Opportunity Cost of Capital and Capital

Budgeting

Chapter Three

Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

Opportunity Cost of CapitalOpportunity cost of capital: benefits of investing capital in a bank account that is forgone when that capital is invested in some other alternative.

Importance for decision making: when expected cash flows occur in different time periods.

Capital budgeting: analysis of investment alternatives involving cash flows received or paid over time.

Capital budgeting is used for decisions about replacing equipment, lease or buy, and plant acquisitions.

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Time Value of MoneyA dollar today is worth more than a dollar tomorrow, because you could invest the dollar today and have your dollar plus interest tomorrow.

Value at endAlternative of one yearA. Invest $1,000 in bank account earning

5 percent per year $1,050

B. Invest $1,000 in project returning $1,000

in one year $1,000

Alternative B forgoes the $50 of interest that could have been earned from the bank account. The opportunity cost of selecting alternative B is $1,050.

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Present Value Concept

Since investment decisions are being made now at beginning of the investment period, all future cash flows must be converted to their equivalent dollars now.

Beginning-of-year dollars (1 Interest rate) = End-of-year dollars

Beginning-of-year dollars = End-of-year dollars(1 Interest rate)

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Interest Rate Fundamentals

FV = Future ValuePV = Present Valuer = Interest rate per period (usually per

year) n = Periods from now (usually years)

Future Value of a single flow: FV = PV (1 + r)n

Present Value of a single flow: PV = FV(1 + r)n

Discount factor = 1 (1 + r)n

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Interest Rate Fundamentals

Present value of a perpetuity (a stream of equal periodic payments for infinite periods)PV = FV r

Present value of an annuity (a stream of equal periodic payments for a fixed number of years)PV = (FV r) {1 – [1 (1 + r)n]}

Multiple cash flows per year - see text.

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NPV Basics1.Identify after-tax cash flows for each period2.Determine discount rate3.Multiply by appropriate present-value factor

(single or annuity) for each cash flow. PV factor is 1.0 for cash invested now

4.Sum of the present values of all cash flows = net present value (NPV)

5. If NPV 0, then accept project6. If NPV < 0, then reject project

NPV is also known as discounted cash flow (DCF).

See examples.

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Some Factors are Difficult to Quantify, but Important to Consider Consider the example of Sue Koerner’s

considering returning to school to get an MBA degree.

How would you account for the additional utility Sue would receive from the prestige of earning an advanced degree?

Could you apply the concept of an indifference point?

What other approaches might be helpful?

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Capital Budgeting - Warnings 1.Discount after-tax cash flows, not accounting earnings

Cash can be invested and earn interest. Accounting earnings include accruals that estimate future cash flows.

2. Include working capital requirementsConsider cash needed for additional inventory and accounts receivable.

3. Include opportunity costs but not sunk costsSunk costs are not relevant to decisions about future alternatives.

4.Exclude financing costsThe firm’s opportunity cost of capital is included in the discount rate.

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Adjustment for Risk

Discount risky projects at a higher discount rate than safe projects= Risk-free rate of interest on government bonds+ Risk premium associated with project i= Risk-adjusted discount rate for project i

(Determining the appropriate discount rate is covered in a corporate finance course. In most problems in the managerial accounting course, the discount rate is given.)

Use expected cash flows rather than highest or lowest cash flow that could occurExample: If cash flow could be $100 or $200 with equal probability, then expected cash flow is $150.

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Adjustment for InflationIf inflation exists in the economy, then the discount rate should be adjusted for inflation.

rnominal = nominal interest rate with inflation i = inflation raterreal = real interest rate if no inflation =

riskless rate + risk premium

(1 + rnominal) = (1 + rreal) (1 + i )

Solving: rnominal = rreal + i + (rreal i )

1.Restate future cash flows into nominal dollars (after inflation)

2.Discount nominal cash flows with nominal interest rate

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After-Tax Cash Flow(ATCF) - Concept

Determine cash flows after taxes

On the firm’s income tax return, they cannot fully deduct the cost of a capital investment in the year purchased. Instead firms depreciate the investment over several years at the rate allowed by the tax law.

Time Cash flowBeginning of project Cash to acquire assets

Future years Depreciation deduction on tax return reduces future tax payments

(depreciation tax shield)

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After Tax Cash Flow (ATCF) - Definitions

t = Tax rate (tax refund rate if negative income)R = Revenue in one year (assume all cash)E = All cash expenses in one year

(excludes depreciation)D = Depreciation allowed in one year on income tax return

Tax expense for one year TAX = (R - E - D) t

After-tax cash flow for yearATCF = R - E - Tax

= R - E - (R - E - D) t = (R - E)(1 - t) + Dt 3-13

ATCF - Equivalent Methods1. Separate tax computation

ATCF = (Cash flow before tax) - TAX = (R - E) - (R - E - D) t

2. Depreciation tax shieldATCF = (After-tax cash flow without depreciation) + Depreciation tax shield

= (R - E) (1 - t) + D t

3. Financial accounting income after tax and add back non-cash expensesATCF = (Accounting income after tax) + (Non-cash expenses)

= (R - E - D) (1 - t) + D

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Alternative Capital Budgeting MethodsMethods that consider time value of

money:1. Discounted cash flow (DCF), also known as

net present value (NPV) method 2. Internal rate of return (IRR)

Methods that do not consider time value of money:

3.Payback method4.Accounting rate of return on investment (ROI)

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Alternative: Payback Method

Payback = the time required until cash inflows from a project equal the initial cash investment.Rank projects by payback and accept those with shortest payback period

Advantages of payback method: Simple to explain and compute

Disadvantages of payback method: Ignores time value of money (when cash is

received within payback period) Ignores cash flows beyond end of payback period

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Alternative: Accounting Return (ROI)Average annual accounting income from project Average annual investment in the project= Return on investment (ROI)

Average annual investment = (Initial investment + Salvage value at end) 2

Advantages of ROI method: Simple to explain and compute using financial

statements

Disadvantages of ROI method: Ignores time value of money (when cash is

received within payback period) Accounting income is often not equal to cash

flow

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Alternative: Internal Return (IRR)Internal rate of return (IRR) is the interest rate

that equates the present value of future cash flows to the cash outflows.

By definition: PV = FV (1 + irr)Solution for a single cash flow: irr = (FV PV) - 1

Comparison of IRR and DCF/NPV methods Both consider time value of cash flows IRR indicates relative return on investment DCF/NPV indicates magnitude of investment’s

return IRR can yield multiple rates of return IRR assumes all cash flows reinvested at project’s

constant IRR DCF/NPV discounts all cash flows with specified

discount rate3-18

Capital Budgeting in Practice

See Table 3-11

DCF/NPV has become the most commonly used capital budgeting method for evaluating new and replacement projects in large US corporations.

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