Chapter Thirteen

1
Chapter Thirteen
Capital Budgeting and Other Time Value of Money
Applications
Richard E. McDermott, Ph.D.
2
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.

3
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 companys basic decision-making
• approach.
• 4) The risk associated with a particular
• project.

4
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

5
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 200,000 Less Costs and
expenses 132,000 Depreciation expense
(130,000/5) 26,000 Selling and
administrative expenses 22,000
180,000 Income before income taxes
20,000 Income tax expense 7,000 Net
income 13,000
6
Computation of Annual Cash Inflow

• Cash income per year equals net income plus
  depreciation expense.

Net income 13,000


7
Computation of Annual Cash Inflow
Net income 13,000
Add Depreciation expense 26,000

8
Computation of Annual Cash Inflow
Net income 13,000
Add Depreciation expense 26,000
Cash flow 39,000
9
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.
10
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.
Review Question

1. 8.00 years.
2. 3.08 years.
3. 5.00 years.
4. 13.33 years.

11
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.
Review Question
Calculation of answer

1. 8.00 years.
2. 3.08 years.
3. 5.00 years.
4. 13.33 years.

First calculate depreciation
100/000/8 years 12,500
Add depn 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.
12
Time Value of Money

• Many cost of capital evaluation techniques
  involve time value money of calculations.
• Lets utilize Excel in learning how to analyze
  various investments or returns involving incoming
  or outgoing streams of money.

13
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
Time
0 1 2 3
14
A Little Theory . . .
We let it grow for three years.
Money
In one year it is worth 100 x 1.10 110 In
two years it is worth 110 x 1.1 121 In
three years it is worth 121 x 1.10 133.10
133.10
130 120 100
Time
0 1 2 3
15
A Little Theory . . .
These figures can be calculated using Excel.
Money
Again we are talking about lump sums!
The future value of 100 for three periods at 10
is 133.10.
133.10
130 120 100
The present value of 133.10 for three periods is
100.
This represents the future value and present
value of a lump sum.
Time
0 1 2 3
16
Practice Problem Future Value of a Lump Sum

• Lets 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.

17
Excel Worksheet
Select Formulas
Select Financial
18
Excel Worksheet
Select FV for future value
19
Excel Worksheet
This box will appear on your screen.
20
Excel Worksheet
Notice that we put nothing in the Pmt box since
the 100 is the only deposit.
21
Excel Worksheet
Hit Ok. The future value of 100 for 3
periods at 10 per period is 133.10.
22
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)

23
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24
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

25
Present Value of Future Lump Sum

• Lets 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!

26
Present Value of Future Lump Sum

• What if you compound the interest yearly instead
  of monthly, does it make a difference?
• Lets see.
• This time lets use the menu approach to solving
  the Excel problem.

27
Calculation

• From the Excel screen select formulas, then
  financial just as we did before.

28
Now Lets Calculate Present Value

• This time select PV from the drop down menu.

29
This Box Will Appear
30
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.
31
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.

32
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.
300 200 100
The future value of 3 payments of 100 at 10
interest per period is 331.
Again, we could calculate this using Excel.
Time
0 1 2 3
33
Calculation of Future Value of an Annuity Problem
Select Formulas
Select Financial
34
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.
35
The Answer is 331.00
The same amount shown on the earlier chart!
36
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.
37
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?

38
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.

39
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

40
Pop-up Box
41
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.
42
Now Lets 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?

43
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.

44
Present Value of an Annuity
Hit ok. The answer is 157,296.81!
45
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?

46
Future Value of a Lump Sum and Annuity

• Select Formulas, and Financial as before.
• Select FV to get the following box.

47
The answer is . . .

• 70,339.57

48
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?

49
Discounting Cash Flows that Are Not Equal

• Why do we care?
• Because this is one way of valuing a business!

50
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.
• Lets do some examples.

51
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).

52
Projected Cash Flow
Today
53
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?

54
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 . . .)

55
Lets 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.
56
Lets Do the Same Thing Using the Pop-up 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.

57
The Answer is the Same!
Note that all of the values are not shown on this
copy of the pop-up box.
58
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.
59
How Much Less

• Lets 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.

60
Lets First Make a Table of Projected Cash Flows
That Looks Like This
61
Now Lets Go To The Menu Like We Did Before . . .

• Select Formulas from the top menu bar
• Then Select Financial
• Select IRR

62
Your pop-up box will look like this
Drag and drop the cash flows from the Excel
Spreadsheet into the values box.
63
You are required to give a guess as to what the
IRR will be
The actual rate of return is approximately 10.15
64
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.

65
Net Present Value

• One of the things I dont 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.

66
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.

67
Example
Time Period Cash Flow
0 -2000000
1 -40000
2 -20000
3 -10000
4 100000
5 400000
6 600000
7 800000
8 1000000
9 1500000
10 1800000

• 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.
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!
68
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!

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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.

14
70
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.

71
Solution
Time Period Cash Flow
0 -2000000
1 -40000
2 -20000
3 -10000
4 100000
5 400000
6 600000
7 800000
8 1000000
9 1500000
10 1800000
Select formulas
72
Solution
Select Insert Function
Select IRR
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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!
74
Review All of this illustrates the theory behind
the discounted cash flow techniquea technique
based on the time value of money.
75
Discounted Cash Flow TechniqueS

• 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

76
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.

77
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.

78
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.

79
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.

80
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?

81
Profitability Index
Project A Project B
Present Value of Net Cash Flows 58,112 110,574


82
The Profitability Index


Project A Project B
Present Value of Net Cash Flows 58,112 110,574
Divide by Initial Investment 40,000 90,000
Profitability Index 1.4528 1.2286
83
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.

84
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?
Review Question

1. Project B.
2. Project A or B.
3. Project A.
4. There is not enough data to answer the question.

85
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?
Review Question

1. Project B.
2. Project A or B.
3. Project A.
4. There is not enough data to answer the question.

86
Post-Audit of Investment Projects

• Performing a post-audit is important for
• a variety of reasons.
• 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.
• A post-audit provides a formal mechanism by which
  the company can determine whether existing
  projects should be supported or terminated.
• Post-audits improve future investment proposals
  because by evaluating past successes and
  failures, managers improve their estimation
  techniques.

87
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 companys cost of capital, which is the rate
of return that management expects to pay on all
borrowed and equity funds.
88
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

89
Solution to Annual Rate of Return Problem
The expected annual rate of return for Reno
Companys 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
managements 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.
90
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.
Review Question

1. 15.
2. 30.
3. 25.
4. 27.3.

91
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.
Review Question

1. 15.
2. 30.
3. 25.
4. 27.3.

92
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.

93
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

94
Review Problem 2

• Jacks 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
95
Review Problem 2

• The equipments salvage value is zero.
• Jack uses straight-line depreciation.
• Jack will not accept any project with a cash
  payback period over 2 years.
• Jacks required rate of return is 12.
• Compute each projects payback period, indicating
  the most desirable and least desirable project
  using this method.

96
Review Problem 2

• Lets do project AA first
• The first years cash flow is 7,000 as shown on
  the chart.
• The second years 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

97
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.

98
Review Problem 2

• Compute the net present value of each project.
  Does your evaluation change?

99
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.

100
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.

101
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

102
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

103
Review Problem 4

• Jo Quick is managing director of Tot Lot Day Care
  Center.
• Tot Lot is currently set up as a full-time child
  care facility for children between 12 months and
  6 years old.

104
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.

105
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.

106
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.

107
Review Problem 4

• Food, diapers, and other miscellaneous items are
  expected to total 6,000 annually.

108
Review Problem 4

• Determine the net income and annual cash flows
  for the nursery.

109
Review Problem 4
Annual Net Income Annual Cash Flow
Fee revenues 11 x 125 x 52 71,500 71,500







Calculation of Income and Cash Flow
110
Review Problem 4
Annual Net Income Annual Cash Flow
Fee revenues 11 x 125 x 52 71,500 71,500
Expenses
Salaries given 60,000 60,000





111
Review Problem 4
Annual Net Income Annual Cash Flow
Fee revenues 11 x 125 x 52 71,500 71,500
Expenses
Salaries given 60,000 60,000
Food and supplies given 6,000 6,000




112
Review Problem 4
Annual Net Income Annual Cash Flow
Fee revenues 11 x 125 x 52 71,500 71,500
Expenses
Salaries given 60,000 60,000
Food and supplies given 6,000 6,000
Depreciation (20,000/5) 4,000 0



Remember, depreciation is not a cash expense.
113
Review Problem 4
Annual Net Income Annual Cash Flow
Fee revenues 11 x 125 x 52 71,500 71,500
Expenses
Salaries given 60,000 60,000
Food and supplies given 6,000 6,000
Depreciation (20,000/5) 4,000 0
Total expenses 70,000 66,000


114
Review Problem 4
Annual Net Income Annual Cash Flow
Fee revenues 11 x 125 x 52 71,500 71,500
Expenses
Salaries given 60,000 60,000
Food and supplies given 6,000 6,000
Depreciation (20,000/5) 4,000 0
Total expenses 70,000 66,000
Net Income 1,500

115
Review Problem 4
Annual Net Income Annual Cash Flow
Fee revenues 11 x 125 x 52 71,500 71,500
Expenses
Salaries given 60,000 60,000
Food and supplies given 6,000 6,000
Depreciation (20,000/5) 4,000 0
Total expenses 70,000 66,000
Net Income 1,500
Cash flows 5,500
116
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
117
Review Problem 4

• Now lets 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 therefore1,500/15,000
  10

118
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

119
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 in-flows.
• So NPV 20,849 - 20,000 849
• Note The PV is positive, so we made over
  10--our minimum required rate of return.

120
Review Problem 4

• Now lets calculate the actual internal rate of
  return.
• IRR 11.65, better than the 10 we hoped for!

121
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.

122
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.

123
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.

124
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).

125
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.

126
Lets Calculate a Mortgage using Excel

• Select Formulas
• Select Financial
• Select PMT (for payment)

127
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. 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.
The monthly payment is 1,028.61.
128
It is important to remember that interest is paid
first, then principal.
Knowing this, lets 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 1,000.00
Amount applied to principal. 28.61
Great! We have paid 1,028.61 but only reduced
our loan by 28.61.
Dont 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
129
Amortization Table
Payments in First 12 Months Payments in First 12 Months Payments in First 12 Months Payments in First 12 Months Payments in First 12 Months Payments in First 12 Months Payments in First 12 Months
Year Month Beginning Balance Payment Principal Interest Ending Balance
2007 Jan 100,000.00 1,028.61 28.61 1,000.00 99,971.39
  Feb 99,971.39 1,028.61 28.90 999.71 99,942.49
  Mar 99,942.49 1,028.61 29.19 999.42 99,913.30
  Apr 99,913.30 1,028.61 29.48 999.13 99,883.82
  May 99,883.82 1,028.61 29.77 998.84 99,854.05
  Jun 99,854.05 1,028.61 30.07 998.54 99,823.98
  Jul 99,823.98 1,028.61 30.37 998.24 99,793.61
  Aug 99,793.61 1,028.61 30.67 997.94 99,762.94
  Sep 99,762.94 1,028.61 30.98 997.63 99,731.96
  Oct 99,731.96 1,028.61 31.29 997.32 99,700.67
  Nov 99,700.67 1,028.61 31.60 997.01 99,669.07
  Dec 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 Januarys payment to
Marchs 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!
130
Amortization Table
Payments in First 12 Months Payments in First 12 Months Payments in First 12 Months Payments in First 12 Months Payments in First 12 Months Payments in First 12 Months Payments in First 12 Months
Year Month Beginning Balance Payment Principal Interest Ending Balance
2007 Jan 100,000.00 1,028.61 28.61 1,000.00 99,971.39
  Feb 99,971.39 1,028.61 28.90 999.71 99,942.49
  Mar 99,942.49 1,028.61 29.19 999.42 99,913.30
  Apr 99,913.30 1,028.61 29.48 999.13 99,883.82
  May 99,883.82 1,028.61 29.77 998.84 99,854.05
  Jun 99,854.05 1,028.61 30.07 998.54 99,823.98
  Jul 99,823.98 1,028.61 30.37 998.24 99,793.61
  Aug 99,793.61 1,028.61 30.67 997.94 99,762.94
  Sep 99,762.94 1,028.61 30.98 997.63 99,731.96
  Oct 99,731.96 1,028.61 31.29 997.32 99,700.67
  Nov 99,700.67 1,028.61 31.60 997.01 99,669.07
  Dec 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.
131
Lets 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!
132
Lets 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?
133
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.

134
Lets Have Some Fun . . .

• Assume there are two twin brothers, Fred and
  Frank.

They have the income, the same taste in houses.
135
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

136
Freds Decision

• Fred has to have it NOW.
• He borrows the money and incurs an 1,834.41
  monthly payment for 30 years.

137
Franks 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
  for1,834.41.
• He an buy a modes 151,195 home.

138
Jump Ahead 10 years

• Franks 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.

139
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.

140
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.

141
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.

142
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!

143
Another Illustration

• Young couples often say they dont 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.

144
Rob and Rich

• Fred and Frank have twin cousins, Rob and Rich.
• Both are concerned about retirement.

145
Rob and Rich

• At age 25, Rob makes five yearly deposits a
  mutual fund earning 12.
• He never makes another deposit.

146
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.

147
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?

148
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 40757.49
• Age 50--2,417.23
• Age 55--4,887.39

149
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
150
Homework
151
Exercise 12-2

• Jacks 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
152
Exercise 12-2

• The equipments salvage value is zero.
• Jack uses straight-line depreciation.
• Jack will not accept any project with a cash
  payback period over 2 years.
• Jacks required rate of return is 12.
• Compute each projects payback period, indicating
  the most desirable and least desirable project
  using this method.

153
Exercise 12-2

• Lets do project AA first
• The first years cash flow is 7,000 as shown on
  the chart.
• The second years 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

154
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.

155
Exercise 12-2

• Compute the net present value of each project.
  Does your evaluation change?

Data Given Data Given Data Given Data Given
Year AA BB CC
1 7,000.00 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 Pres values of cash flows years 1-3 Pres values of cash flows years 1-3 Pres values of cash flows years 1-3 24,101.45 22,817.40 27,408.66
Present value of investments Present value of investments Present value of investments (21,000.00) (21,000.00) (21,000.00)
Net present values of investments Net present values of investments Net present values of investments Net present values of investments 3,101.45 1,817.40 6,408.66
Best option
156
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.

157
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

158
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

159
The End

• What other problems can you come up with to work
  using Excel?