Managerial Economics (chapter 14)

Long-run investment decisions: capital Budgeting Instructor: Maharouf Oyolola

Introduction • One of the most important decisions managers must make concerns investment. • The investment decision involves how much to invest, what capital should be purchased, how to finance the investment and so forth.

• We should note that when we speak of investment by a firm, we generally do not mean investment in stocks and bonds. • Rather, investment is simply an addition to the firm’s stock of resources, generally involving the purchase of capital equipment or land.

Capital budgeting • It refers to the process of planning expenditures that give rise to revenues or returns over a number of years. • Capital budgeting is of crucial importance to the firm. • The application of new technological breakthroughs may lead to new and more efficient production techniques, changes in consumer tastes may take a firm’s existing product line obsolete

The capital budgeting process • In this section we discuss how the firm projects the cash flows from an investment project, how it calculates the net present value of and the internal rate of return on the project, and how the two are related.

Project cash flows • One of the most important and difficult aspects of capital budgeting is the estimation of the net cash flow from a project. • A typical project involves making an initial investment and generates a series of net cash flows over the life of the project.

Example • Suppose that a firm estimates that it needs to make an initial investment of $1 million in order to introduce a new product. • The marketing division of the firm expects the life of the product to be five years.

Net Present Value (NPV) • One method of deciding whether or not a firm should accept an investment project is to determine the net present value of the project. • The net present value (NPV) of a project is equal to the present value of the expected stream of net cash flows from the project, discounted at the firm’s cost of capital, minus the initial cost of the project.

Net Present Value (NPV) n

Ri NPV = ∑ − C 0 t t =1 (1 + k ) Ri refers to the estimated net cash flow from the project in each of the n years considered. K is the risk-adjusted discount rate Co is the initial cost of the project

Estimated cash flow from project year 1 Sales less :

2

3

4

5

$1,000,000

$1,100,000

$1,210,000

$1,331,000

$1,464,100

variable costs

500,000

550,000

605,000

665,500

732,050

fixed costs

150,000

150,000

150,000

150,000

150,000

Depreciation

200,000

200,000

200,000

200,000

200,000

$150,000

$200,000

$255,000

$315,500

382,050

60,000

80,000

102,000

126,200

152,820

Profit after tax

$90,000

120,000

153,000

189,300

229,230

plus: Depreciation

200,000

200,000

200,000

200,000

200,000

$290,000

$320,000

$353,000

$389,300

$429,230

Profits before taxes Less: income tax

Net cash flow

Plus:

salvage value of equipment

250,000

Recovery of working capital

100,000

Net cash flow in year 5

$779,230

Example 1 $290,000 $320,000 $353,000 $389,300 $779,230 NPV = + + + + − $1,000,000 1 2 3 4 5 (1 + 0.12) (1 + 0.12) (1 + 0.12) (1 + 0.12) (1 + 0.12) = $1,454,852 − $1,000,000 = $454,852

This project would thus add $454,852 to the value of the firm, and the firm should undertake it.

Example 2 • Hershey Foods is considering an investment in a new “Kiss” wrapping machine. The machine has an initial cost (net investment) of $2.5 million. It is expected to produce cost savings from reduced labor and to generate additional revenues because of its increased reliability and productivity. Over its anticipated economic life of five years, the new “Kiss” wrapping machine is expected to generate the following stream of net cash flows (NCF):

Example 2 Year (t)

Net cash flow (NCF)

1

$600,000

2

800,000

3

800,000

4

600,000

5

250,000 If Hershey requires a return (k) of 15 percent on a project of this type, should it make the investment?

year (t)

present value interest factor at 15 percent (3)

cash flow (2)

Present value (4)= (2) x (3)

0

($2,500,000)

1

($2,500,000)

1

600,000

0.86957

$521,742

2

800,000

0.75614

$604,912

3

800,000

0.65752

$526,016

4

600,000

0.57175

$343,050

5

250,000

0.49718

$124,295

($379,985)

Because this project has a negative net present value, it does not contribute to the goal of maximizing shareholder wealth

Internal Rate of Return (IRR) • Another method of determining whether a firm should accept an investment project is to calculate the internal rate of return on the project. • The IRR on a project is the discount rate that equates the present value of the net cash flow from the project to the initial cost of the project.

The internal rate of return • The following equation is used to find the IRR: n

NCFt = C0 ∑ * t k ) t= 1 (1 + IRR =k * An investment should be accepted if the internal rate of return is greater than or equal to the firm’s required rate of return (cost of capital); if not, the project should be rejected.

Example • The internal rate of return for the Hamilton-Beach is calculated as follows: 5

290,000 = 1,000,000 ∑ t t =1 (1 + r ) 5

1 1,000,000 = = 3.4483 ∑ t 290,000 t =1 (1 + r )

Example • The term

5  1 ∑(1 +r ) t  t =1 

represents the present value of a $1annuity for 5 years discounted at r percent

3.5172 − 3.4483 r = 0.13 + (0.14 − 0.13) 3.5172 − 3.4331 = 0.1382 If Hamilton-Beach requires a rate of return of 12 percent on projects of this type, then the project should return (12 percent).

Summary of the capital budgeting decision criteria Criterion

Project acceptance Decision Rule

Benefits

Weaknesses

Net Present Value (NPV) Internal Rate of Return (IRR)

Accept project if project has a positive or zero NPV; that is, if the present value of net cash flows, evaluated at the firm’s cost of capital, equals or exceeds the net investment required.

Considers the timing of cash flows. Provide an objective, return-based criterion for acceptance or rejection.

Difficult in interpreting the meaning of the NPV computation

Accept project if IRR equals or exceeds the firm’s cost of capital.

Easy to interpret the meaning of IRR. Considers the timing of cash flows. Provides an objective, return-based criterion for acceptance or rejection

Sometimes gives decision that conflicts with NPV. Multiple rates of return problem

Capital rationing and the profitability index • In cases of capital rationing (i.e., when the firm cannot undertake all the projects with positive NPV), the firm should rank projects according to their index of profitability and choose the projects with the highest profitability indexes rather than those with the highest NPVs.

The profitability index (PI) • It is measured by:

∑[R n

PI = t =1

t

/(1 +k ) C0

t

]

Comparison of NPV and PI rankings of projects with unequal costs Project A Present value of net cash flows (PVNCF)

Project B

Project C

Initial cost of project (Co)

$2,600,00 $1,400,00 $1,400,00 0 0 0 2,000,000 1,000,000 1,000,000

NPV

$600,000

$400,000

$400,000

PI

1.3

1.4

1.4

The cost of capital • In this section, we examine how the firm estimates the cost of raising the capital to invest. • The firm can raise investment funds internally (i.e., from undistributed profits) or externally (i.e., by borrowing and from selling stocks). • The cost of using internal funds is the opportunity cost or forgone return on these funds outside the firm. The cost of external funds is the lowest rate of return that lenders and stockholders require to lend to or invest their funds in the firm.

The cost of capital • In this section, we examine how the cost of debt (i.e., the cost of raising capital by borrowing) and the cost of equity capital (i.e., the cost of raising capital by selling stocks) are determined. • On the other hand, there are at least three methods of estimating the cost of equity capital: the risk-free plus premium, the divided valuation model, and the capital asset pricing model (CAPM).

The cost of Debt • The cost of debt is the return that lenders require to lend their funds to the firm. Since the interest payments made by the firm on borrowed funds are deductible from the firm’s taxable income. • The after-tax cost of debt capital is: Kd=r(1-t)

The cost of equity capital: the riskfree rate plus premium • The cost of equity capital is the rate of return that stockholders require to invest in the firm. • One method employed to estimate the cost of equity capital (ke) is to use the risk-free (rf) plus a risk premium (rp). That is: ke= rf + rp The risk-free rate is usually taken to be the six-month U.S. Treasury bill rate.

The cost of equity capital: The capital asset pricing model (CAPM)