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MNGT4621 Corporate Finance, Final Examination, September 2001

常用公式

Description	Formula
Future value of $P invested today for n periods at a periodic interest rate of r%	$F_{n}=P(1+r)^{n}$
Present value of a $F cashflow received in n periods time if periodic interest rate is r%	$P={\frac {F_{n}}{(1+r)^{n}}}$
Future value of an $R annuity lasting n periods at periodic interest rate r%	$F_{n}=R{\begin{bmatrix}{\frac {(1+r)^{n}-1}{r}}\end{bmatrix}}$
Present value of an $R annuity lasting n periods at periodic interest rate r%	$P=R{\begin{bmatrix}{\frac {1-(1+r)^{-n}}{r}}\end{bmatrix}}$
Present value of a perpetual cashflow of $R per period at periodic interest rate of r%	$P={\frac {R}{r}}$
Present value of a perpetual cashflow growing at g% when interest rate is r% per period. The first payment is $di and occurs in one period's time.	$P={\frac {d_{1}}{r-g}}$

$\beta _{j}={\frac {{\mbox{cov}}(r_{j},r_{M})}{{\mbox{var}}(r_{M})}}={\frac {\sigma _{j,M}}{\sigma _{M}^{2}}}$

$CAPM:E(r_{j})=r_{f}+\beta _{j}\lfloor E(r_{M})-r_{f}\rfloor$

${\mbox{var}}(r_{p})=\sigma _{p}^{2}=\omega _{1}^{2}\sigma _{1}^{2}+\omega _{2}^{2}\sigma _{2}^{2}+2\omega _{1}\omega _{2}\rho _{1,2}\sigma _{1}\sigma _{2}$

$\rho _{1,2}={\frac {{\mbox{cov}}(r_{1},r_{2})}{\sigma _{1}\sigma _{2}}}={\frac {\sigma _{1,2}}{\sigma _{1}\sigma _{2}}}$

$r_{*}^{L}=r_{e}^{L}\left({\frac {E^{L}}{V^{L}}}\right)+r_{d}(1-\tau )\left({\frac {D^{L}}{V^{L}}}\right)$

$r_{e}^{L}=r_{*}^{U}+(r_{*}^{U}-r_{d})(1-\tau )\left({\frac {D^{L}}{E^{L}}}\right)$