第四章 資本投資之評估
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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
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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
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