Capital Allocation over Time 1 Principles of Allocation

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

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) …. . FV．Table 2 (s ．Table 1) Future Value (FV) …. . PV．Table 1 i: discount rate = (riskless equity return + inflation rate + risk premium) 5

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 PV = FV / Table 3 or or FV = PV / Table 4 PV = FV．Table 4 6

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Application of the Time Value of Money • Bond valuation : (p. 63) 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 Table 4 1 0 2 0 Table 2 3 4 5. . . . ………. 20 0 $100 …. . . $100 $1, 200 Table 2 $100 13