Chapter Thirteen

Capital Budgeting Capital Budgeting and Other Time and Other Time Value of Money Value of Money

ApplicationsApplicationsRichard 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:

• 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 $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

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

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 outflowof cash.

Net income$13,00

0

Computation of Annual Cash Inflow

Net income$13,00

0 Add: Depreciation

expense 26,000

Computation of Annual Cash Inflow

Net income$13,00

0 Add: Depreciation

expense 26,000

Cash flow$39,00

0

Cash Payback Period

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, and2) the risk of loss from obsolescence and changed economic conditions is less in a shorter payback period.

The cash payback period in this example is therefore 3.33 years, computed as follows:The cash payback period in this example is therefore 3.33 years, computed as follows:

$130,000 ÷ $39,000 = 3.33 years$130,000 ÷ $39,000 = 3.33 years

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 QuestionReview 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 QuestionReview Question

First calculate depreciation:

$20,000 + $12,500 = $32,500

$100,000/$32,500 = 3.08 years.

Calculation of answer:

$100/000/8 years = $12,500

Add dep’n to income to get net cash flow:

Divide investment by yearly cash flow toget payback period:

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 . . .

Time

Money

Assume we invest a lump sum of $100 in time period zero.

0 1 2 3

$300

$200

$100

The interest rate is 10% per year.

A Little Theory . . .

Time

Money

0 1 2 3

$130

$120

$100

We let it grow for three years.

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

A Little Theory . . .

Time

Money

0 1 2 3

$130

$120

$100

$133.10 The future value of $100 for threeperiods at 10% is $133.10.

The present value of $133.10 for threeperiods is $100.

This represents the future value and present value of a lump sum.

These figures can be calculated using Excel.

Again we are talking about lump sums!

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 WorksheetNotice that we put nothing in the Pmtbox 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. =Rate(nper,pmt,pv, fv.type,guess) PMT calculates the payment for a loan based on constant payments and a constant interest rate =PMT(rate,nper,pv,[fv],[type])

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 . . .

Time

Money

0 1 2 3

$300

$200

$100

New Axis

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.

$331

At the end of three years we have$331 from the annuity.

The future value of 3 payments of$100 at 10% interest per period is $331.

Again, we could calculate this using Excel.

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 earlierchart!

What does this mean?

If you deposit three yearly payments of $100each, 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 0Year 1 20000Year 2 25000Year 3 32000Year 4 37000Year 5 45000Year 6 50000Year 7 40000Year 8 35000Year 9 25000Year 10 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 $15,000from operations plus the $10,000 salvage valueof the equipment when the Laundry is sold.

The answer is $184,238.35.

Let’s 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.

The Answer is the Same!

Note that all of the values are not shown on this copy of the pop-up box.

What this Means

What this means is that if you wish to earn12% 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

• Select Formulas from the top menu bar

• Then Select Financial• Select IRR

Now Lets Go To The Menu Like We Did Before . . .

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 approximately10.15%

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%.

Time Period Cash Flow0 -20000001 -400002 -200003 -100004 1000005 4000006 6000007 8000008 10000009 1500000

10 1800000

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!

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.

SolutionTime Period Cash Flow

0 -20000001 -400002 -200003 -100004 1000005 4000006 6000007 8000008 10000009 1500000

10 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 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

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 Profitability Index

Project A Project B

Present Value of Net Cash Flows

$58,112 $110,574

The Profitability Index

÷ =Present Value of Net Cash Flows

Initial Investment 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

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.

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 QuestionReview 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 QuestionReview Question

Post-Audit of Investment Projects

Performing a post-audit is important fora 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.

• The annual rate of return technique is based on accounting data. It indicates the profitability of a capital expenditure. The formula is:

Annual Rate of Return Formula

The annual rate of return is compared with its requiredminimum 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 onall borrowed and equity funds.

Formula for Computing Average Investment

For Reno, average investment is $65,000: [($130,000 + $0)/2]

Expected annual net income ($13,000) is obtained fromthe projected income statement. Average investment isderived from the following formula:

Solution to Annual Rate of Return Problem

$13,000 ÷ $65,000 = 20%

The expected annual rate of return for Reno Company’s investment in new equipment is therefore 20%, computedas follows:

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.

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 QuestionReview 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 QuestionReview Question

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 full-time 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

Annual NetIncome

Annual Cash Flow

Fee revenues 11 x $125 x 52 $71,500 $71,500

Calculation of Income and Cash Flow

Annual NetIncome

Annual Cash Flow

Fee revenues 11 x $125 x 52 $71,500 $71,500

Expenses

Salaries given 60,000 60,000

Review Problem 4

Annual NetIncome

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

Review Problem 4

Annual NetIncome

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.

Review Problem 4

Annual NetIncome

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

Review Problem 4

Annual NetIncome

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

Review Problem 4

Annual NetIncome

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

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 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.

Review Problem 4

• Now let’s calculate the actual internal rate of return.

• IRR = 11.65%, better than the 10% we hoped for!

Review Problem 4

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.

• The backup for the calculations are on the website in an Excel Format entitled “Financial Planning with Time Value of Money.”

Other Interesting Computations with Financial Calculators

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.

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.

It is important to remember that interest is paid first, then principal.

Monthly Payment $1,028.61

Less interest 1,000.00

Amount applied to principal. $28.61

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.

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 shownon the following page.

Happy Banker

Amortization TablePayments in First 12 Months

Year MonthBeginning

BalancePaymen

t Principa

l Interest

Ending Balance

2007 Jan $100,000.00 $1,028.6

1 $28.61

$1,000.00

$99,971.39

  Feb $99,971.39 $1,028.6

1 $28.90 $999.71

$99,942.49

  Mar $99,942.49 $1,028.6

1 $29.19 $999.42

$99,913.30

  Apr $99,913.30 $1,028.6

1 $29.48 $999.13

$99,883.82

  May $99,883.82 $1,028.6

1 $29.77 $998.84

$99,854.05

  Jun $99,854.05 $1,028.6

1 $30.07 $998.54

$99,823.98

  Jul $99,823.98 $1,028.6

1 $30.37 $998.24

$99,793.61

  Aug $99,793.61 $1,028.6

1 $30.67 $997.94

$99,762.94

  Sep $99,762.94 $1,028.6

1 $30.98 $997.63

$99,731.96

  Oct $99,731.96 $1,028.6

1 $31.29 $997.32

$99,700.67

  Nov $99,700.67 $1,028.6

1 $31.60 $997.01

$99,669.07

  Dec $99,669.07 $1,028.6

1 $31.92 $996.69

$99,637.15

What if when we pay the first payment of $1,028.61, we enclose an additional amountfor $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 TablePayments in First 12 Months

Year MonthBeginning

BalancePaymen

t Principa

l Interest

Ending Balance

2007 Jan $100,000.00 $1,028.6

1 $28.61

$1,000.00

$99,971.39

  Feb $99,971.39 $1,028.6

1 $28.90 $999.71

$99,942.49

  Mar $99,942.49 $1,028.6

1 $29.19 $999.42

$99,913.30

  Apr $99,913.30 $1,028.6

1 $29.48 $999.13

$99,883.82

  May $99,883.82 $1,028.6

1 $29.77 $998.84

$99,854.05

  Jun $99,854.05 $1,028.6

1 $30.07 $998.54

$99,823.98

  Jul $99,823.98 $1,028.6

1 $30.37 $998.24

$99,793.61

  Aug $99,793.61 $1,028.6

1 $30.67 $997.94

$99,762.94

  Sep $99,762.94 $1,028.6

1 $30.98 $997.63

$99,731.96

  Oct $99,731.96 $1,028.6

1 $31.29 $997.32

$99,700.67

  Nov $99,700.67 $1,028.6

1 $31.60 $997.01

$99,669.07

  Dec $99,669.07 $1,028.6

1 $31.92 $996.69

$99,637.15

What if we pay the sum of the remaining principal payments for the year (red)? Thistotals to $334.24. Just include that with the first check of $1,028.61 and you will skip sothat 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 inhouses.

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 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 $24,101.45 $22,817.40 $27,408.66

Present value of investments (21,000.00) (21,000.00) (21,000.00)

Net present values of investments $3,101.45 $1,817.40 $6,408.66

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?