January 10 2014

Unit 2 Notes: Corporate Finance Mathematics

Leonard Vun Corporate Finance, MBA emba, lecture notes, MNGT6321, unsw 0

Corporate Finance lecture notes for the EMBA at UNSW.

Time value of money

Time affects value – we would rather to have money now so that we can invest money now and then have a lot in 10 years’ time.

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Future Value, ${\rm FV\ =\ PV\ \times }{{\rm (1+r)}}^n$ ,

Present Value,PV = $$\frac{{\rm FV}}{{{\rm (1+r)}}^{{\rm n}}}$ ,

Annuities~~
Conditions/Assumptions~~
Regular sets of cash flows~~
Identical~~
Repeated amount for set period of time~~
The first amount occurs in the next period,,

Future Value (R), $S = R $\times$ $\left[\frac{{\left({\rm 1+r}\right)}^{{\rm n}}-1}{{\rm r}}\right]$$ ,

Present Value (A), $A = R $\times$ $\left[\frac{{\rm 1-}{\left({\rm 1+r}\right)}^{{\rm -n}}}{{\rm r}}\right]$\newline A = present value\newline R = Regular identical cash flows$ ,

Perpetuity – cash flows that goes on forever, ${{A}}_{\infty }=\frac{{\rm R}}{{\rm r}}$ ~~A = Present value~~ R = Regular identical cash flow~~ R = return per period,

Growing Perpetuity~~

Use in shares~~

Real rate of return = no inflation, ${{A}}_{\infty{,g}}=\frac{{\rm R}}{{\rm (r-g)}}$ ~~ g can be +ve or -ve ,

Equivalent Rates~~,

Annual Equivalent Rate (AER), $AER = ${\left(1+r\right)}^m-1$$ ~~ r = rate of return~~ m = compounded m times per year,

Generic AER, $ER = ${\left(1+\frac{j}{m}\right)}^n-1$$ ~~ j = nominal interest rate (per year)~~ m~~ n ,

Part period rate, $r${}_{k}$= (1+r)${}^{k}$ -1$ ~~ k = fraction of time~~ r = annual rate,

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Applying to Mortgage

Calculating principle outstanding

Forward Method

Remaining Periods	Principle at start	Repayment per month	Interest on principal	Principle reduction	Principle at end
Order of Calc	(1)	(2)	(3)	(4)	(5)
Calculation		PV of Annuity formula	(1) x j/m	(1) – (3)	(1) – (4)

Backward Method

Remaining Periods	Principle at start	Repayment per month	Interest on principal	Principle reduction	Principle at end
Order of Calc	(1)	(2)	(5)	(4)	(3)
Calculation		PV of Annuity formula	(2) – (4)	(1) – (3)	PV of all future repayments at the start of the next period

Lookout

Different n in the PV formula for (1) and (3) gives you the amount for that period.
n to calculate (1) and (3) is the number of remaining period usually in months
Repayment is per month (2). May need to be adjusted to calculate Interest on Principal.

i.e Repayment per month x 12 subtract Principle reduction in 1 year

Unit 2 Notes: Corporate Finance Mathematics

Applying to Mortgage

Calculating principle outstanding

Forward Method

Backward Method

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