1 第三章 資本在時間上的配置 Capital Allocation over Time

2 分配原則： ( Principles of Allocation )

3 Effect of the rate of return (i) ：

4 Time Value of Money ： $100 today or a year later ？ today is better ∵ uncertainty alternative uses, inflation

5 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)

6 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 → ∞ annuity FV = PV ． Table 3 or FV = PV / Table 4 PV = FV / Table 3 or PV = FV ． Table 4

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13 Application of the Time Value of Money Bond valuation : (p.63) Valuation of farm real estate: (p.65) end of year ……… $100 $100 ….....… $100 $1,200 Table 4 Table 2 Table 2 $100 eg ： Bond face value: $1000, interest rate: 5%, time value of money: 7%, mature in 10 yrs. $1000 × 5% × ＋ $1000 × ＝ $ （ Table 4 ） （ Table 2 ）