Chapter Thirteen
Capital Budgeting and
Other Time Value of
Money Applications
Richard E. McDermott, Ph.D.
Capital Budgeting Evaluation Process
Many companies follow a carefully prescribed
process in capital budgeting. At least once a
year:
1) Proposals for projects are requested from
each department.
2) The proposals are screened by a capital
budgeting committee, which submits its
finding to officers of the company.
3) Officers select projects and submit a list of
projects to the board of directors.
Capital Budgeting Evaluation Process
The capital budgeting decision depends on a
variety of considerations:
1) The availability of funds.
2) Relationships among proposed
projects.
3) The company’s basic decision-making
approach.
4) The risk associated with a particular
project.
Cash Payback Formula
• The cash payback technique identifies the time
period required to recover the cost of the capital
investment from the annual cash inflow produced by
the investment.
• The formula for computing the cash payback period
is:
Estimated Annual Net Income from
Capital Expenditure
Assume that Reno Co. is considering an investment of $130,000 in
new equipment. The new equipment is expected to last 5 years. It
will have zero salvage value at the end of its useful life. The
straight-line method of depreciation is used for accounting purposes.
The expected annual revenues and costs of the new product that will
be produced from the investment are:
Sales
Less:
$200,000
Costs and expenses
$132,000
Depreciation expense ($130,000/5)
26,000
Selling and administrative expenses
22,000
Income before income taxes
Income tax expense
Net income
180,000
20,000
7,000
$ 13,000
Computation of Annual Cash Inflow
Cash income per year equals net income plus depreciation
expense.
Annual (or net) cash inflow is approximated by taking net income and adding
back depreciation expense. Depreciation expense is added back because
depreciation on the capital expenditure does not involve an annual outflow
of cash.
Net income
$13,000
Computation of Annual Cash Inflow
Net income
Add: Depreciation expense
$13,000
26,000
Computation of Annual Cash Inflow
Net income
Add: Depreciation expense
Cash flow
$13,000
26,000
$39,000
Cash Payback Period
The cash payback period in this example is therefore
3.33 years, computed as follows:
$130,000
÷
$39,000
=
3.33 years
When the payback technique is used to decide among acceptable
alternative projects, the shorter the payback period, the more
attractive the investment. This is true for two reasons:
1) The earlier the investment is recovered, the sooner the cash
funds can be used for other purposes, and
2) the risk of loss from obsolescence and changed economic
conditions is less in a shorter payback period.
Review Question
A $100,000 investment with a zero scrap value has an 8-year life.
Compute the payback period if straight-line depreciation is used and net
income is determined to be $20,000.
a. 8.00 years.
b. 3.08 years.
c. 5.00 years.
d. 13.33 years.
Review Question
A $100,000 investment with a zero scrap value has an 8-year life.
Compute the payback period if straight-line depreciation is used and net
income is determined to be $20,000.
a. 8.00 years.
b. 3.08 years.
c. 5.00 years.
d. 13.33 years.
Calculation of answer:
First calculate depreciation:
$100/000/8 years = $12,500
Add dep’n to income to get net cash flow:
$20,000 + $12,500 = $32,500
Divide investment by yearly cash flow to
get payback period:
$100,000/$32,500 = 3.08 years.
Time Value of Money
• Many cost of capital
evaluation techniques
involve time value money
of calculations.
• Let’s utilize Excel in
learning how to analyze
various investments or
returns involving
incoming or outgoing
streams of money.
A Little Theory . . .
Assume we invest a lump
sum of $100 in time period
zero.
Money
The interest rate is 10% per year.
$300
$200
$100
0
1
2
3
Time
A Little Theory . . .
We let it grow for three
years.
Money
In one year it is worth
$100 x 1.10 = $110
$133.10
In two years it is worth
$110 x 1.1 = $121
$130
In three years it is worth
$121 x 1.10 = $133.10
$120
$100
0
1
2
3
Time
A Little Theory . . .
These figures can be calculated using Excel.
Money
Again we are talking about lump sums!
$133.10
$130
The future value of $100 for three
periods at 10% is $133.10.
The present value of $133.10 for three
periods is $100.
$120
$100
This represents the future value and
present value of a lump sum.
0
1
2
3
Time
Practice Problem – Future Value of a
Lump Sum
• Let’s use Excel to work this problem.
• This is future value of a lump sum
problem.
• We deposit a lump sum of $100, today,
make no additional payments, and leave
the money in the bank for three periods
at 10% per period interest.
Excel Worksheet
Select Formulas
Select Financial
Excel Worksheet
Select FV for “future value”
Excel Worksheet
This box will appear on your screen.
Excel Worksheet
Notice that we put nothing in the Pmt
box since the $100 is the only deposit.
Excel Worksheet
Hit “Ok.”
The future value of
$100 for 3 periods at
10% per period is
$133.10.
Another Method
• One can also type financial commands
into Excell.
• The command for future value is =fv
• Enter “=fv(“ and you get the following
on your screen
• FV(rate,nper,pmt,[pv],[type])
• Entering the values
• =fv(.10,3,0,100,0)
• The answer given is ($133.10)
Formulas used in Excel Spreadsheet for Time Value of Money and Capital Budgeting Problems
NPV returns the net present value of an investment based on a rate, and a series of future payments.
=NPV(rate, value 1,[value 2], [value 3] . . .)
Note if there in an investment in time period zero, you must add that to the npv.
IRR returns the internal rate of return of a series of cash flows.
=IRR(values, guess)
Note with IRR, include the investment in time period 0.
Note: When IRR = discount rate, then the net present value is zero
PV returns the present value of a future series of payments.
=PV (rate, nper, pmt, [fv},[type])
FV returns the future value of an investment based on periodic, constant payments and a constant rate of return
=FV(rate, nper,pmt, pv,type)
RATE returns the interest rate per period of a loan or an investment.
Future Value of Lump Sum Problem
• Assume you are 25 years of age and
inherit $25,000 from your grandfather.
• You decide to save this money for
retirement at age 65.
• You deposit it in a certificate of
deposit earning 4% per year.
• How much will you have at retirement?
• Answer: $120,025.52
Present Value of Future Lump Sum
• Let’s say you want to leave $1,000,000
to your great-grandson 100 years from
now. You can invest your money at 10%
per year (compounded monthly).
• What lump sum must you invest today
to accrue that amount.
• =pv(rate,nper,pmt,[fv],[type])
• =pv(.10/12,1200,0,1000000,0)
• The answer is $47.32!
Present Value of Future Lump Sum
• What if you compound the interest
yearly instead of monthly, does it make
a difference?
• Let’s see.
• This time let’s use the menu approach
to solving the Excel problem.
Calculation
• From the Excel screen select formulas,
then financial just as we did before.
Now Let’s Calculate Present Value
• This time
select PV
from the drop
down menu.
This Box Will Appear
Present Value of a Future Lump Sum
Hit OK. The amount you
must deposit today is
$72.57..
Compunding monthly
instead of yearly obviously
makes a difference.
A Little More Theory . . .
• A lump sum is one sum of money
invested at some point in time.
• We can also have annuities.
• An annuity is a series of payments of
the same amount received or paid at
equal periods of time.
• $100 invested for 3 periods is an
annuity.
To Illustrate . . .
The first year we make a payment
of $100. That amount grows with
interest until we make a second
payment which in turn grows with
interest until we make a third
payment.
Money
New
Axis
$331
At the end of three years we have
$331 from the annuity.
$300
The future value of 3 payments of
$100 at 10% interest per period is $331.
$200
$100
Again, we could calculate this using
Excel.
0
1
2
3
Time
Calculation of Future Value of an Annuity
Problem
Select Formulas
Select Financial
We are still going to use the FV function
However we are going to fill the
pop up box in differently. Now
we will insert $100 in the Pmt
box.
The Answer is $331.00
The same amount shown on the earlier
chart!
What does this mean?
If you deposit three yearly payments of $100
each, at the end of three years you will have
$331.00 in savings.
Practice Problem
• An individual saves $500 a month for
thirty years at 8% interest a year.
• How much will he have in savings at the
end of thirty years?
Things to Be Aware of
• Make sure you pay attention to the fact
that the money is deposited in savings
monthly.
• The pop-up box, interest, periods, and
payments must all be consistent.
• The interest rate will not be .08 but
.08/12 months = .006667.
• The number of periods will be 30 years
x 12 months = 360.
Calculation
• From the menu at the top of the
screen, select Formulas and then
Financial just as we have before.
• Select FV as before, and fill the box
that appears in as shown on the
following screen:
Pop-up Box
The Answer is:
At the end of thirty
years, you will have
$745,785.11 in the
bank!
Again, this problem is a
future value of an annuity
problem. The annuity is
$500 per month.
Now Let’s do a Present Value of an
Annuity
• Your daughter is going away to college.
• Living expenses and tuition and books
will cost $33,000 for six years (she
wants to get a graduate degree)
• You can invest money at 7% a year.
• How much must you deposit today so
that she can draw out $33,000 a year
six years earning a 7% return on money
in the bank?
Present Value of An Annuity
• Select Formulas and Financial from the
Excel menu as before.
• Select PV as before (remember PV and
FV can be used for both lump sums and
annuities).
• You will get the following pop-up box.
Present Value of an Annuity
Hit ok. The answer is $157,296.81!
PV and FV Functions
• With the PV and FV functions, we can
combine and annuity and a lump sum
calculation.
• For example, assume you have $25,000
to deposit in the bank today at 6%.
• Then for the next ten years you will
deposit $5,000 a year at 6%.
• How much will you have (what will the
future value be) at the end of ten
years?
Future Value of a Lump Sum and Annuity
• Select Formulas, and Financial as
before.
• Select FV to get the following box.
The answer is . . .
• $70,339.57
Discounting Cash Flows that Are Not
Equal
• Earlier we said that an annuity was a
series of equal payments, equally
spaced.
• What if we are to receive payments
that are unequal in amount but equally
spaced?
• How do we find the present value?
Discounting Cash Flows that Are Not
Equal
• Why do we care?
• Because this is one way of valuing a
business!
Why We Care
• Most business valuations are done by
discounting projected cash flows.
• Also, stocks, bonds, and businesses are
valued by taking the present value of
future cash flows.
• Let’s do some examples.
Valuing a Business
• You are looking at purchasing a small
jewelry store from your brother-in-law.
• The business will grow each year.
• You forecast the cash inflows from the
business for the next ten years (shown
on the next slide).
Projected Cash Flow
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 9
Year 10
0
20000
25000
32000
37000
45000
50000
40000
35000
25000
15000
Today
Valuing a Business
• At the end of ten years you will close
the business and sell the equipment for
$10,000 (scrap value).
• Assume you could invest money
elsewhere, in an investment with
approximately the same risk, for 12%
annual return.
• What is the jewelry store worth?
Solution
• We could select Formulas, Financial, and
NPV, at which time we would get a pop
up box into which we would enter the
values, or . . .
• In this case it might be easier to write
out the formula in an Excel cell.
• The formula is:
– =npv(rate, value 1, value 2 . . .)
Let’s See What it Looks Like on The
Excel Sheet
Note: the last cash flow consists of the $15,000
from operations plus the $10,000 salvage value
of the equipment when the Laundry is sold.
The answer is $184,238.35.
Let’s Do the Same Thing Using the Popup Box
• Select from the
menu at the top of
the page,
Formulas, and then
Financial, as we
have done before.
• Then select from
the drop down box
NPV.
The Answer is the Same!
Note
that all
of the
values
are not
shown
on this
copy of
the popup box.
What this Means
What this means is that if you wish to earn
12% a year, you should pay no more than
$184,238.35 for this business.
If you pay more than that, you will
earn less than your desired 12% rate
of return.
How Much Less
• Let’s assume you actually pay $200,000
for the shop.
• Assuming the projected cash flows are
correct, what will be your actual rate of
return?
• To determine this we will use the
internal rate of return (IRR) function.
Lets First Make a Table of Projected
Cash Flows That Looks Like This
Now Lets Go To The Menu Like We Did
Before . . .
• Select Formulas from the top menu bar
• Then Select Financial
• Select IRR
Your pop-up box will look like this
Drag and drop the cash flows from the Excel Spreadsheet into the
“values” box.
You are required to give a “guess” as to
what the IRR will be
The actual rate of return is approximately
10.15%
Net Present Value
• There is one more concept we should
talk about when talking about
discounting cash flows.
• The concept is net present value.
• Net present value discounts at a
specified interest rate both cash
outflows (i.e. the initial investment) and
inflows from operations to give a total
value.
Net Present Value
• One of the things I don’t like about Excel is
that it uses the term net present value to mean
the cash flows from periods 1 though X (in
other words the investment in period 0 is not
included in the net present value calculation.
• Time period 0 is, however, included in the
calculation of net present value.
• It is best to illustrate what I am saying with an
actual problem.
Example
• Community Hospital is considering
building an outpatient surgery center.
• The hospital can borrow money to build
the center ($2,000,000) for 14%.
– The 14% is the required rate of return
that will be used in determining whether it
will accept or reject a project.
Example
• Given the cash flow
schedule on the right,
calculate the net
present value at 14%.
Today we invest $2,000,000. Today is always period 0.
The first year we have a loss of $40,000.
Time Period
0
1
2
3
4
5
6
7
8
9
10
Cash Flow
-2000000
-40000
-20000
-10000
100000
400000
600000
800000
1000000
1500000
1800000
In Excel the calculation is a two step process. First we use NPV to determine the net
present value of cash flows in periods 1 through 10. Then we add the present value of
$2.000.000 today (which of course is $2,000,000) to get the net present value.
Lets do it!
Solution
• =npv(rate, value 1, value 2, . . .)
• =npv(.14,-40000,-20000,10000,100000,400000,600000,800000
,1000000,1500000,1800000)
• Answer = $2,100,150.32.
• Now add this to the present value of
$2,000,000 today to get a net present
value of $100,150.32!
Solution
• What does the $100,050.32 mean?
• It means that the hospital will earn
$100,050.32 in addition to a 14% return
on the $2,000,000.
Solution
• Okay, so what is the actual rate of
return?
• We cannot use =irr(values, guess) to
calculate this as Excel does not allow
these many functions when typing in the
formula.
• Instead we must use the drop down
menus and drag and drop the range of
values.
Solution
Time Period
0
1
2
3
4
5
6
7
8
9
10
Cash Flow
-2000000
-40000
-20000
-10000
100000
400000
600000
800000
1000000
1500000
1800000
Select
formulas
Solution
Select
Insert
Function
Select IRR
Solution
Although it is hard to see using PowerPoint, when I drag and drop the values
into the values box, I do include the value for time period 0.
The answer you should receive is 14.6957%!
Review: All of this illustrates the theory behind
the discounted cash flow technique—a technique
based on the time value of money.
Discounted Cash Flow Technique
S
• The discounted cash flow technique is
generally recognized as the best conceptual
approach to making capital budgeting decisions.
• This technique considers both the estimated
total cash inflows and the time value of money.
• As discussed, the two methods used with the
discounted cash flow technique are:
1) net present value and
2) internal rate of return
Net Present Value Method
• Under the net present value method, cash
inflows are discounted to their present value
and then compared with the capital outlay
required by the investment.
• The interest rate used in discounting the
future cash inflows is the required minimum
rate of return.
• A proposal is acceptable when NPV is zero or
positive.
• The higher the positive NPV, the more
attractive the investment.
Additional Considerations
• The previous NPV example relied on
tangible costs and benefits that can be
relatively easily quantified.
• By ignoring intangible benefits, such as
increased quality, improved safety, etc.
capital budgeting techniques might
incorrectly eliminate projects that
could be financially beneficial to the
company.
Additional Considerations
To avoid rejecting projects that actually should be
accepted, two possible approaches are suggested:
1. Calculate net present value ignoring intangible
benefits. Then, if the NPV is negative, ask
whether the intangible benefits are worth at
least the amount of the negative NPV.
2. Project rough, conservative estimates of the
value of the intangible benefits, and incorporate
these values into the NPV calculation.
Profitability Index
• Another way of evaluating competing
capital projects is through the
profitability index.
• The formula for the profitability index
is: calculated by taking the present
value of the net cash flow and dividing
it by the initial investment.
Profitability Index
• Assume we are evaluating two projects, projects A and
B.
• The initial investment of Project A is $40,000, and the
initial investment of Project B is $90,000.
• Also assume that we have calculated the present value
of net cash flows for each project.
• The present value of Project A is $58,112, and the
present value of Project B is $110,574.
• What is the profitability index of each project?
Profitability Index
Present Value of Net Cash
÷
Flows
Initial Investment
=
Project A
Present Value
of Net Cash
Flows
$58,112
Profitability
Index
Project B
$110,574
The Profitability Index
Present Value of Net Cash
Flows
Initial Investment
÷
=
Project A
Present Value
of Net Cash
Flows
Divide by
Initial
Investment
Profitability
Index
Profitability
Index
Project B
$58,112
$110,574
$40,000
$90,000
1.4528
1.2286
Profitability Index
• In the previous slide, the
profitability index of Project A
exceeds that of Project B.
• Thus, Project A is more desirable.
• If the projects are not mutually
exclusive, and if resources are not
limited, then the company should
invest in both projects, since both
have positive NPVs.
Review Question
Assume Project A has a present value of net cash inflows of $79,600
and an initial investment of $60,000. Project B has a present value of
net cash inflows of $82,500 and an initial investment of $75,000.
Assuming the projects are mutually exclusive, which project should
management select?
a.
Project B.
b. Project A or B.
c. Project A.
d. There is not enough data to answer the question.
Review Question
Assume Project A has a present value of net cash inflows of $79,600
and an initial investment of $60,000. Project B has a present value of
net cash inflows of $82,500 and an initial investment of $75,000.
Assuming the projects are mutually exclusive, which project should
management select?
a.
Project B.
b. Project A or B.
c. Project A.
d. There is not enough data to answer the question.
Post-Audit of Investment Projects
Performing a post-audit is important for
a variety of reasons.
1. If managers know that their estimates will be
compared to actual results they will be more likely
to submit reasonable and accurate data when
making investment proposals.
2. A post-audit provides a formal mechanism by
which the company can determine whether
existing projects should be supported or
terminated.
3. Post-audits improve future investment proposals
because by evaluating past successes and failures,
managers improve their estimation techniques.
Annual Rate of Return Formula
• The annual rate of return technique is based
on accounting data. It indicates the
profitability of a capital expenditure. The
formula is:
The annual rate of return is compared with its required
minimum rate of return for investments of similar risk.
This minimum return is based on the company’s cost of capital,
which is the rate of return that management expects to pay on
all borrowed and equity funds.
Formula for Computing
Average Investment
Expected annual net income ($13,000) is obtained from
the projected income statement. Average investment is
derived from the following formula:
For Reno, average investment is $65,000:
[($130,000 + $0)/2]
Solution to Annual Rate of Return Problem
The expected annual rate of return for Reno Company’s
investment in new equipment is therefore 20%, computed
as follows:
$13,000 ÷ $65,000 = 20%
The decision rule is:
A project is acceptable if its rate of return is greater than management’s
minimum rate of return. It is unacceptable when the reverse is true.
When choosing among several acceptable projects, the higher the rate of
return for a given risk, the more attractive the investment.
Review Question
Bear Company computes an expected annual net income from an
investment of $30,000. The investment has an initial cost of $200,000
and a terminal value of $20,000. Compute the annual rate of return.
a. 15%.
b. 30%.
c. 25%.
d. 27.3%.
Review Question
Bear Company computes an expected annual net income from an
investment of $30,000. The investment has an initial cost of $200,000
and a terminal value of $20,000. Compute the annual rate of return.
a. 15%.
b. 30%.
c. 25%.
d. 27.3%.
Review Problem 1
• Marcus Company is considering
purchasing new equipment for
$450,000.
• It is expected that the equipment will
produce net annual cash flows of
$55,000 over its 10-year useful life.
• Compute the cash payback period.
Review Problem 1
• Net cash flow is already calculated
($55,000).
– If it were not, one would add annual
depreciation to net income to calculate it.
• Divide investment by cash flow:
– $450,000/$55,000 = 8.2 years
Review Problem 2
• Jack’s Custom Manufacturing Company is
considering three new projects, each requiring
an equipment investment of $21,000.
• Each project will last for 3 years and produce
the net annual cash flows shown below:
Year
AA
BB
CC
1
$7,000
$9,500
$13,000
2
9,000
9,500
10,000
3
15,000
9,500
11,000
Total
$31,000
$28,500
$34,000
Review Problem 2
• The equipment’s salvage value is zero.
• Jack uses straight-line depreciation.
• Jack will not accept any project with a
cash payback period over 2 years.
• Jack’s required rate of return is 12%.
• Compute each project’s payback period,
indicating the most desirable and least
desirable project using this method.
Review Problem 2
• Let’s do project AA first:
• The first year’s cash flow is $7,000 as shown on
the chart.
• The second year’s cash flow is $9,000 which
brings the cumulative cash flow to $16,000.
• At the end of the third year we only need
$5,000 to reach payback.
• It takes $5,000/$15,000 = .33 of a year to get
this cash.
• The payback period, therefore, is 2.33 years
Review Problem 2
• Using the same methodology we get
2.21 years for project BB, and 1.8 years
for project CC.
• The most desirable project is CC
because it has the shortest payback
period.
• The least desirable is AA because it
has the longest payback period.
Review Problem 2
• Compute the net present value of each
project. Does your evaluation change?
Review Problem 2
• Which project is therefore most
desirable?
• Project CC since it has the highest NPV
of $6,409.
• The least desirable project is BB with a
NPV of $1,817.
Review Problem 3
• Mane Event is considering a new hair salon in
Pompador, California.
• The cost of building a new salon is $300,000.
• The new salon will normally generate annual
revenues of $70,000 with annual expenses
(excluding depreciation) of $40,000.
• At the end of 15 years, the salon will have a
salvage value of $75,000.
Review Problem 3
• Okay, since depreciation is included in the
expenses, we can expenses as given from
revenues to get accounting income.
• Remember, we need accounting income for
annual rate of return, not cash flows as with
NPV.
• Annual income is $70,000 - $40,000 = $30,000.
• The average investment is calculated using the
following formula:
(Investment + Salvage Value)/2
Review Problem 3
• So the average investment is:
– ($300,000 + $75,000)/2 = $187,50
• So annual rate of return is:
– Income $30,000/Avg. Investment
$187,500 = 16%
Review Problem 4
• Jo Quick is managing director of Tot
Lot Day Care Center.
• Tot Lot is currently set up as a fulltime child care facility for children
between 12 months and 6 years old.
Review Problem 4
• Jo Quick is trying to determine
whether the center should expand its
facilities to incorporate a newborn care
room for infants between the ages of 6
weeks and 12 months.
Review Problem 4
• The necessary space already exists.
• An investment of $200,000 would be
needed, however, to purchase cribs,
high chairs, etc.
• The equipment purchased for the room
would have a 5-year useful life with
zero salvage value.
Review Problem 4
• The newborn nursery would be staffed
to handle 11 infants on a full-time basis.
• The parents of each infant would be
charged $125 weekly, and the facility
would operate 52 weeks of the year.
• Staffing the nursery would require two
full-time specialists and five part-time
assistants at an annual cost of $60,000.
Review Problem 4
• Food, diapers, and other miscellaneous
items are expected to total $6,000
annually.
Review Problem 4
• Determine the net income and annual
cash flows for the nursery.
Review Problem 4
Fee revenues
11 x $125 x 52
Annual Net
Income
Annual
Cash Flow
$71,500
$71,500
Calculation of Income and Cash Flow
Review Problem 4
Fee revenues
Annual Net
Income
Annual
Cash Flow
11 x $125 x 52
$71,500
$71,500
given
60,000
60,000
Expenses
Salaries
Review Problem 4
Annual Net
Income
Annual
Cash Flow
11 x $125 x 52
$71,500
$71,500
Salaries
given
60,000
60,000
Food and supplies
given
6,000
6,000
Fee revenues
Expenses
Review Problem 4
Annual Net
Income
Annual
Cash Flow
11 x $125 x 52
$71,500
$71,500
Salaries
given
60,000
60,000
Food and supplies
given
6,000
6,000
($20,000/5)
4,000
0
Fee revenues
Expenses
Depreciation
Remember, depreciation is not a
cash expense.
Review Problem 4
Annual Net
Income
Annual
Cash Flow
11 x $125 x 52
$71,500
$71,500
Salaries
given
60,000
60,000
Food and supplies
given
6,000
6,000
($20,000/5)
4,000
0
70,000
66,000
Fee revenues
Expenses
Depreciation
Total expenses
Review Problem 4
Annual Net
Income
Annual
Cash Flow
11 x $125 x 52
$71,500
$71,500
Salaries
given
60,000
60,000
Food and supplies
given
6,000
6,000
($20,000/5)
4,000
0
70,000
66,000
Fee revenues
Expenses
Depreciation
Total expenses
Net Income
$1,500
Review Problem 4
Annual Net
Income
Annual
Cash Flow
11 x $125 x 52
$71,500
$71,500
Salaries
given
60,000
60,000
Food and supplies
given
6,000
6,000
($20,000/5)
4,000
0
70,000
66,000
Fee revenues
Expenses
Depreciation
Total expenses
Net Income
Cash flows
$1,500
$5,500
Review Problem 4
• Cash payback period:
• Formula: Investment/cash flow
• $20,000/($1,500 + $4,000) = 3.64
years
We need to add depreciation
back to income to get cash
flow
Calculation of Payback Period
Review Problem 4
Now let’s calculate the annual rate of
return.
• Remember, the formula is:
Net income/Average Annual Investment
• Average annual investment is:
($20,000 + 0)/2 = $10,000
• Annual rate of return is therefore:
$1,500/$15,000 = 10%
Review Problem 4
• Now we are asked for the present value
of net annual cash flows, assuming a 10%
discount rate.
• Using tables the present value of future
cash flows are: ($5,500 x 3.79097) =
$20,849
• The capital investment is $20,000
Review Problem 4
• Remember, the Net Present Value is
calculated by netting the present value
of the capital investments with the
present value of the future cash inflows.
• So NPV = $20,849 - $20,000 = $849
• Note: The PV is positive, so we made
over 10%--our minimum required rate of
return.
Review Problem 4
• Now let’s calculate the actual internal
rate of return.
• IRR = 11.65%, better than the 10% we
hoped for!
Other Interesting Computations with
Financial Calculators
• Here are some calculations on financial
decisions people make during their lives.
• The purpose is not to tell you there is
one way to approach a problem, only to
show you there is approach for reaching
an answer.
• All examples are based on assumptions
that may different in your situation.
Other Interesting Computations with
Financial Calculators
• The backup for the calculations are on
the website in an Excel Format entitled
“Financial Planning with Time Value of
Money.”
Mortgages
• Almost everyone during their life has
one or more home mortgages.
• Understanding how mortgages work,
and the impact of time and compounding
of interest on the amount you
eventually pay for a home using a
mortgage can save tens of thousands of
dollars.
First a Little Theory
• A mortgage payment is a form of
annuity
– Equal payments
– Equally spaced
• Payment payoff periods vary
considerable (typically from 15 to 30
years).
Mortgage Calculation
• Lets assume a small mortgage of
$100,000 at 12% annually, for thirty
years or 360 months (payments are
made monthly).
• The rate will be the monthly rate since
payments are made monthly (12%/12 =
1%).
• The number of periods will be 360.
Let’s Calculate a Mortgage using Excel
• Select Formulas
• Select Financial
• Select PMT (for payment)
Pop-up Window
The PV (present value) is
$100,000, the amount of
the mortgage.
The FV (future value) is
zero since the mortgage will
be paid off at the end of 360
periods.
The monthly payment is $1,028.61.
If payments are made at the
beginning of the month the
type is 1, if they are made
at the end of the period the
type is 0. Most mortgages
are of type 0.
It is important to remember that interest
is paid first, then principal.
Knowing this, let’s figure out how much is applied to the loan the first month.
Since we owe $100,000 and the interest rate is 12% or 1% per month, the
interest
paid 1% x $100,000 or $1,000 as shown below.
Monthly Payment
$1,028.61
Less interest
Amount applied to principal.
1,000.00
$28.61
Great! We have paid $1,028.61 but only reduced our
loan by $28.61.
Don’t worry. Things get better, next month it is $28.90.
The first year amortization schedule for this loan is shown
on the following page.
Happy Banker
Amortization Table
Payments in First 12 Months
Year Month
2007 Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Beginning
Ending
Payment Principal Interest
Balance
Balance
$100,000.00 $1,028.61
$28.61 $1,000.00 $99,971.39
$99,971.39 $1,028.61 $28.90 $999.71 $99,942.49
$99,942.49 $1,028.61
$29.19 $999.42 $99,913.30
$99,913.30 $1,028.61
$29.48 $999.13 $99,883.82
$99,883.82 $1,028.61
$29.77 $998.84 $99,854.05
$99,854.05 $1,028.61
$30.07 $998.54 $99,823.98
$99,823.98 $1,028.61
$30.37 $998.24 $99,793.61
$99,793.61 $1,028.61
$30.67 $997.94 $99,762.94
$99,762.94 $1,028.61
$30.98 $997.63 $99,731.96
$99,731.96 $1,028.61
$31.29 $997.32 $99,700.67
$99,700.67 $1,028.61
$31.60 $997.01 $99,669.07
$99,669.07 $1,028.61
$31.92 $996.69 $99,637.15
What if when we pay the first payment of $1,028.61, we enclose an additional amount
for $28.90? Will jump from January’s payment to March’s payment. For and additional
$28.90 we will never make that $1,028.61 payment.
Not a bad investment! Pay $28.90, save $1,028.61!
Amortization Table
Payments in First 12 Months
Year Month
2007 Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Beginning
Ending
Payment Principal Interest
Balance
Balance
$100,000.00 $1,028.61
$28.61 $1,000.00 $99,971.39
$99,971.39 $1,028.61 $28.90 $999.71 $99,942.49
$99,942.49 $1,028.61 $29.19 $999.42 $99,913.30
$99,913.30 $1,028.61 $29.48 $999.13 $99,883.82
$99,883.82 $1,028.61 $29.77 $998.84 $99,854.05
$99,854.05 $1,028.61 $30.07 $998.54 $99,823.98
$99,823.98 $1,028.61 $30.37 $998.24 $99,793.61
$99,793.61 $1,028.61 $30.67 $997.94 $99,762.94
$99,762.94 $1,028.61 $30.98 $997.63 $99,731.96
$99,731.96 $1,028.61 $31.29 $997.32 $99,700.67
$99,700.67 $1,028.61 $31.60 $997.01 $99,669.07
$99,669.07 $1,028.61 $31.92 $996.69 $99,637.15
What if we pay the sum of the remaining principal payments for the year (red)? This
totals to $334.24. Just include that with the first check of $1,028.61 and you will skip so
that next month instead of making the February payment, you will now be on the January
2008 payment, a savings of $10,980.47 in interest.
Let’s look at how little difference in
monthly payments a change in the length
of the mortgage makes.
Number of Years
Number of Months
Payment
Total Paid
15
180
$1,200.17
$219,090.60
20
240
$1,101.09
$264,261.60
30
360
$1,028.61
$370,299.60
40
480
$1,008.50
$484,080.00
50
600
$1,002.56
$601,536.00
100
1,200
$1,000.01
$$1,200,012.00
The difference in the monthly payment from cutting your length of mortgage in half is only
$171.56.
However, the difference in the amount you wind up paying for the house is $151,209!
Let’s look at how little difference in
monthly payments a change in the length
of the mortgage makes.
Number of Years
Number of Months
Payment
Total Paid
15
180
$1,200.17
$219,090.60
20
240
$1,101.09
$264,261.60
30
360
$1,028.61
$370,299.60
40
480
$1,008.50
$484,080.00
50
600
$1,002.56
$601,536.00
100
1,200
$1,000.01
$$1,200,012.00
I have actually hear (on a radio interview) bankers complaining about how hard it is for
young people to make mortgage payments with higher interest rates (I have seen 17%
In my lifetime) and advocate going to 40 or 50 year mortgages.
Who do you think that proposal is designed to benefit. The “poor young couples” or the
bankers?
Objective
• Remember the purpose of this exercise
is not to tell you what to do, only to
show you how, through the use of Excel,
you can determine the actual impact of
different decision options.
Let’s Have Some Fun . . .
• Assume there are two twin brothers,
Fred and Frank.
They have the income, the same taste in
houses.
Dream Home
• They both have plans for the same
dream home, a rambler costing
$250,000.
– To simplify calculations assume no down
payment
– Interest rate of 8%
– No inflation
Fred’s Decision
• Fred has to have it NOW.
• He borrows the money and incurs an
$1,834.41 monthly payment for 30
years.
Frank’s Decision
• Frank is a little more patient.
• He has the same payment to make on a
house.
• He takes his computer and determines
how much house he can buy with a 10
year mortgage for
$1,834.41.
• He an buy a modes
$151,195 home.
Jump Ahead 10 years
• Frank’s home is paid for. He has
$151,195 in equity.
• Fred, having made the same number of
payments in the same amount still owes
$219,312. He has $250,000 - $219,312
= $30,688 in equity.
Jump Ahead 10 years
• Frank takes his $151,195 equity and
makes a down payment on the $250,000
home.
• His mortgage is for $98,805.
• He continues making the $1,834.41
payment each month.
We are now 187 months out
• It takes 67 months (5 years 7 months
for Frank to retire mortgage).
• He owns the home outright.
• Fred still owes $187,993. He still has
173 payments to make.
Investment
• Since Frank no longer has to make a
mortgage payment, he invests the
amount he would pay each month the
stock market.
– The historical return on the stock market
is 10% a year.
30 Years After Their Initial Purchase
• Fred finally finishes paying for his 30
year home.
– At that time he has a $250,000 home.
• Frank also has the same home, but in
addition he has a savings account worth
$710,850. His net worth is $960,851.
• Both have made the same payments for
the same amount of years!
Another Illustration
• Young couples often say they don’t have
a lot of money to save for retirement.
• That may be true, but what they do
have is a lot of time, and the earlier you
start the better.
• The following illustration was taken
from an insurance company brochure.
Rob and Rich
• Fred and Frank have twin cousins, Rob
and Rich.
• Both are concerned about retirement.
Rob and Rich
• At age 25, Rob makes five yearly
deposits a mutual fund earning 12%.
• He never makes another deposit.
Rob and Rich
• Rich during those six years deposits
nothing.
• He spends his money on wine, women,
and song.
• The rest of it he plain wastes.
Rob and Rich
• It takes Rich almost 25 years to catch
his brother.
• When they both retire at age 65:
– Rob who made six $2,000 deposits has
$856,957.79 in his savings account.
– Rob who has made thirty-four $2,000
deposits has $861,326.99 in his account.
• How important is time when you are
compounding interest?
New Question
• How much do you have to deposit monthly at
10% to have $1,000,000 when you retire?
• Age 25--$158.12
• Age 30--$161.69
• Age 35--$446.07
• Age 40—757.49
• Age 50--$2,417.23
• Age 55--$4,887.39
Last Example
• You decide you want to surprise your
great-grand daughter with a
$1,000,000 inheritance 100 years from
now.
• How much do you have to deposit today,
assuming you can get 10% a year,
compounded monthly, to reach that
goal?
Answer: $47.32
Homework
Exercise 12-2
• Jack’s Custom Manufacturing Company is
considering three new projects, each requiring
an equipment investment of $21,000.
• Each project will last for 3 years and produce
the net annual cash flows shown below:
Year
AA
BB
CC
1
$7,000
$9,500
$13,000
2
9,000
9,500
10,000
3
15,000
9,500
11,000
Total
$31,000
$28,500
$34,000
Exercise 12-2
• The equipment’s salvage value is zero.
• Jack uses straight-line depreciation.
• Jack will not accept any project with a
cash payback period over 2 years.
• Jack’s required rate of return is 12%.
• Compute each project’s payback period,
indicating the most desirable and least
desirable project using this method.
Exercise 12-2
• Let’s do project AA first:
• The first year’s cash flow is $7,000 as shown on
the chart.
• The second year’s cash flow is $9,000 which
brings the cumulative cash flow to $16,000.
• At the end of the third year we only need
$5,000 to reach payback.
• It takes $5,000/$15,000 = .33 of a year to get
this cash.
• The payback period, therefore, is 2.33 years
Exercise 12-2
• Using the same methodology we get
2.21 years for project BB, and 1.8 years
for project CC.
• The most desirable project is CC
because it has the shortest payback
period.
• The least desirable is AA because it
has the longest payback period.
Exercise 12-2
• Compute the net present value of each
project. Does your evaluation change?
Data Given
Year
AA
1 $ 7,000.00
BB
CC
$ 9,500.00
$ 13,000.00
2
9,000.00
9,500.00
10,000.00
3
15,000.00
9,500.00
11,000.00
31,000.00
28,500.00
34,000.00
Pres values of cash flows years 1-3
$24,101.45
$22,817.40
$27,408.66
Present value of investments
(21,000.00)
(21,000.00)
(21,000.00)
$3,101.45
$1,817.40
$6,408.66
Net present values of investments
Best option
Exercise 12-6
• Mane Event is considering a new hair salon in
Pompador, California.
• The cost of building a new salon is $300,000.
• The new salon will normally generate annual
revenues of $70,000 with annual expenses
(excluding depreciation) of $40,000.
• At the end of 15 years, the salon will have a
salvage value of $75,000.
Exercise 12-6
• Okay, since depreciation is included in the
expenses, we can expenses as given from
revenues to get accounting income.
• Remember, we need accounting income for
annual rate of return, not cash flows as with
NPV.
• Annual income is $70,000 - $40,000 = $30,000.
• The average investment is calculated using the
following formula:
(Investment + Salvage Value)/2
Exercise 12-6
• So the average investment is:
– ($300,000 + $75,000)/2 = $187,50
• So annual rate of return is:
– Income $30,000/Avg. Investment
$187,500 = 16%
The End
• What other problems can you come up
with to work using Excel?