios look better.
• Different accounting and operating practices can distort comparisons.
• Sometimes it is difficult to tell if a ratio value is “good” or “bad.”
• Often, different ratios give different signals, difficult to tell whether a
company is in a strong or weak financial condition.
Financial Calculator
Display 8 decimal places
:
[2
nd
] [.]
FORMAT
[8]
Clear all memory
: [2
nd
] [FV]
CLR TVM
and [2
nd
] [CE/C]
CLR WORK
Toggle beginning/end mode
: [2
nd
] [PMT]
BGN
then [2
nd
] [ENTER]
SET
For
annuity due (first cash flow occur immediately)
TVM
:
1. set P/Y compounding frequency.
2. Set BGN/END mode
3. If EAR given, compute APR
Debt increases, ROA
decreases
Interest Expense lowers
net income, which
lowers ROA
Debt lowers equity, if
equity is lowered more
than net Y, ROE increase
Substitution of
equipment for
labourers,
decrease FA

4. Input I/Y. No need to divide by compounding frequency
since P/Y is already set. Same goes if APR is given. Just input
the given APR without dividing.
5. N = number of years x compounding frequency
(input [no.
of years] [2
nd
] [N]
xP/Y
)
6. If computing N or I/Y, PMT and/or PV must be input as a
negative number.
If annuity VS fixed payment now, e.g. pay $100 for lifetime or $10 every
year
PV = 10 – 100 = 90. FV = 0, PMT = 10, I/Y = given. Compute N
how long
you need to live to profit
Find Effective rate:
[2
nd
] [2]
ICONV
input NOM nominal rate, C/Y compounding frequency
(pressing [ENTER] [
↓
] after entering each) then [
↓
] to EFF effective rate
and press [CPT]
display effective rate
PV of Ordinary Annuity:
N=3, I/YR=10, PMT=100,
FV=0, CPT PV=??
Time Value of Money
Future Value
= the amount of money an investment will grow to over some
period of time at some given interest rate.
Future Value – Compounding || Present Value – Discounting
FV = PV(1+r)
t
r: interest rate ; t: time period
Present Value
= the current value of future CFs discounted at the
appropriate discount rate
PV
=
FV
(
1
+
r
)
n
=
FV ×
1
(
1
+
i
)
n
For a given amount to be received in the future and for a given
interest rate, the longer into the future that amount is to be received,
the lower the present value of that amount
For a given amount to be received at a given time period in the
future, the higher the interest rate, the smaller the present value of
that amount
Interest/Discount rate/Required return
Simple Interest
FV
=
PV
+
(
PV ×i ×n
)
where I
and r = i/r and n and t = #periods
Compound Interest
FV
=
PV
(
1
+
i
)
n
Effect of compounding is small for a small # periods; increases as # periods
increases.
i
=(
FV
PV
)
1
/
n
−
1
t
=
ln
(
FV
PV
)
ln
(
1
+
r
)
Annuity
= series of cash flows; same CF takes place each period for a set
#periods
Ordinary Annuity
first cash flow occurs one period from now
Annuity Due
first cash flow occurs immediately
Perpetuity
a set of equal payments that are paid forever
Growing Perpetuity
set of payments which grow at a constant rate each period and
continue forever
Annuity PV
=
PMT ×
[
1
r
∗(
1
−
1
(
1
+
r
)
t
)
]

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- Spring '11
- tohmunheng
- Corporate Finance, Investing