Chapter 11Advanced Topics in Capital Budgeting

Learning Objectives

• Estimate project cash flows

• Describe the difference between independent and mutually exclusive projects

• Compare projects with different lives using the equivalent annual series technique

Estimating Project Cash Flows

Guidelines

• Add back depreciation to net income.

• Ignore interest expense.

• All project cash flows must be incremental.

• Ignore allocated costs and sunk costs.

• Include opportunity costs.

• Net working capital.

Add back depreciation

• Depreciation is a non-cash expense

• Tax deductible

• Add the depreciation back to the net income

cash flow = net income + depreciation expense

• Commonly referred to as free cash flow

Ignore interest expense

• A project’s value (desirability) is determined by the cash flows that generates, not by how the project is financed.

• In determining a project’s cash flows, we ignore it’s financing cost, i.e., the interest expense.

All project cash flows must be incremental

• To evaluate a project, we look at the cash flows which it contributes towards the firm’s existing cash flows. In other words, we look at project’s incremental cash flows.

• How to determine incremental cash flows?

1. Look at the firm’s cash flows without the project.

2. Look at the firm’s cash flows with the project.

3.The difference is the incremental cash flows.

Ignore allocated costs and sunk costs

• Allocated costs: rent, supervisory salaries, administrative costs, and various overhead expenses

These costs are not incremental. They don’t change even if the project is undertaken. Thus, they should not be considered in estimating the project’s incremental cash flows.

• Sunk (irrecoverable) costs: costs which cannot be recovered regardless of whether the firm undertakes the project.

Examples: R&D expenses, consultant fees.

Include opportunity costs

• Suppose the project requires the use of some asset owned by the firm.

• If the asset is not used by the project, the firm can sell the asset for $X. This $X is the opportunity cost of the asset. Such a cost should be included in the project’s cost.

• An asset’s opportunity cost is the money that the firm can receive if the asset is put to the next best use. The ‘next best’ use may be to sell the asset.

Net working capital

• Very often, a project will require an initial increase in net working capital. This increase in net working capital must be added to the project’s costs.

• Assume that this additional working capital is liquidated (sold for cash) at the end of the project’s life.

• This liquidation is a cash inflow in the last period.

• The opposite pattern is also possible. In other words, if taking on a project reduces the net working capital, then the size of this reduction is subtracted from the project’s initial cost and the last period cash inflow

Capital budgeting example

Problem 11.6: You are given the responsibility of conducting theproject selection analysis in your firm. You have to calculate the NPV of a given project. The appropriate cost of capital is 12 percent and the firm is in the 30 percent tax bracket. You are provided the following pieces of information regarding the project:

Calculate initial cost

• Initial cost is the sum of:o Market value of land: $1 million (opportunity cost)o Land improvement $100,000o Plant & machinery: $20 milliono Incremental working capital: $1 million

• = 1,000,000 + 100,000 + 20,000,000 + 1,000,000 = $22,100,000

Calculate the annual incremental cash flow: Step one

Calculate the annual depreciation expense, for this project, fixed assets refer to $20million plant & machinery. Therefore, Depreciation = (20,000,000 – 3,000,000)/10 = $1,700,000

Calculate incremental salesIncremental sales = 0.8 x 15,000,000 = $12,000,000

Calculate the annual incremental cash flow: Step two

Draw up the incremental income statement

Incremental sales 12,000,000

Less Incremental variable cost 9,000,000

Less Incremental managerial salaries 200,000

Less Incremental depreciation 1,700,000

Equals Incremental taxable income 1,100,000

Less Incremental tax @30% 330,000

Equals Incremental net income 770,000

Add back depreciation 1,700,000

Incremental cash flow $2,470,000

Consider other cash flows at end of project

• At the end of project’s life (t=10), company Recovers $1 m additional working capital (item 9) Receives $3 m salvage value from plant & machinery (item 8)

• Additional cash flows at end of project = 1,000,000 + 3,000,000 = $4,000,000

Bring all the cash flows together

• CF0 (initial cost) = $22,100,000

• Annual incremental after-tax cash flow (Year 1 through Year 10) = $2,470,000

• Additional cash flow in Year 10 = $4,000,000

• Finally, we compute the NPV using a discount rate of 12 percent

• NPV = -$6,856,056.17

• Decision: reject the project.

Mutually Exclusive Projects

• Projects are mutually exclusive if accepting one implies that the other projects will be foregone.

• When projects are mutually exclusive and have equal lives, you have to

o Rank the projects based on their NPVso Choose the best project, provided the project’s NPV is

positive• With mutually exclusive projects that have equal lives,

choosing the project with the highest NPV is always correct.

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Mutually Exclusive Projects Example

Consider the following two mutually exclusive projects that have equal lives, for a firm using a discount rate of 10%, which project(s) should we accept?

Project NPV IRR PIA $100,000 10.2% 1.04B $1 11% 1.11C $70,000 23% 1.32D $24,000 13% 1.44

Comparing projects with unequal lives: Equivalent annual series (EAS)

• When projects are mutually exclusive but have unequal lives

o We construct the equivalent annual series (EAS) of each projecto We choose the project with the highest EAS

• A project’s EAS is the payment on an annuity whose life is the same as that of the project and whose present value, using the discount rate of the project, is equal to the project’s NPV.

EAS example

Consider Projects J & K, with the following cash flows. The

discount rate is 10%.

Project C0 C1 C2 C3 C4

J -12000 6000 6000 6000

K -18000 7000 7000 7000 7000

EAS for Project J

• Compute Project J’s NPV Verify that NPV(J) = $2,921.11

• Find the payment on the 3-year (life of project J) annuity whose PV is equal to $2,921.11.

N=3, I/Y=10, PV=-2921.11, FV=0, Then CPT, PMT.

• PMT = 1,174.62, which is Project J’s EAS.

• So, finding EAS is nothing more than finding the payment of an annuity.

EAS for Project K

• Verify that Project K’s NPV= $4,189.06• Find the payment on the 4-year (life of project K) annuity

whose PV is equal to $ 4,189.06. N=4, I/Y=10, PV=- 4,189.06, FV=0, Then CPT, PMT. PMT = 1,321.53, which is Project K’s EAS.

• Recall that Project J’s EAS=1174.62 • So, choose Project K since it has the higher EAS.

Congratulations!

FI 3300: Corporate Finance

Accounting Review (2)

Statement of Cash Flows (3)

Financial statement Analysis (4)

Strategic Financial Management (5)

Firm’s Financial Statements Valuation

Time Value of Money (6, 7)

Financial Securities & Markets (8)

Valuation of Bond & Stock (9)

Capital Budgeting Basics (10)

Capital Budgeting Advanced (11)