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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 )

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Effect of the rate of return (i) ：

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Time Value of Money ：$100 today or a year later ？

today is better

∵ uncertainty alternative uses, inflation

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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 (s ． Table 1)

Present Value (PV) Future Value (FV)

….. FV ． Table 2 ….. PV ． Table 1

i: discount rate = (riskless equity return + inflation rate + risk premium)

niFV

PV

1

niPVFV 1

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Mathematics of Compound Interest（續）The present value of a sequence of annual incomes ：

if n →∞ and FV constant (annuity)

if FV constant but n → ∞

n

t ni

nFV

i

FV

i

FV

i

FV

ni

tFVPV

1 1.....

31

321

21

1

1

i

FVPV

4 Table

11

1

11

FV

i

niFV

nii

niFVPV

annuity

FV = PV ． Table 3 or FV = PV / Table 4

PV = FV / Table 3 or PV = FV ． Table 4

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8

9

10

11

12

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Application of the Time Value of Money

• Bond valuation : (p.63)

• Valuation of farm real estate: (p.65) end of year 0 1 2 3 4 5 ........………. 20 0 0 0 0 $100 $100 ….....….......$100 $1,200 Table 4 Table 2 Table 2

$100

n

t ti

tI

ni

nPPV1 11

%8,20200,1$%8,3%8,17 yrPVyrPVyrPV

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 ）