Financial Management

재무 관리

Valuation of Future Cash Flows

• Future Value (FV)

  $\mathrm{FV} = \mathrm{PV} (1 + \mathrm{r})^\mathrm{t}$

• Present Value (PV)

• return (r)

  $\mathrm{r} = (\frac{\mathrm{FV}}{\mathrm{PV}})^{\frac{1}{t}} - 1$

• Number of Periods (t)

• Simple interests

  Interests are earned only on the original principal
  단리
  $\mathrm{FV} = \mathrm{PV} + \mathrm{PV} \times \mathrm{r}^\mathrm{t}$

• Compound interests

  Interests are earned on the principal and on the interests received
  복리
  $\mathrm{FV} = \mathrm{PV} \times (1 + \mathrm{r})^\mathrm{t}$

• Annuity

  연금
  1년 뒤 부터 t년까지 C 를 받는 것.

  $\mathrm{PV} = \mathrm{C}\left[\frac{1 - \frac{1}{(1 + \mathrm{r})^t}}{r}\right]$
  $\mathrm{FV} = \mathrm{C}\left[\frac{(1 + \mathrm{r})^t - 1}{r}\right]$

  • Annuity due

    지금 당장부터 t - 1년까지 C 를 받는 것.

    $\mathrm{PV} = \mathrm{C}\left[\frac{1 - \frac{1}{(1 + \mathrm{r})^t}}{r}\right] \times (1 + \mathrm{r})$
    $\mathrm{FV} = \mathrm{C}\left[\frac{(1 + \mathrm{r})^t - 1}{r}\right] \times (1 + \mathrm{r})$

• Annual Percentage Rate (APR)

  period rate times the number of periods per year
  1년에 몇 번 주기가 도는지 * 해당 주기 마다의 이자율
  period rate = APR / number of periods per year

• Effective Annual Rate (EAR)

  actual rate considering compounding the interests that occurs during the year.

  $\mathrm{EAR} = \left[1 + \frac{\mathrm{APR}}{\mathrm{m}}\right]^{\mathrm{m}} - 1$
  m = number of compounds per year

  투자 결정자는 EAR을 기반으로 투자를 결정해야 한다. (시험엔 안나온다네?)