第三章 資本在時間上的配置
Capital Allocation over Time
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分配原則：
( Principles of Allocation )
2
Effect of the rate of return (i)：
3
Time Value of Money：
$100 today or a year later ？
today is better
∵ uncertainty
alternative uses,
inflation
4
Mathematics of Compound Interest
Simple interest：
S = s．(1 + i．n) i: interest
Compound interest：interest is paid more than once
(interests add to principal)
S = s．(1 + i )n
Present Value (PV)
PV 
FV
1  i n ….. FV．Table 2
(s ．Table 1)
Future Value (FV)
FV  PV  1  i  ….. PV．Table 1
n
i: discount rate = (riskless equity return + inflation rate + risk premium)
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Mathematics of Compound Interest（續）
The present value of a sequence of annual incomes：
n FVt
FV3
FVn
FV1
FV2
PV  



 .....
1  i  1  i 2 1  i 3
1  i n
t 1 1  i n
if n →∞ and FV constant (annuity)
PV 
FV
i
if FV constant but n → ∞
PV

1  i n  1
1  1  i n
 FV 
 FV 
n
i
i 1  i 
FV = PV．Table 3
PV = FV / Table 3
or
or
 FV  Table 4
annuity
FV = PV / Table 4
PV = FV．Table 4
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Application of the Time Value of Money
• Bond valuation : (p.63)
n
It
PV 
 
1  i n t 1 1  i t
Pn
eg：Bond face value: $1000 , interest rate: 5%, time
value of money: 7%, mature in 10 yrs.
$1000 × 5% × 7.0236＋$1000 × 0.5083＝$859.48
（Table 4）
（Table 2）
• Valuation of farm real estate: (p.65)
end of year 0
0
1
0
2
0
Table 4 Table 2

3 4 5
........………. 20
0 $100 $100 ….....….......$100
$1,200
Table 2

$100  PV17yr,8%  PV3yr,8%  $1,200 PV20yr,8%
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