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Principles of Capital Allocation over Time: The Impact of Time Value of Money

Explore the principles of capital allocation over time, focusing on the effect of the rate of return and the time value of money. Learn about compound and simple interest, present and future value calculations, annuity, and applications in bond and real estate valuation.

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Principles of Capital Allocation over Time: The Impact of Time Value of Money

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

  7. 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 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）

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