Chapter 10

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Entrepreneurial Finance, 4th EditionBy Adelman and Marks

PRENTICE HALL©2007 by Pearson Education, Inc.Upper Saddle River, NJ 07458

10-1

Capital Budgeting

Chapter 10

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10-2

Learning Objectives

Understand the purpose and need for capital budgeting. Explain the impact that government regulations may have

on a company’s capital budgeting decision. List and explain the steps required in making a capital

budgeting decision. Distinguish between startup costs, working capital

commitment costs, and tax factor costs and the role each plays in the capital budgeting decision.

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10-3

Compare the relationship between increased efficiency benefits and tax factor benefits and understand their effect on a company’s cash flow.

Understand payback, net present value, profitability index, internal rate of return, and accounting rate of return as techniques of capital budgeting.

Compute the payback of a capital budgeting project. Using time value of money, compute the net present value

of a capital budgeting project.

Learning Objectives (continued)

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10-4

Given a company’s investment costs, calculate the weighted average cost of capital.

Calculate and compare a company’s internal rate of return to its accounting rate of return.

Determine how a company’s capital budgeting decision makes a project mutually exclusive.

Determine how a company’s capital budgeting decision is influenced by capital rationing.

Understand the importance of following up, controlling, and taking corrective action after a capital budgeting decision has been made.

Learning Objectives (continued)

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10-5

Capital Budgeting

Capital budgeting is the method we use to justify the acquisition of capital goods (those items that have a useful life in excess of one year).

Assumptions:› Long-term assets generate increased cash flow by improving

efficiency and effectiveness.› Rates of return on investments and current inflation rate will

remain the same.

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10-6

Factors Affecting Capital Budgeting

Changes in government regulations Research and development Changes in business strategy

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10-7

Steps in Capital Budgeting

Formulate a proposal Evaluate the data Make a decision Follow up Take corrective action

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10-8

Formulating a Proposal Costs in capital budgeting

› Startup costs› Working capital commitment cost› Tax factor costs

Benefits in capital budgeting› Increased efficiency› Reducing taxable income› Tax factor benefits› Depreciation

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10-9

Table 10-1 Annual Interest Payments and Tax Savings for a Five-Year LoanAmount

Borrowed Annual Interest

RateNumber of

MonthsMonthly Payment

Income Tax Rate

100,000.00$ 11.00% 60 $2,174.24 27.00%

1 26,090.91$ 15,875.48$ 10,215.43$ $2,758.172 26,090.91 17,712.57$ 8,378.34 2,262.153 26,090.91 19,762.24$ 6,328.67 1,708.744 26,090.91 22,049.11$ 4,041.80 1,091.295 26,090.91 24,600.61$ 1,490.30 402.38

Totals 130,454.54$ 100,000.00$ $30,454.54 $8,222.73Note: Rounding may cause what appears to be an error of a penny in some columns.

Principal Payment

Interest Payment Tax SavingsYear

Annual Loan Payment

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10-10

Evaluating the Data-techniques of Capital Budgeting

There are six methods that are used to evaluate the capital budgeting proposal.1) Payback

2) Net present value (NPV)

3) Profitability index (PI)

4) Internal rate of return (IRR)

5) Accounting rate of return (ARR, also known as average rate of return)

6) Lowest total cost (LTC)

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10-11

Payback

Payback deals with the number of years that it will take a business to get back the money that it has invested in a project or asset.

WhereC = Cost of the project

ATB = Annual after-tax benefit of the project

ATB

CPayback =

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10-12

Net Present Value, or NPV

The net present value method of capital budgeting uses the time value of money by discounting future benefits and costs back to the present. › It applies the present-value-of-a-stream-of-payments technique for

even cash flows and the present-value-of-a-future-lump-sum technique for unequal yearly cash flows.

› The calculations are made using an interest rate that matches our cost of capital for the investment. This rate is used because the company must pay this cost on an annual basis to obtain the financial capital necessary to make the investment.

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10-13

There are two interest rates that we must consider: 1) The interest rate charged by the supplier of funds, or the lender

2) The interest rate that the borrower could receive by investing in some other enterprise (the latter is the borrower’s opportunity cost)

Net Present Value, or NPV (continued)

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10-14

There are three components that determine the lenders’ interest rate:1) The real rate of return (the return that will be received after

factoring out inflation)

2) The inflation premium (the expected average inflation rate for the term of the investment)

3) The risk premium (the rate added to the interest rate to take into account the risk of the investment)


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10-15

Weighted average cost of capital (WACC) is obtained by multiplying the cost of debt (rate that the lender charges) by its proportion of total funds raised, and multiplying the cost of equity (opportunity cost to the owner) by its proportion of total funds raised.


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10-16

WACC Example: You are buying a piece of equipment for $100,000. You will put $30,000 down and finance the remaining $70,000. Your opportunity cost is 4.00% for the $30,000 and 8.75% for the $70,000 loan.


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10-17


Calculations of WACC:

70.0000,100$

000,70$

Paidamount Total

FinancedAmount ProportionDebt

30.0000,100$

000,30$

Paidamount Total

equity sOwner' ProportionEquity

$100,000 $70,000 $30,000

paidamount Total financedamount equity sOwner'

===

===

=+=+

7.33%or 0.0733,

0.06130.0120

.70)(0.0875)(0 0)(0.04)(0.3

)proportion cost)(Debt(Debt )proportionty cost)(Equi(Equity WACC

=

+=

+=

+=

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10-18

NPV considers all of the future cash flows over the asset’s entire economic life.

Where› NPV = Net present value of the investment› PVB = Present value of the benefit as calculated in the following

example› PVC = Present value of the cost of the investment as calculated in

the following example


PVCPVBNPV −=

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10-19

Making the decision using NPV:› If NPV is positive using the WACC, the investment should be

made.› If NPV is negative using the WACC, the investment should not

be made.

NPV has two primary advantages:1) Future cash flows that will be paid and received can be

discounted back to the present so that a decision on the investment can be made now.

2) Interest rates are determined by and based on the weighted average cost of capital that takes risk into consideration.


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10-20


Table 10-2 NPV of an Automobile Purchase

Present Present

BENEFITS PVAF at Value PVAF at ValueItem 10.00% at 10% 14.00% at 14%

Cash flow $10,000.00 per year 3.7908 $37,908.00 3.4331 $34,331.00Salvage value $4,000.00 end of 5 years 0.6209 2,483.60 0.5194 2,077.60

PVB $40,391.60 $36,408.60COSTS

Purchase price ($20,000.00) Present Value ($20,000.00) ($20,000.00)Insurance ($100.00) per month 47.4576 (4,745.76) 43.4784 (4,347.84)

Gas and maintenance ($300.00) per month 47.4576 (14,237.28) 43.4784 (13,043.52)PVC ($38,983.04) ($37,391.36)

NPV=PVB-PVC $1,408.56 ($982.76)

Cash Flow per time period

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10-21

Profitability Index, or PI

The profitability index is the ratio of the present value of the benefits to the present value of the costs. The formula for PI is:

PVC

PVBPI =

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10-22

Internal Rate of Return, or IRR

The internal rate of return is the actual rate of return of an investment and uses the time value of money in its calculation. The IRR is the interest rate that matches the present value of the cost of our investment directly with the present value of the future benefits received.

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10-23

The future benefits can be in the form of a stream of payments over a period of time or a lump sum (salvage value) received.

The IRR is the interest rate that occurs when the NPV is zero. If the NPV is zero, then by definition, the present value of the costs must equal the present value of the benefits.

The IRR is an interest rate that corresponds to a present value annuity factor that is found by dividing the present value of the cost by the period’s cash flow.

Internal Rate of Return, or IRR (continued)

flow cash sPeriod'

investment the of cost the of valuePresent factorIRR =

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10-24


Table 10-3, Five-Year Projected Cash FlowInitial Investment: 66,000.00$

Year Projected Cash Flow

1 21,000.00$ 2 29,000.00 3 36,000.00 4 16,000.00 5 8,000.00

Table 10-4, Present Value of an Unequal Stream of Projected Cash Benefits

Projected

PVF Factor for Interest of

Present Value in

PVF Factor for Interest of

Present Value in

Year Cash Flow 20.00% Dollars 25.00% Dollars1 21,000.00$ 0.8333 17,499.30$ 0.8000 16,800.00$ 2 29,000.00 0.6944 20,137.60 0.6400 18,560.00 3 36,000.00 0.5787 20,833.20 0.5120 18,432.00 4 16,000.00 0.4823 7,716.80 0.4096 6,553.60 5 8,000.00 0.4019 3,215.20 0.3277 2,621.60

Total PV 69,402.10$ 62,967.20$

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10-25


This is interpolation based on the data in the previous tables:

90.434,6$10.402,3$

00.000,66$

10.402,69$20?

5

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡⎥⎦

⎤⎢⎣

⎡−−−−−−

62,967.20$---25

x

( )( )

%64.22%6435.2%20?

6435.290.434,6$

50.010,17$

)90.434,6($

)10.402,3)($5(?

90.434,6$

10.402,3$

5

?

20.967,62$10.402,69$

00.000,66$10.402,69$

2520

?

25%PV$)-(20%PV$ distance Total

x%PV$)-(20%PFV$ distance Partial?

1

21

≈+=+=

===

=

−

−=

−

=−

iIRR

ii

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10-26

Accounting Rate of Return, or ARR

The accounting rate of return is the average annual income from a project divided by the average cost of the project.

The formula is:

› Example: Invest $10,000. Receive royalties of $3,000 per year. Using ARR, $3,000 divided by $10,000 is a 30% accounting rate of return.

⎟⎟⎠

⎞⎜⎜⎝

⎛=

life its over investment of cost Average

income annual AverageARR

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10-27

Lowest Total Cost

The lowest total cost (LTC) method of capital budgeting is similar to the net present value (NPV) method because it uses the time value of money by discounting future costs and benefits back to the present.

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10-28

The method used to determine the lowest present value of total cost is as follows:› Include all costs associated with two or more competing

investments. › Calculate the present value of these costs. Add the present value of

any benefits (salvage value) that may be obtained on the investment.

› Select the investment with the lowest overall total cost.

Lowest Total Cost (continued)

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10-29

Lowest Total Cost (continued)

Table 10-5 Lowest Total Cost (LTC) of a Truck Purchase

Category QuantityFuel cost per gallon 1.50$ Annual mileage 25,000WACC 12.00%Ownership in years 6PVAF Table B-5 or formula 4.1114PVF Table B-2 or formula 0.5066

Category (Costs) and Benefits PV(Costs) and

Benefits PV(Costs) and

BenefitsMileage per gallon 16 13 15Purchase price (26,955.00)$ (26,955.00)$ (25,695.00)$ (25,695.00)$ (30,556.00)$ Annual fuel costs (2,343.75) (9,636.11) (2,884.62) (11,859.83) (2,500.00) Annual insurance cost (1,347.40) (5,539.71) (1,532.44) (6,300.49) (1,358.52) Salvage value 10,800.00 5,471.62 10,800.00 5,471.62 12,250.00 Total cost for 6 years (36,659.20)$ (38,383.70)$

Truck Model A Truck Model B Truck Model C

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10-30

Making the Decision The methods previously discussed are often used in

making a capital budgeting decision. However, two other scenarios exist.› Mutually Exclusive: Some investments are mutually exclusive

because one is chosen and the others are automatically sacrificed or excluded.

› Capital Rationing: Capital rationing is a constraint placed on the amount of funds that can be invested in a given time period.

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10-31

Capital Cumulative NetBusiness Investment Investment PresentLocation Cost Cost Value

1 50,000$ 50,000$ 125,000$ 2 46,000 96,000 121,000 3 52,000 148,000 119,000 4 47,500 195,500 116,000 5 67,300 262,800 115,000 6 48,000 310,800 113,000 7 63,000 373,800 112,500 8 48,700 422,500 111,000 9 54,200 476,700 110,250 10 62,500 539,200 (15,000) 11 48,500 587,700 (17,000) 12 65,000 652,700 (25,000)

Table 10-6 Capital Budgeting Choices

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10-32

Following Up› Following up consists of monitoring and controlling our cash

flows. › A post-audit requires the owner or manager to establish

procedures that will determine how well the outcome of the decision correlates with the proposal.

› Controlling, as we have said before, is a three-step process: (1) establish standards for measuring the project, (2) measure actual performance against the standards established, and (3) take corrective action if required.

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10-33

Table Solutions to Problems

The following slides contain the Excel spreadsheets for problems that require solutions using tables.

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10-34

Answer to problem 6a Cost of

capital = 10.00%

Year Amount PV Factor Present Value1 21,000 0.9091 $19,090.912 29,000 0.8264 23,966.94 3 36,000 0.7513 27,047.33 4 16,000 0.6830 10,928.22 5 8,000 0.6209 4,967.37

$86,000.77

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10-35

Answer to problem 6b Cost of

capital = 20.00% Cost of

capital = 25.00%

Year Amount PV FactorPresent Value PV Factor

Present Value

1 21,000 0.8333 $17,500.00 0.8000 $16,800.002 29,000 0.6944 20,138.89 0.6400 18,560.00 3 36,000 0.5787 20,833.33 0.5120 18,432.00 4 16,000 0.4823 7,716.05 0.4096 6,553.60 5 8,000 0.4019 3,215.02 0.3277 2,621.44

$69,403.29 $62,967.04

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10-36

Answer to problem 8b Cost of Capital= 8.00%

Item Cost PV Factor Present

Value

Install Cable 200.00$ 1 200.00$ Computer 5,100.00 1 5,100.00 Cable Usage Fee 50.00 40.9619 2,048.10

7,348.10$

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10-37

Answer to question 9

Item Freezer A PV Factor Present Value Freezer B Present Value Investment required ($29,000) 1.0000 (29,000.00)$ ($25,000) (25,000.00)$ Annual electrical bill (3,000) 7.1390 (21,417.00) (4,000) (28,556.00) Salvage value 6,000 0.4289 2,573.30 5,000 2,144.41

(47,843.70)$ (51,411.59)$ Project life in years 11 11The LJB Company cost of capital is 8.00%

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10-38

Solution to problem 12c

Item Cost Time Period PV Factor PV of CostsFAX 500.00$ Now 1 500.00$ Installation 300.00 Now 1 300.00 Van down payment 4,000.00 Now 1 4,000.00 FAX service 60.00 per month 49.31844 2,959.11 Driver 600.00 per month 49.31844 29,591.06 Van maintenance 300.00 per month 49.31844 14,795.53 Van payment 305.62 per month 49.31844 15,072.70

Total monthly 1,265.62$ PV of total costs 67,218.40$

Note: 5-year expected lifetime 12 months per year = 60 monthly payments. Use ordinary annuity as we assume payments are made at the end of the month.

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