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MAF 203 Business Finance APPENDIX 1 – FORMULA SHEET DESCRIPTION Present value of an ordinary annuity (PVA)

Future value of an ordinary annuity (FVA)

PMT (or CF) from FVA Present value of a perpetuity Value of an annuity due

1 ฀฀฀฀ × �1 − � ฀ ฀ (1 + ฀฀ )฀฀ 1 1− (1 + ฀฀)฀฀ = ฀฀฀฀ × � � ฀ ฀

FORM FORMULA ULA ฀฀฀฀฀฀฀ ฀ =

= ฀฀฀฀ × ฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀ ฀฀฀฀฀฀฀ ฀ = × [(1 + ฀฀)฀ ฀ − 1] ฀ ฀ (1 + ฀฀)฀ ฀ − 1 � = ฀฀฀฀ × � ฀ ฀ = ฀฀฀฀ × ฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀ (1 + ฀฀)฀ ฀ − 1 � ฀฀฀฀฀฀ = ฀฀฀฀฀฀/ � i ฀฀฀฀ ฀฀฀฀฀฀∞ = ฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ = ฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ × ฀฀ ฀฀฀฀1 1 + ฀฀ � � ฀฀฀฀฀฀฀ ฀ = × �1 − � 1+฀฀ ฀฀ − ฀฀ ฀฀฀฀1 ฀฀฀฀฀฀∞ = ฀฀ − ฀฀

Present value of a growing annuity Present value of a growing perpetuity ฀฀ Effective annual interest ฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀ � −1 ฀฀฀฀฀฀ = �1 + ฀ ฀ rate ฀฀1 − ฀฀0฀฀฀฀1 Total holding period ฀฀฀ ฀ = ฀฀฀฀฀฀ + ฀฀฀ ฀ = + ฀฀0 ฀฀0 return ฀฀ Expected return on an ฀฀(฀฀฀฀฀฀฀฀฀฀฀฀ ) = �(฀฀฀ ฀ × ฀฀฀฀ ) asset Variance of return on an asset Standard deviation of return on an asset Expected return for a portfolio

฀฀=1 ฀฀

฀฀฀฀฀฀(฀฀) = �{(฀฀฀ ฀ × [฀฀฀ ฀ − ฀฀ (฀฀฀฀ )]2 } ฀฀=1

฀฀

} )] ฀฀฀฀฀฀฀฀฀฀(฀฀) = ��{(฀฀฀ ฀ × [฀฀฀ ฀ − ฀฀ (฀฀2฀฀ ฀฀=1 ฀฀

฀฀(฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ) = �[฀฀฀ ฀ × ฀฀(฀฀฀฀ )] ฀฀=1

Expected return and systematic risk (CAPM) Portfolio beta Price of a bond Price of a bond making multiple payments per year Price of a zero coupon bond The general dividend valuation model

฀฀(฀฀฀฀ ) = ฀฀฀ ฀ + ฀฀฀฀ [฀฀(฀฀฀฀ ) − ฀฀฀฀ ] ฀฀

฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ = �(฀฀฀ ฀ × ฀฀฀฀ ) ฀฀฀

฀

฀฀=1

฀฀ 1 ฀฀฀฀ = × �1 − � +(1 + ฀฀)฀฀ ฀฀ ฀ ฀ (1 + ฀฀ )

฀฀/฀฀ ฀฀฀฀฀฀ 1 ฀฀฀ ฀ = �+ × �1 − ฀฀฀฀ (1 + ฀฀/฀฀ ) (1 + ฀฀/฀฀)฀฀฀฀ ฀฀/฀ ฀

฀฀฀฀฀฀ ฀฀฀ ฀ = (1 + ฀฀/฀฀)฀฀฀฀ ฀฀4 ฀฀3 ฀฀2 ฀฀1 + + + ฀฀0 = +⋯ (1 + ฀฀) (1 + ฀฀ )2 (1 + ฀฀ )3 (1 + ฀฀ )4 ฀฀∞ + (1 + ฀฀)∞ ∞

฀฀0 = �

Zero growth dividend model Value of a dividend at time t in a constant growth scenario Constant growth dividend model Value of a share at time t when dividends grow at a constant rate Supernormal growth share valuation model Value of a preference share with a fixed maturity Value of a preference share in perpetuity Net present value

฀฀0 =

฀฀฀฀ (1 + ฀฀ )฀฀

฀฀=1

฀฀1 ฀฀

฀฀฀ ฀ = ฀฀0 × (1 + ฀฀)฀฀ ฀฀0 =

฀฀1 ฀฀ − ฀฀

฀฀0 =

฀฀฀฀ ฀฀฀฀ ฀฀2 ฀฀1 + + ⋯ + + (1 + ฀฀ )฀ ฀ (1 + ฀฀ )฀฀ (1 + ฀฀) (1 + ฀฀ )2

฀฀฀฀+1 ฀฀฀ ฀ = ฀฀ − ฀฀

฀฀฀฀0 = ฀฀฀฀0 =

฀฀/฀฀ ฀฀฀฀฀฀ 1 �+ × �1 − ฀฀฀฀ (1 + ฀฀/฀฀ ) (1 + ฀฀/฀฀)฀฀฀฀ ฀฀/฀ ฀ ฀฀ ฀฀

฀฀฀฀฀฀1 ฀฀฀฀฀฀2 ฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀ = ฀฀฀฀฀฀0 + + + ⋯+ 2 (1 + ฀฀)฀฀ 1 + ฀ ฀ (1 + ฀฀)

∞

฀฀฀฀฀฀฀฀ ฀฀ ฀฀฀฀฀฀ = ฀฀=0 � (1 + ฀฀) ฀฀฀฀ = ฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ Payback period ฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀ ฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ + ฀฀฀฀฀฀ℎ ฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀ℎ฀฀ ฀฀฀฀฀฀฀฀ Accounting rate of return ฀฀฀฀฀฀ = ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ Incremental free cash flow ฀฀฀฀฀฀ = [(฀฀฀฀฀฀฀฀฀฀฀฀฀฀ − ฀฀฀฀฀฀฀฀ − ฀฀&฀฀) × (1 − ฀฀฀฀ )] + ฀฀&฀฀ − ฀฀฀฀฀฀฀฀฀฀฀฀ − ฀฀฀฀฀฀ ฀฀฀฀ calculation

Inflation and real components of cost of capital (Fisher Effect) Incremental additions to working capital Net present value in perpetuity Equivalent Annual cost Degree of pre-tax cash flow operating leverage Degree of accounting operating leverage Pre-tax operating cash flow break-even point Crossover level of unit sales for EBITDA Accounting operating profit break-even point Crossover level of unit sales for EBIT Profitability index

After tax cost of debt CAPM formula for cost of ordinary shares Constant growth dividend formula for the cost of ordinary shares

1 + ฀ ฀ = (1 + ∆฀฀฀฀ ) × (1 + ฀฀)

Add WC = Change in cash & cash equivalents + Change in accounts receivable +Change in inventories – Change in accounts payable (1 + ฀฀)฀฀ ฀฀฀฀฀฀∞ = ฀฀฀฀฀฀0 � � (1 + ฀฀)฀ ฀ − 1 (1 + ฀฀)฀฀ � ฀฀฀฀฀฀0 = ฀ ฀ × ฀฀฀฀฀฀0 � (1 + ฀฀)฀ ฀ − 1 ฀฀฀฀ ฀฀฀฀฀฀ℎ ฀฀฀฀฀฀฀฀ ฀฀฀฀฀ ฀ = 1 + ฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀ + ฀฀&฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀ ฀ = 1 + ฀฀฀฀฀฀฀฀

฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ − ฀฀฀฀฀฀฀฀ = ฀฀฀฀฀฀฀฀฀฀ − ฀฀฀฀฀฀฀฀ ฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ 1 − ฀฀฀฀฀฀฀฀฀฀2 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ = ฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ 1 − ฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ 1

฀฀฀฀ + ฀฀&฀฀ ฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ − ฀฀฀฀฀฀฀฀ = ฀฀฀฀฀฀฀฀฀฀ − ฀฀฀฀฀฀฀฀ ฀฀฀฀ (฀฀฀฀ + ฀฀&฀฀)฀฀฀฀฀฀ 1 − (฀฀฀฀ + ฀฀&฀฀)฀฀฀฀฀฀ 2 ฀฀฀฀฀฀฀฀฀฀฀฀ = ฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ 1 − ฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ 1 ฀฀฀฀฀฀ + ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀ = ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀−฀฀฀฀฀ ฀ = ฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀−฀฀฀฀฀ ฀ × (1 − ฀฀ )

฀฀฀฀฀฀ = ฀฀฀฀฀฀ + (฀฀฀฀฀฀ × ฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀) ฀฀1 ฀฀฀฀฀฀ = + ฀฀ ฀฀0

Perpetuity formula for the cost of preference shares Traditional WACC Days sales outstanding (DSO) Days sales inventory (DSI)

฀฀฀฀฀฀ ฀฀฀฀฀฀ =฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀ = ฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀(1 − ฀฀ ) + ฀฀฀฀฀฀ ฀฀฀฀฀฀ + ฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀ = ฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀/365 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀ = ฀฀฀฀฀฀฀฀ ฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀/365 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀ = ฀฀฀฀฀฀฀฀ ฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀/365 Operating cycle =DSO + DSI

Days payables outstanding (DPO) Operating cycle Cash conversion cycle = DSO + DSI - DPO Cash conversion cycle Economic Order Quantity 2 × ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ × ฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀ ฀฀ ฀฀฀฀฀฀ = � (EOQ) ฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ WACC for company with no tax and no preference shares Cost of ordinary shares – M&M proposition 2

฀฀฀฀฀฀฀฀ = ฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ + ฀฀฀฀฀฀ ฀฀฀฀฀฀

฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀ = ฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀ + � � × (฀฀฀฀฀฀฀฀฀฀฀฀฀฀ − ฀฀฀฀฀฀฀฀฀฀ ) ฀฀฀฀฀฀...