Learning Objectives
1. Use excel to solve annuity and perpetuity problems, NPV, IRR, PV
2. Understand how to use non-annual time intervals
Lesley Tims
Chapter 4 (Part 3): The
Time Value of Money
FNCE 317: Introduction to
Finance
Term: 2022
3. Given 4 of 5 inputs (PV, FV, N, r, PMT), compute the missing (for a
single sum with no PMT it could be 3 out of 4 inputs)
• Understand the use of the formulas/calculator
• Solve for cash flow (a consumer loan problem)
• Compute the IRR for a series of cash flows, given cash flows and
either PV or FV
• Solve for N periods given cash flows and rate
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FNCE 317: 2022
Using a Spreadsheet/Calculator
❖
❖
❖
If you have 4 out of 5
variables, you can solve
for the last one!
Predefined functions : PV,
NPV, IRR
Understand the inputs
and signage
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Spreadsheet
Calculator
Meaning
Trick
PV
PV
Present
Value
Usually
negative
PMT
PMT
Payment
Constant
RATE
I/Y
FV
FV
NPER
N
Do not put
decimal # in
calculator
Error if
Future
there isn’t a
Value
negative
Not
Number
necessarily
of
in years Periods
match rate
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Make An Excel Annuity Calculator
❖
Understand the assumptions of the predefined functions
❖
Be sure to understand inputs
❖
Inputs are not consistent across functions
❖
Use simple formula with smart referencing
Rate
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❖
IF formulas can help here
❖
Double check your work!
❖
Use goal seek for numerical solutions
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Excel Spreadsheets
Date
❖
❖
1
2
3
PV
PMT
PMT
PMT
NPER
PMT+FV
The excel functions are all based on a timeline of an annuity
❖
Test out your excel calculator:
❖
What would it cost us today to receive $30 every year
for 6 years at 4% interest rate?
They all solve the problem:
NPV = PV + PMT *
❖
…
0
Excel Example
1
1
FV
1−
+
RATE (
(1 + RATE)N ) (1 + RATE)N
Where you input four variables and solve for the fifth,
ensuring the NPV=0
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Excel Example
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Non-Annual Time Intervals
❖
Determine the correct rate for the specific time interval
and the number of periods of this interval
❖
Test out your excel calculator:
❖
Ie. If it is a semiannual rate;
❖
What would it cost us today to receive $30 every year
for 6 years at 4% interest rate?
❖
How many semiannual periods are there? => n
❖
Or make it an annual equivalent rate
❖
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Example: How many months does it take a $100 GIC to
grow 15% at a monthly rate of 0.25%?
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Non-Annual Time Intervals
❖
❖
Determine the correct rate for the specific time interval
and the number of periods of this interval
❖
Ie. If it is a semiannual rate;
❖
How many semiannual periods are there? => n
❖
Or make it an annual equivalent rate
Savings Example on Excel
❖
You are considering a promotional savings account that
pays interest of 2% every 18 months. You plan to
deposit $600 every 18 months and keep the interest
invested, starting in 18 months with your first deposit.
What will the balance be in 9 years?
Example: How many months does it take a $100 GIC to
grow 15% at a monthly rate of 0.25%?
You can use the excel calculator and/or you can use a timeline on excel and
calculate the PVs and/or FVs
PV=-100 FV=115 r=0.25 PMT=0 n=?
n = 55.97 months or 4.66 years…. So 5 years!
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Savings Solution
FNCE 317: 2022
You may know the amount you would like to borrow (PV) and the
amount you have to pay back (FV), but you might not know the
loan payments (cash flow/constant = C)
❖
Blended payments of principal and interest
❖
A normal consumer loan is an arrears annuity (starts in one
period)
❖
Solve for PMT by manipulating the annuity equation
PV =
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A Consumer Loan (Solve for C using PV)
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C
1
* 1−
r (
(1 + r)n )
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C=
!12
PV * r
(1 −
1
(1 + r)n )
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Example - Consumer Loan
A Consumer Loan (Solve for C using FV)
❖
You may know the amount you would like to borrow (PV) and the
amount you have to pay back (FV), but you might not know the
loan payments (cash flow/constant = C)
❖
❖
❖
❖
Blended payments of principal and interest
A normal consumer loan is an arrears annuity (starts in one
period)
You plan to purchase a house for $350,000. You need to
make a down payment of 20% of the purchase price for the
bank to lend you the rest on a 30-year loan. If the interest
rate is 5% per year, what are your annual payments to the
bank?
C=
Solve for PMT by manipulating the annuity equation
C=
FV = C/r * ((1 + r)n − 1)
FV * r
(1 + r)n − 1
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You plan to purchase a house for $350,000. You need to
make a down payment of 20% of the purchase price for the
bank to lend you the rest on a 30-year loan. If the interest
rate is 5% per year, what are your annual payments to the
bank?
C=
PV * r
(1 −
1
(1 + r)n )
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IRR (Internal Rate of Return)
❖
When you know the cash flows and the PV of an investment
opportunity, you might want to know the IRR:
❖
Internal Rate of Return = The interest rate that sets the NPV to zero
❖
Also known, in business as a discount rate or cost of capital
❖
There is no formula to solve for this (can’t manipulate annuity to solve
for r)
PV =
❖
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1
(1 + r)n )
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= (280,000*0.05)/ (1- (1/(1.05)30)) = $18,214
You can use this equation or your calculator and solve for PMT/C
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(1 −
You can use this equation or your calculator and solve for PMT/C
Example - Consumer Loan
❖
PV * r
C
1
* 1−
r (
(1 + r)n )
Good thing your exam is multiple choice - Use trial and error!
❖
Or use your calculator 5 buttons and solve for I/Y
❖
Or use CF function and CPT IRR
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Calculator Logistics (IRR)
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IRR Calculator
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IRR Solution
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Solving for the Number of Periods PV
❖
Can solve the equation for n, however we need to use ln
❖
If your algebra is not strong, thankfully the exam is
multiple choice- Use trial and error!
❖
PV =
Or Use your calculator 5 buttons with proper signs
C
1
* 1−
r (
(1 + r)n )
1
1−
C
PV * r
ln
= (1 + r)n
( 1 − PVC* r )
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FNCE 317: 2022
1
1−
PV * r
C
= n * ln(1 + r)
1
ln(1 + r)
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ln
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=n
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Solving for the Number of Periods FV
❖
We can do this using the FV equation as well
❖
Can solve the equation for n, however we need to use ln
❖
If your algebra is not strong, thankfully the exam is
multiple choice- Use trial and error!
Example - Solve for Number of Periods
❖
❖
Or Use your calculator 5 buttons with proper signs
FV = C/r * ((1 + r)n − 1)
(1 + r)n =
FV * r
+1
C
n=
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ln (
FV * r
C
ln
+ 1)
ln(1 + r)
You plan to purchase a house for $350,000. You need to make a
down payment of 20% of the purchase price for the bank to
lend you the rest. If the interest rate is 5% per year and the
annual payments are $15,000, how long will it take you to pay
back the loan? What if the payments were $20,000? Or $10,000?
ln
(1−
1
PV * r
C
ln(1 + r)
)
=n
1
=n
You can use this equation or your calculator or excel and solve for N (make sure your
signs make sense)
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Example - Solve for Number of Periods
❖
Instead you make a $70,000 investment today and add
$20,000 every year to that account. If the interest rate is
5% per year, how many years until your investment is
worth $1,200,000?
FV = [P * (1 + r)n] + [C/r * ((1 + r)n − 1)]
For $15,000
ln(15)/ln(1.05) = 2.708/0.04879 = 55.5 years
Investment in
future
For $20,000 payment
ln(3.3333)/ln(1.05) = 2.708/0.04879 = 24.6 years
For $10,000 ln(1/(1-1.4))/ln(1.05) =ln(1/(-0.4))/ln(1.05)
—> Can’t take ln of x<0
Therefore this won’t work if your PV*r > C
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FNCE 317: 2022
( 1 − PVC* r )
ln(1 + r)
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Example - Solve for Number of Periods
❖
You plan to purchase a house for $350,000. You need to make
a down payment of 20% of the purchase price for the bank to
lend you the rest. If the interest rate is 5% per year and the
annual payments are $15,000, how long will it take you to pay
back the loan? What if payments were $20,000? Or $10,000?
FV of annuity
payments
How good is your algebra?? —> Use your calculator and solve for N
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FNCE 317: 2022
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CHALLENGER PART 2
Example - Solve for Number of Periods
❖
Instead you make a $70,000 investment today and add
$20,000 every year to that account. If the interest rate is
5% per year, how many years until your investment is
worth $1,200,000?
n
n
FV = [P * (1 + r) ] + [C/r * ((1 + r) − 1)]
Investment in
future
FV of annuity
payments
❖
How long will it take you to save for your down
payment of $70,000? If you save $15,000 per year
starting next year and the interest rate is still 5%.
❖
What if you start with savings of $10,000?
❖
What if you start with debt of $10,000?
How good is your algebra?? —> Use your calculator and solve for N
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CHALLENGER
❖
How long will it take you to save for your down
payment of $70,000? If you save $15,000 per year
starting next year and the interest rate is still 5%.
❖
What if you start with savings of $10,000?
❖
What if you start with debt of $10,000?
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