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Agenda – 4/17/2013
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Discuss interest and the time value of money
Explore the Excel time value of money functions
Examine the accounting measures of profitability
Course Evaluations
Some Excel financial functions
Function
Description
CUMIPMT** Cumulative Interest Payments
CUMPRINC Cumulative Principal Payments
FV
Future Value
IPMT**
Interest Payment
IRR
Internal Rate of Return
NPER
Number of periods
NPV
Net Present Value
PMT**
Payment
PPMT**
Principal Payment
PV
Present Value
RATE
Interest Rate
SLN
Straight Line Depreciation
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Excel Functions are
Excel Functions
To use them, you must
understand the
TIME VALUE OF MONEY
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Understanding time value of money
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Money will increase in value over time if the money is
invested and can make more money.
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If you have $1,000 today, it will be worth more tomorrow if
you invest that $1,000 and it earns additional money
(interest or some other return on that investment).
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If you have $1,000 today, it will NOT be worth more
tomorrow if you put it in an envelope and hide it in a
drawer. Then the time value of money does not apply as
an increase. It will most likely decrease in value because
of inflation. Of course, you won’t lose the whole $1,000
either…
Introduction to Interest Calculations
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When you borrow money you pay interest
When you loan money, you receive interest
When you make a payment
 part of the payment is applied to interest
 Part of the payment is applied to principal
Types of Interest
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Simple interest
 Interest is paid only on the principal
 Many certificates of deposit work this way
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Compound interest
 Interest is added to the principal each period
 Interest is calculated on the principal plus any accrued interest
 Compounding can occur on different periods
• Annually, quarterly, monthly, daily
Difference between simple and compound interest
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Assume that you have $1,000 to invest. $1,000 is
the present value (PV) of your money.
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You can invest it and receive “simple” interest or you
can earn “compound” interest.
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The money that you have at the end of the time you
have invested it is called the “future value” (FV) of
your money.
Future value of money
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Simple interest is always calculated on the initial
$1,000. 5% interest on $1,000 is $50. Always $50.
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When interest is paid on not only the principal
amount invested, but also on any previous interest
earned, this is called compound interest.
FV = Principal + (Principal x Interest)
= 1000 + (1000 x .05)
= 1000 (1 + i)
= PV (1 + i)
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Simple vs. compound interest comparison
Year
Simple Interest
Compound Interest
0
$1,000
$1,000
1
$1,050
$1,050
2
$1,100
$1,102.50
3
$1,150
$1,157.62
4
$1,200
$1,215.61
5
$1,250
$1,276.28
10
$1,500
$1,628.89
20
$2,000
$2,653.30
30
$2,500
$4,321.94
$1,000 Invested at 5% return
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How much money would you have
if you invested $1000 for 5 years at
an interest rate of 5% a year?
How much money would you have if
you invested $1000 each year for 5
years at an interest rate of 5% a year?
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Time Value of Money Functions
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We are just solving the same equation for a different
variable
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RATE determines the interest rate
NPER determines the number of periods
PMT determines the payment
PV determines the present value of a transaction
FV determines the future value of a transaction
The RATE Function
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Determines the interest rate per period based on
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The number of periods
The payment
The present value
The future value
The type
The NPER Function
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Determines the number of periods based on
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The interest rate
The payment
The present value
The future value
The type
Future Value Function
FV(rate, nper, pmt, pv, type)
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Argument
Description
rate
Interest rate per compounding period
nper
Number of compounding periods
Pmt
Payment made each compounding period
Pv
Present value of current amount
type
Designates when payments or deposits
are made
Type 0 – end of period. Default.
Type 1 – beginning of period
If you receive $5000 5 years from now,
and the “going” interest rate is 5%,
how much is that money worth
today?
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Present Value Function
PV(rate, nper, pmt, fv, type)
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Argument
Description
rate
Interest rate per compounding period
nper
Number of compounding periods
pmt
Payment made each period
fv
Future value of the amount received today
type
Designates when payments are made
Type 0 – end of period. Default.
Type 1 – beginning of period
What about if you borrow money?
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If you borrow money, the lender wants to earn
“compound” money on his/her/its investment.
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If you borrow $1000 at 10%, then you won’t pay back
just $1,100 (unless you pay it back at once during the
initial time period).
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You will pay it back “compounded”. Interest will be
calculated each period on your remaining balance.
Amortization table $1,000 loan, pay $100 year, 5% year interest
Year
Amount Owed
Payment
1
$1,000.00
$1,050.00
$100.00
2
$950.00
$997.50
$100.00
3
$897.50
$942.38
$100.00
4
$842.38
$884.49
$100.00
5
6
7
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9
$784.49
$723.72
$659.90
$592.90
$522.54
$823.72
$759.90
$692.90
$622.54
$548.67
$100.00
$100.00
$100.00
$100.00
$100.00
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11
12
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15
$448.67
$371.11
$289.66
$204.14
$114.35
$20.07
$471.11
$389.66
$304.14
$214.35
$120.07
$21.07
$100.00
$100.00
$100.00
$100.00
$100.00
$21.07
Total Paid
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Amount Plus
Interest
$1,421.07
What would that same
amortization table (also called a
schedule) look like if the interest
was compounded AFTER you
paid, rather than BEFORE you
paid?
(this is a type 1 on Excel financial functions)
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Amortization table $1,000 loan, pay $100 year, 5% year interest
Year
Amount Owed
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Total Paid
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$1,000.00
$945.00
$887.25
$826.61
$762.94
$696.09
$625.89
$552.19
$474.80
$393.54
$308.22
$218.63
$124.55
$25.78
Payment
$100.00
$100.00
$100.00
$100.00
$100.00
$100.00
$100.00
$100.00
$100.00
$100.00
$100.00
$100.00
$100.00
$25.78
$1,325.78
Amount Plus
Interest
$945.00
$887.25
$826.61
$762.94
$696.09
$625.89
$552.19
$474.80
$393.54
$308.22
$218.63
$124.55
$25.78
$0.00
Types of financial questions asked
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How much will it cost each month to pay off a loan if I
want to borrow $150,000 at 4% interest each year for
30 years? (PMT function)
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Assume that you need to have exactly $40,000 saved
10 years from now. How much must you deposit
each year in an account that pays 2% interest,
compounded annually, so that you reach your goal of
$40,000? (PMT function)
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If you invest $2,000 today and accumulate $2,676.45
after exactly five years, what rate of annual
compound interest did you earn? (INTRATE function)
Payment function
PMT(rate, nper, pv, fv, type)
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Argument
Description
rate
Interest rate per compounding period
nper
Number of compounding periods
pv
Present value
fv
Future value, residual left over after the
loan is completed. Could be a balloon
payment. Can be omitted if = 0.
type
Designates when payments are made
Type 0 – end of period. Default.
Type 1 – beginning of period
The PMT Function (Example)
The IPMT Function (Introduction)
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Use IPMT to calculate the interest applicable to a
particular period
 Use the initial balance for the present value no matter the
period
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Use PPMT to calculate the principal applicable to a
particular period
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The arguments to both functions are the same
Interest Payment
IPMT(rate, per, nper, pv, fv, type)
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Argument
Description
rate
Interest rate per compounding period
per
Period for which interest should be calculated.
nper
Number of compounding periods
pv
Present value
fv
Future value, residual left over after the loan is completed.
Could be a balloon payment. Can be omitted if = 0.
type
Designates when payments are made
Type 0 – end of period. Default.
Type 1 – beginning of period
Principal Payment
PPMT(rate, per, nper, pv, fv, type)
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Argument
Description
rate
Interest rate per compounding period
per
Period for which principal payment should be calculated.
nper
Number of compounding periods
pv
Present value
fv
Future value, residual left over after the loan is completed.
Could be a balloon payment. Can be omitted if = 0.
type
Designates when payments are made
Type 0 – end of period. Default.
Type 1 – beginning of period
The CUMIPMT Function (Introduction)
• CUMIPMT calculates the cumulative interest between
two periods
• CUMPRINC calculates the cumulative principal
between two periods
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The arguments to both functions are the same
Functions require the analysis tool pack add-in
Cumulative Interest Payments
CUMIPMT(rate, nper, pv, start_period, end_period, type)
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Argument
Description
rate
Interest rate per compounding period
nper
Number of compounding periods
pv
Initial loan amount (Present value).
Start_period
Starting period. Begins at 1 and increments by 1.
End_period
Ending period. Begins at 1 and increments by 1
type
Designates when payments are made
Type 0 – end of period. Default.
Type 1 – beginning of period
Financial questions
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If you borrow $1,000 for 5 years and pay 4% yearly
interest compounded monthly, how much interest will
you pay?
 First do the calculation.
 Second, what Excel formula would you use to do the
calculation for you?
 Third, what Excel formula would calculate the payment?
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If you invest $1,000 and receive 3% yearly interest
compounded quarterly, how much will you have at
the end of 10 years?