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第四章 資本投資之評估

Evaluating Capital Investment (Capital Budgeting)

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Capital investment → output (revenue) ↑/ cost ↓

Steps in Investment Analysis：(1) identifying potentially profitable investment alternatives

(2) collecting relevant data on capital outlays costs, and returns

(3) using an appropriate method to analyze the data

(4) deciding whether to accept or reject the investment or selecting

the top ranking amons mutually exclusive projects.

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Alternative Measures of Investment Worth ：

A B

0 -10.0 -10.0

1 2.5 3.0

2 2.5 2.5

3 2.5 2.5

4 2.5 2.0

5 2.5 2.5

5 2.0 3.0

eg:

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Alternative Measures of Investment Worth （續） ：

(1) Payback Method P=V/I V: initial investment I: annual cash return

(2) Simple rate of return

where

It does not recognize the time value of money

09.010

6.15.2

Ar 11.0

10

4.15.2

Br

life useful

valuesalvage-investment/ nSOD

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Alternative Measures of Investment Worth （續） ：

(3) Discounted Cash Flow Measures

A. Net Present Value (NPV) method

B. Internal Rate of Return (IRR) method

= ” yield ”

accept NPV 0≧ IRR min. acceptable rate of return≧

NPV=PV of cash inflows – initial cash outflow

i = 10% NPVA = 719

NPVB = 1452

profitability index = outflow cash initial

inflow cash of PV

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IRR： the discount rate that gives an NPV equal to zero

A i 12% 13%

NPV 147 -121

IRR =12+ %55.12121147

147

B i 15% 16%

NPV 22 -231

IRR =15+ %1.1523122

22

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NPV vs. IRR

discount rate (i)

NPV

0

-

+

12.5515.1

B

A

10

NPV vs. IRR

i

NPV

0

15.1

16.6

B

B

12.55

C

C

NPV↓, as discount rate↑

when IRR method is applied, the cash flow are assumed to be reinvested at the IRR rate. The conflicting rankings result from the difference between the two methods concerning the rate at which cash inflows are assumed to be reinvested. (p.78)

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Comparing investments with unequal lives : (p.79)

(1) longest useful life

(2) lowest common denominator of their useful lives NPV$ annuity

(3) NPV$ => annuity

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Handling Risk and Uncertainty

A. adjust discount rate: little risk with less discount rate

B. Probability Approach

C.Certainty Equivalent Approach

Cash flow (Ei) × certainty equivalent coefficients (Ci)

= certainty equivalents

r: risk-free discount rate

iEiPEmean

iEiEiPVVariance 22

2VSD =VE

VCVVariationoftCoefficien )(

i ir

iEiCCNPV

1

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Adjust Cash Flows for Inflation

use real rate instead of nominal rate as the discount rate

Estimating Cost of Capital

Kt = WdKd + WeKe

Kd = i (1-t) + Re

Ke = E / P + G

internal credit rationing premium for financial risk and credit reserves loss

weight cost of capital cost of debt capital

cost of equity capital

interest rate tax rate

earning per share net amount of capital raised per share

expected growth rate