Chapter 1: Corp Finance & Financial Managers 𝐶1
∆𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 = 𝑁𝑒𝑤 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 · 𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑁𝑒𝑤 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
Present Value of a Perpetuity: 𝑃𝑉0 =
Sole Proprietorship: One individual owns and manages the business, Bears all the costs, but keep all of 𝑟
𝐷𝑖𝑣1+𝑃1 𝐷𝑖𝑣1 𝐷𝑖𝑣2 𝐷𝑖𝑣𝑛 𝑃𝑛
1 1
the profits, No separation of business and individual, ADV: Ease of establishment and lack of regulation, Present Value of an Annuity: 𝑃𝑉0 = 𝐶 × ( 𝑟 ) × (1 − ( 𝑛 )) 𝑃0 = → 𝑀𝑢𝑙𝑡𝑖𝑦𝑟 = + 2 +···+ 𝑛 + 𝑛
(1+𝑟) 1+𝑟 1+𝑟 (1+𝑟) (1+𝑟) (1+𝑟)
DIS-ADV: Unlimited liability – that individual is personally liable for all of the firm’s liabilities (financial 1 𝑛
FV of an Annuity at the end of the Annuity: 𝐹𝑉𝑛 = 𝐶 × ( ) × ((1 + 𝑟) − 1) 𝐷𝑖𝑣1+𝑃1 𝐷𝑖𝑣 𝑃 −𝑃
and legal), Limited life, Difficult to transfer ownership 𝑟
𝑇𝑜𝑡𝑎𝑙 𝑟𝑒𝑡𝑢𝑟𝑛 = −1= + 1𝑃 0
General partnership (only general partners, similar to sole proprietorship) 𝑃 1 𝑃0 𝑃0
Solving For CF (loan Payment): 𝐶 = 1/𝑟
× (1 − 𝑛 ) 0
Limited partnership (general partners and limited partners) (1+𝑟) 𝐷𝑖𝑣1
Limited liability partnership (LLP) in Canada 𝑛 𝐹𝑉
1
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝐺𝑟𝑜𝑤𝑡ℎ 𝑀𝑜𝑑𝑒𝑙 = 𝑟−𝑔
Rate of Return: 𝑃 × (1 + 𝑟) = FV OR 1 + 𝑟 = ( 𝑃
) 𝑛
Chapter 2: Fin Statement Analysis 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠𝑡
CF From Assets = CF to Bondholders + CF to Shareholders Value of Growing Perpetuity: 𝑃𝑉0 =
𝐶1
𝐷𝑖𝑣𝑡 = 𝑆ℎ𝑎𝑟𝑒𝑠 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔
· 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑃𝑎𝑦𝑜𝑢𝑡 𝑅𝑎𝑡𝑒
(𝑟−𝑔)
Or Operating CF – Net capital spending – 1 𝑛 𝑛 Share of stock gives owner right to elect board, vote on mergers, receive divs.
FV Growing Annuity: 𝐹𝑉𝑛 = 𝐶1 × ( 𝑟−𝑔 ) × ((1 + 𝑟) − (1 = 𝑔) )
Changes in NWC Total return of stock is made of div payments and capital appreciation of stock
Operating CF = Net Income + Interest Expense + Chapter 6: Bonds Dividend-discount model: Value of stock = PV of all future payments received
Depreciation or = EBIT + Depreciation – Taxes FV = Maturity (last period of bond)/ Face Value = 1000 by default Return>cost of capital = increase in stock price & vice versa
Net Capital Spending = Ending Fixed Assets – Beg PMT = Coupon Rate x Face Value (if semi-annual divide by 2) Adjust for differences in scale by expressing value in terms of valuation multiple
Fixed Assets + Depreciation CPN PMT = (CR x FV) / # CPN PMT per year Efficient Market: Competition among firms eliminates all (+) NPV trade opp.
Changes in NWC = (End CA – End CL) – (Beg. CA – CPN Rate (%) = (CPN PMT/FV) x # CPN PMT per year Excessive Trading and Overconfidence, Disposition Effect, Investor Attention/Moods/Experience: Trading
Beg CL)(End NWC – Beg NWC) YTMn = (FVn/P)1/n – 1 Biases
CF to Bondholders “Creditors” = Interest – Net New FV = PV x (1 + r)n Preferred Stock: Higher div returns but cash payout
Borrowing Or = Interest – (Ending LTD – Beg LTD) CPN Price = FV / (1 + YTM)n To forecast Divs: earnings, payout rate, and future share count
CF to Shareholders = Dividends – Net New Equity Issued Price of a CPN bond = [CPN/(1 + YTM1)] + [CPN/(1 + YTM2)2] + ….[(CPN + FV)/(1 + YTM^n)^n] Excessive trading leads to lower realized return as it increases supply which
Or = Dividends – (Ending common stock – Beg common stock) When given a # like, “currently selling for 108” that is a QUOTE, PV bond = (Quote/100) x Face Value Chapter 8: Inv Decision Rules
= Dividends – (Ending common stock – Beg common stock) IR Risk NPV = -investment + PV of cash flows (For PV Benefits-Costs)
Dupont Identity/ ROE = (Net Income/Sales) x (Sales/Assets) x (Assets/Equity) = Profit Margin x Total - The LONGER the maturity of the bond, the MORE sensitive the bond price is to interest Profitability Index (PI) = PV of CF/PV of CF outflows
Asset Turnover x Equity Multiplier rate changes Or PI = NPV/Costs
Net Working Capital = Current Assets – Current Liabilities - The LOWER the coupon rate, the MORE sensitive bond price is to interest rate changes NPV of IRR w/ a Perpetuity = -Investment + [Yearly benefit/r (1 + r)]
Enterprise Value = Market Value of Equity + Debt – Cash - The LONGER the compounding period, the MORE sensitive bond price is to interest rate Payback period: Time taken for project to pay back initial investment (does not adjust CF for time val of
Debts Equity Ratio = Debt/Equity changes money & ignores all CF beyond payback period)
Quick Ratio = Currents Assets - Inventory/ Current Liability Bond Types NPV Decision Rule: Take alternative with highest NPV (correct decision)
Current Ratio = Current Assets Stripped Bonds:Pays no coupons, only a lump sum at the end IRR Decision Rule: IRR>cost of capital → Accept project (N/A when >1 IRRs)
EPS = Net Income/ # of shares Floating-Rate Bonds: Coupon rate is not fixed Multiple IRRs occur when sign changes in stream of CFs
Return on Assets = (Net Income + Interest Expense) / Total Assets Convertible Bonds: Can be exchanged for a # of shares before maturity Cost of capital>Crossover rate: Both NPV and IRR select same project
Gross Margin = Gross Profit/Sales Retractable/Callable Bonds:Issuer can buy back the bonds at anytime at a specified price Difference between cost of capital and IRR is amount of estimation error that can exist without altering
Net Profit Margin = Net Profit/Sales Redeemable Bonds:Investor can sell back bonds to issuer at anytime at a specified price original decision
Operating Margin = Operating Income/Sales Fischer’s Effect Equivalent Ann. Annuity used when deciding between 2 mutually exclusive
Capital Turnover Ratio=Sales/Equity = Sales/(Assets-liabilit) Nominal rate “R”, Real rate of return “r”, Inflation “h” Profitability index: Value created per $1 investment
Market-to-Book Ratio = Market Value of Equity/book value of equity Inflation = (1+R) = (1+r) x (1+h) OR r x (1 + h) + h Chapter 9: Capital Budgeting – Corporate taxes and Changing CF
𝑀𝑎𝑟𝑘𝑒𝑡 𝐶𝑎𝑝 = 𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝑆𝑡𝑜𝑐𝑘 × 𝑇𝑜𝑡𝑎𝑙 # 𝑜𝑓 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑆ℎ𝑎𝑟𝑒𝑠 *always remember to use nominal rate with nominal CF and real rate with real CF* CCA$ = UCCn x CCA%
Chapter 18: Pro Forma Investment Yields EndingUCC = Beg. UCC – CCA$
Payout Ratio = Dividend/Net Income Capital Gains Return = (New – Old)/Old PV(CCA Tax Shield) or PVCCATS =
Retention Ratio(R) = (1- Payout Ratio) If you sell the bond BEFORE maturity Holding Period Return =Capital Gains Return
Pro-Forma EFN = ProForma Assets - ProForma (Liabilities + Equity) Holding Period Return = Capital Gains Return +Interest IncomeReturn
IGR = ROA x Retention Ratio ROA = NI / Total Assets Interest income Return = (CF1 +CF2 +CF3…) / Price Purchased
Substantial Growth Rate = ROE x Retention Ratio Current Yield = Interest / Principle amount
ROE = ROA x Equity Multiplier Dividend YIeld = Dividend/Price
Equity Multiplier = Assets/Equity Price-Earning Ratio = Share Price/EPS
NNF= Pro forma assets – Pro forma operating liabilities – Debt – (Equity + Pro forma retained earning) Market Book = Market Value per share/Book Value per share PV Tax Shield for the WHOLE project:
NNF= Change in assets – Change in operating liabilities Bonds: Governments and corporations borrow money for the long term by issuing securities Step 1: UCCn = C[1-(0.5x d)] x [(1-d ¿
– Addition to retained earning Bondholders: Bondholders own the securities, have rights to the cash flows described, and can trade these n−2
Chapter 3: Valuation Principles financial assets ¿ Take and input into 2
Simple Interest: FV = PV(1+r^n) Coupon: The interest payment paid to the bondholders Step 2: CCAn = UCCn x CCArate Take this and input into 3
Compound interest: FV = PV (1+r)^n Maturity Date: The date on which the loan will be paid off Step 3: CCAtax shield = CCAn x Tax rate
Discount Factor = 1/(1+r^)n used for discount payback period Term: the time remaining until the maturity date face value, par value, maturity value, or principal: The 𝑃𝑉𝐶𝐶𝐴𝑇𝑆 =
𝐶𝐴𝑃𝐸𝑋·𝑑·𝑇
·
1+0.5𝑟
−
𝑆𝑉·𝑑·𝑇
·
1
𝑛
𝑟+𝑑 1+𝑟 𝑟+𝑑 (1+𝑟)
- PV = FN / (1+r)n payment at the maturity of the bond (the amount borrowed)
Coupon Rate: The coupon rate describes the cash flows a bond will produce 𝐹𝐶𝐹 = (𝑅𝑒𝑣𝑒𝑛𝑢𝑒 − 𝑐𝑜𝑠𝑡𝑠) · (1 − 𝑇𝑒) − 𝐶𝐴𝑃𝐸𝑋 − ∆𝑁𝑊𝐶 + 𝑇𝑒 · 𝐶𝐶𝐴
- PV = Present value OUTFLOW FV = Future Value, n= number of periods, i = interest rate
Chapter 5: Interest Rates Discount Rate (or Yield to Maturity): is the market interest rate at which the cash flows from the bond 𝐴𝑛𝑛𝑢𝑎𝑙 𝐼𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡 = (𝑅𝑒𝑣 − 𝐶𝑜𝑠𝑡𝑠 − 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛) × (1 − 𝑇𝑎𝑥 𝑅𝑎𝑡𝑒)
Real interest rate = (Nominal rate – Inflation rate)/1 + Inflation rate ~ Nominal rate – Inflation rate (face value and coupons) are discounted to determine its present value Question 1
PV of cash flows = [C1/(1 + r1)] + [C2/(1 + r2)²] + [C3/(1 + r3)³] + … +[Cn/(1 + rn)^n] – A series of Chapter 7: Stock 16M to purchase equipment, CCA Rate 25%, Managerial 3%
(equal) cash flows lasting several periods Currents Stock Price: P0 = D1/r-g (div is in the year AFTER t= 1 UCCT=0.5 𝐶𝑎𝑝𝐸𝑥 = 8, 000, 000 = 0. 5 × 16
Equivalent n Period Effective Rate = [(1 + r)^n] – 1 the price) 8M - 0.25 = 2,000,000 𝑈𝐶𝐶𝑇 = 0. 5 × (1 −
𝑑
) × (1 − 𝑑)
𝑡−2
2
Nominal IR / APR = The annual percentage rate quoted in the question ANYTHING compounded Payout Ratio = Payout last year x (1+g)
0.25 2−2
monthly, quarterly, daily, when APR is annual APR = EAR Div = Rate x par 0. 5 × (1 − 2
) × (1 − 0. 25)
Mortgage questions: Given in APR and always compounded SEMI-ANNUALLY, C/Y = 2 Dividend with a certain g = D1 = Div0 x (1 x g) Incremental earnings (doesn’t correctly capture timing of when cash is put to work; CAPEX not cash
Effective IR / EAR = The annual rate of return Dn = Div0 x (1+g)n outflow) are amount by which firm’s earnings change as a result of investmentment decision; Pro forma
Ordinary Annuity = Stream of equal CF at the END of the Div Yield = Div1/P0 indicates earnings are estimated
period that eventually ends Capital Gain Rate = (P1 – P0)/P0 Sensitivity analysis is performed by measuring NPV of investment as you alter an assumption of NPV
Annuity Due = Stream of equal CF at the BEG of the period that eventually ends Total Return = RE = Div yield + Capital gain rate analysis (sales growth rate, discount rate, tax rate, etc.)
Perpetuity = Stream of CF that goes on forever (n= 999) Total Return = Equity Cost of Capital = RE = [(Div1 + P1)/P0] – 1 Sunk cost: Unrecoverable cost for which firm is already liable (not incremental)
Principle: Amount of mortgage and Outstanding liability or balance owing Div Growth Rate = Retention rate x Return on new investment Rapid dep. schedule=quicker write-off of cap. asset=more tax savings+earlier CF
Amortization Period: Time period over which you completely pay off the principal Div Next Year = EPS x Payout ratio Real option: Right, but not obligation, to make particular business decision
Nominal IR: Interest rates quoted by banks and other financial institutions that indicate the rate at which Dividend Discount Model: P0 = Div1/(1 + rE) + Div2/(1 + rE) Capital budget: List of projects firm plans to undertake during next period
money will grow if invested for a certain period of time 2 + …Divn/(1 + rE)^n + Pn/(1 + rE)^n Opportunity cost: Value a resource could have provided in best alt use
Real IR: The rate of growth of purchasing power after adjusting for inflation Constant Div Growth Model/Value of a Share = P0 = Div1/(rE – g) Project Ext.: Indirect effect of project that may inc/dec. profits of other business
Chapter 4: TVM (Same as CH.3 +) Total Payout Model = P0 = (PV x Future total div/repurchases)/Shares outstanding; Future total div = Cannibalization: Displacement of sales from existing prod. by sales of new prod.
Ordinary Annuity = Stream of equal CF at the END of the payout last year x (1 + g) Chapter 10: Risk & Return on Markets
period that eventually ends Enterprise Value = Mkt value of equity + Debt – Cash Realized Return: Rt + 1 = Div + (Pnew – Pold) / Pold
Annuity Due = Stream of equal CF at the BEG of the period that eventually ends Free Cash Flow = EBIT x (1 – Tax rate) + Depreciation – Capitalexpenditures – Increases in Net working Return from Dividend Yield: Rt +1 = Div/Pt
Perpetuity = Stream of CF that goes on forever (n= 999) capital (NWC) Return from Capital Gain: Rt + 1 = realized return formula
𝐶 𝐶 𝐶 𝐶 ∆𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 without dividend: (new-old)/old
Present Value of a Cash Flow Stream: 𝑃𝑉 = 𝐶0 + ( (1+𝑟1 ) ) + ( (1+𝑟2 ) + ( (1+𝑟3 ) +..... +( (1+𝑟𝑛 ) 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝐺𝑟𝑜𝑤𝑡ℎ 𝑅𝑎𝑡𝑒 = 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠
= 𝑅𝑒𝑡𝑒𝑛𝑡. 𝑅𝑎𝑡𝑖𝑜 · 𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑛𝑒𝑤 𝑖𝑛𝑣𝑠𝑡𝑚𝑒𝑛𝑡
1 2 3 𝑛
∆𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 = 𝑁𝑒𝑤 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 · 𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑁𝑒𝑤 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
Present Value of a Perpetuity: 𝑃𝑉0 =
Sole Proprietorship: One individual owns and manages the business, Bears all the costs, but keep all of 𝑟
𝐷𝑖𝑣1+𝑃1 𝐷𝑖𝑣1 𝐷𝑖𝑣2 𝐷𝑖𝑣𝑛 𝑃𝑛
1 1
the profits, No separation of business and individual, ADV: Ease of establishment and lack of regulation, Present Value of an Annuity: 𝑃𝑉0 = 𝐶 × ( 𝑟 ) × (1 − ( 𝑛 )) 𝑃0 = → 𝑀𝑢𝑙𝑡𝑖𝑦𝑟 = + 2 +···+ 𝑛 + 𝑛
(1+𝑟) 1+𝑟 1+𝑟 (1+𝑟) (1+𝑟) (1+𝑟)
DIS-ADV: Unlimited liability – that individual is personally liable for all of the firm’s liabilities (financial 1 𝑛
FV of an Annuity at the end of the Annuity: 𝐹𝑉𝑛 = 𝐶 × ( ) × ((1 + 𝑟) − 1) 𝐷𝑖𝑣1+𝑃1 𝐷𝑖𝑣 𝑃 −𝑃
and legal), Limited life, Difficult to transfer ownership 𝑟
𝑇𝑜𝑡𝑎𝑙 𝑟𝑒𝑡𝑢𝑟𝑛 = −1= + 1𝑃 0
General partnership (only general partners, similar to sole proprietorship) 𝑃 1 𝑃0 𝑃0
Solving For CF (loan Payment): 𝐶 = 1/𝑟
× (1 − 𝑛 ) 0
Limited partnership (general partners and limited partners) (1+𝑟) 𝐷𝑖𝑣1
Limited liability partnership (LLP) in Canada 𝑛 𝐹𝑉
1
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝐺𝑟𝑜𝑤𝑡ℎ 𝑀𝑜𝑑𝑒𝑙 = 𝑟−𝑔
Rate of Return: 𝑃 × (1 + 𝑟) = FV OR 1 + 𝑟 = ( 𝑃
) 𝑛
Chapter 2: Fin Statement Analysis 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠𝑡
CF From Assets = CF to Bondholders + CF to Shareholders Value of Growing Perpetuity: 𝑃𝑉0 =
𝐶1
𝐷𝑖𝑣𝑡 = 𝑆ℎ𝑎𝑟𝑒𝑠 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔
· 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑃𝑎𝑦𝑜𝑢𝑡 𝑅𝑎𝑡𝑒
(𝑟−𝑔)
Or Operating CF – Net capital spending – 1 𝑛 𝑛 Share of stock gives owner right to elect board, vote on mergers, receive divs.
FV Growing Annuity: 𝐹𝑉𝑛 = 𝐶1 × ( 𝑟−𝑔 ) × ((1 + 𝑟) − (1 = 𝑔) )
Changes in NWC Total return of stock is made of div payments and capital appreciation of stock
Operating CF = Net Income + Interest Expense + Chapter 6: Bonds Dividend-discount model: Value of stock = PV of all future payments received
Depreciation or = EBIT + Depreciation – Taxes FV = Maturity (last period of bond)/ Face Value = 1000 by default Return>cost of capital = increase in stock price & vice versa
Net Capital Spending = Ending Fixed Assets – Beg PMT = Coupon Rate x Face Value (if semi-annual divide by 2) Adjust for differences in scale by expressing value in terms of valuation multiple
Fixed Assets + Depreciation CPN PMT = (CR x FV) / # CPN PMT per year Efficient Market: Competition among firms eliminates all (+) NPV trade opp.
Changes in NWC = (End CA – End CL) – (Beg. CA – CPN Rate (%) = (CPN PMT/FV) x # CPN PMT per year Excessive Trading and Overconfidence, Disposition Effect, Investor Attention/Moods/Experience: Trading
Beg CL)(End NWC – Beg NWC) YTMn = (FVn/P)1/n – 1 Biases
CF to Bondholders “Creditors” = Interest – Net New FV = PV x (1 + r)n Preferred Stock: Higher div returns but cash payout
Borrowing Or = Interest – (Ending LTD – Beg LTD) CPN Price = FV / (1 + YTM)n To forecast Divs: earnings, payout rate, and future share count
CF to Shareholders = Dividends – Net New Equity Issued Price of a CPN bond = [CPN/(1 + YTM1)] + [CPN/(1 + YTM2)2] + ….[(CPN + FV)/(1 + YTM^n)^n] Excessive trading leads to lower realized return as it increases supply which
Or = Dividends – (Ending common stock – Beg common stock) When given a # like, “currently selling for 108” that is a QUOTE, PV bond = (Quote/100) x Face Value Chapter 8: Inv Decision Rules
= Dividends – (Ending common stock – Beg common stock) IR Risk NPV = -investment + PV of cash flows (For PV Benefits-Costs)
Dupont Identity/ ROE = (Net Income/Sales) x (Sales/Assets) x (Assets/Equity) = Profit Margin x Total - The LONGER the maturity of the bond, the MORE sensitive the bond price is to interest Profitability Index (PI) = PV of CF/PV of CF outflows
Asset Turnover x Equity Multiplier rate changes Or PI = NPV/Costs
Net Working Capital = Current Assets – Current Liabilities - The LOWER the coupon rate, the MORE sensitive bond price is to interest rate changes NPV of IRR w/ a Perpetuity = -Investment + [Yearly benefit/r (1 + r)]
Enterprise Value = Market Value of Equity + Debt – Cash - The LONGER the compounding period, the MORE sensitive bond price is to interest rate Payback period: Time taken for project to pay back initial investment (does not adjust CF for time val of
Debts Equity Ratio = Debt/Equity changes money & ignores all CF beyond payback period)
Quick Ratio = Currents Assets - Inventory/ Current Liability Bond Types NPV Decision Rule: Take alternative with highest NPV (correct decision)
Current Ratio = Current Assets Stripped Bonds:Pays no coupons, only a lump sum at the end IRR Decision Rule: IRR>cost of capital → Accept project (N/A when >1 IRRs)
EPS = Net Income/ # of shares Floating-Rate Bonds: Coupon rate is not fixed Multiple IRRs occur when sign changes in stream of CFs
Return on Assets = (Net Income + Interest Expense) / Total Assets Convertible Bonds: Can be exchanged for a # of shares before maturity Cost of capital>Crossover rate: Both NPV and IRR select same project
Gross Margin = Gross Profit/Sales Retractable/Callable Bonds:Issuer can buy back the bonds at anytime at a specified price Difference between cost of capital and IRR is amount of estimation error that can exist without altering
Net Profit Margin = Net Profit/Sales Redeemable Bonds:Investor can sell back bonds to issuer at anytime at a specified price original decision
Operating Margin = Operating Income/Sales Fischer’s Effect Equivalent Ann. Annuity used when deciding between 2 mutually exclusive
Capital Turnover Ratio=Sales/Equity = Sales/(Assets-liabilit) Nominal rate “R”, Real rate of return “r”, Inflation “h” Profitability index: Value created per $1 investment
Market-to-Book Ratio = Market Value of Equity/book value of equity Inflation = (1+R) = (1+r) x (1+h) OR r x (1 + h) + h Chapter 9: Capital Budgeting – Corporate taxes and Changing CF
𝑀𝑎𝑟𝑘𝑒𝑡 𝐶𝑎𝑝 = 𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝑆𝑡𝑜𝑐𝑘 × 𝑇𝑜𝑡𝑎𝑙 # 𝑜𝑓 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑆ℎ𝑎𝑟𝑒𝑠 *always remember to use nominal rate with nominal CF and real rate with real CF* CCA$ = UCCn x CCA%
Chapter 18: Pro Forma Investment Yields EndingUCC = Beg. UCC – CCA$
Payout Ratio = Dividend/Net Income Capital Gains Return = (New – Old)/Old PV(CCA Tax Shield) or PVCCATS =
Retention Ratio(R) = (1- Payout Ratio) If you sell the bond BEFORE maturity Holding Period Return =Capital Gains Return
Pro-Forma EFN = ProForma Assets - ProForma (Liabilities + Equity) Holding Period Return = Capital Gains Return +Interest IncomeReturn
IGR = ROA x Retention Ratio ROA = NI / Total Assets Interest income Return = (CF1 +CF2 +CF3…) / Price Purchased
Substantial Growth Rate = ROE x Retention Ratio Current Yield = Interest / Principle amount
ROE = ROA x Equity Multiplier Dividend YIeld = Dividend/Price
Equity Multiplier = Assets/Equity Price-Earning Ratio = Share Price/EPS
NNF= Pro forma assets – Pro forma operating liabilities – Debt – (Equity + Pro forma retained earning) Market Book = Market Value per share/Book Value per share PV Tax Shield for the WHOLE project:
NNF= Change in assets – Change in operating liabilities Bonds: Governments and corporations borrow money for the long term by issuing securities Step 1: UCCn = C[1-(0.5x d)] x [(1-d ¿
– Addition to retained earning Bondholders: Bondholders own the securities, have rights to the cash flows described, and can trade these n−2
Chapter 3: Valuation Principles financial assets ¿ Take and input into 2
Simple Interest: FV = PV(1+r^n) Coupon: The interest payment paid to the bondholders Step 2: CCAn = UCCn x CCArate Take this and input into 3
Compound interest: FV = PV (1+r)^n Maturity Date: The date on which the loan will be paid off Step 3: CCAtax shield = CCAn x Tax rate
Discount Factor = 1/(1+r^)n used for discount payback period Term: the time remaining until the maturity date face value, par value, maturity value, or principal: The 𝑃𝑉𝐶𝐶𝐴𝑇𝑆 =
𝐶𝐴𝑃𝐸𝑋·𝑑·𝑇
·
1+0.5𝑟
−
𝑆𝑉·𝑑·𝑇
·
1
𝑛
𝑟+𝑑 1+𝑟 𝑟+𝑑 (1+𝑟)
- PV = FN / (1+r)n payment at the maturity of the bond (the amount borrowed)
Coupon Rate: The coupon rate describes the cash flows a bond will produce 𝐹𝐶𝐹 = (𝑅𝑒𝑣𝑒𝑛𝑢𝑒 − 𝑐𝑜𝑠𝑡𝑠) · (1 − 𝑇𝑒) − 𝐶𝐴𝑃𝐸𝑋 − ∆𝑁𝑊𝐶 + 𝑇𝑒 · 𝐶𝐶𝐴
- PV = Present value OUTFLOW FV = Future Value, n= number of periods, i = interest rate
Chapter 5: Interest Rates Discount Rate (or Yield to Maturity): is the market interest rate at which the cash flows from the bond 𝐴𝑛𝑛𝑢𝑎𝑙 𝐼𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡 = (𝑅𝑒𝑣 − 𝐶𝑜𝑠𝑡𝑠 − 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛) × (1 − 𝑇𝑎𝑥 𝑅𝑎𝑡𝑒)
Real interest rate = (Nominal rate – Inflation rate)/1 + Inflation rate ~ Nominal rate – Inflation rate (face value and coupons) are discounted to determine its present value Question 1
PV of cash flows = [C1/(1 + r1)] + [C2/(1 + r2)²] + [C3/(1 + r3)³] + … +[Cn/(1 + rn)^n] – A series of Chapter 7: Stock 16M to purchase equipment, CCA Rate 25%, Managerial 3%
(equal) cash flows lasting several periods Currents Stock Price: P0 = D1/r-g (div is in the year AFTER t= 1 UCCT=0.5 𝐶𝑎𝑝𝐸𝑥 = 8, 000, 000 = 0. 5 × 16
Equivalent n Period Effective Rate = [(1 + r)^n] – 1 the price) 8M - 0.25 = 2,000,000 𝑈𝐶𝐶𝑇 = 0. 5 × (1 −
𝑑
) × (1 − 𝑑)
𝑡−2
2
Nominal IR / APR = The annual percentage rate quoted in the question ANYTHING compounded Payout Ratio = Payout last year x (1+g)
0.25 2−2
monthly, quarterly, daily, when APR is annual APR = EAR Div = Rate x par 0. 5 × (1 − 2
) × (1 − 0. 25)
Mortgage questions: Given in APR and always compounded SEMI-ANNUALLY, C/Y = 2 Dividend with a certain g = D1 = Div0 x (1 x g) Incremental earnings (doesn’t correctly capture timing of when cash is put to work; CAPEX not cash
Effective IR / EAR = The annual rate of return Dn = Div0 x (1+g)n outflow) are amount by which firm’s earnings change as a result of investmentment decision; Pro forma
Ordinary Annuity = Stream of equal CF at the END of the Div Yield = Div1/P0 indicates earnings are estimated
period that eventually ends Capital Gain Rate = (P1 – P0)/P0 Sensitivity analysis is performed by measuring NPV of investment as you alter an assumption of NPV
Annuity Due = Stream of equal CF at the BEG of the period that eventually ends Total Return = RE = Div yield + Capital gain rate analysis (sales growth rate, discount rate, tax rate, etc.)
Perpetuity = Stream of CF that goes on forever (n= 999) Total Return = Equity Cost of Capital = RE = [(Div1 + P1)/P0] – 1 Sunk cost: Unrecoverable cost for which firm is already liable (not incremental)
Principle: Amount of mortgage and Outstanding liability or balance owing Div Growth Rate = Retention rate x Return on new investment Rapid dep. schedule=quicker write-off of cap. asset=more tax savings+earlier CF
Amortization Period: Time period over which you completely pay off the principal Div Next Year = EPS x Payout ratio Real option: Right, but not obligation, to make particular business decision
Nominal IR: Interest rates quoted by banks and other financial institutions that indicate the rate at which Dividend Discount Model: P0 = Div1/(1 + rE) + Div2/(1 + rE) Capital budget: List of projects firm plans to undertake during next period
money will grow if invested for a certain period of time 2 + …Divn/(1 + rE)^n + Pn/(1 + rE)^n Opportunity cost: Value a resource could have provided in best alt use
Real IR: The rate of growth of purchasing power after adjusting for inflation Constant Div Growth Model/Value of a Share = P0 = Div1/(rE – g) Project Ext.: Indirect effect of project that may inc/dec. profits of other business
Chapter 4: TVM (Same as CH.3 +) Total Payout Model = P0 = (PV x Future total div/repurchases)/Shares outstanding; Future total div = Cannibalization: Displacement of sales from existing prod. by sales of new prod.
Ordinary Annuity = Stream of equal CF at the END of the payout last year x (1 + g) Chapter 10: Risk & Return on Markets
period that eventually ends Enterprise Value = Mkt value of equity + Debt – Cash Realized Return: Rt + 1 = Div + (Pnew – Pold) / Pold
Annuity Due = Stream of equal CF at the BEG of the period that eventually ends Free Cash Flow = EBIT x (1 – Tax rate) + Depreciation – Capitalexpenditures – Increases in Net working Return from Dividend Yield: Rt +1 = Div/Pt
Perpetuity = Stream of CF that goes on forever (n= 999) capital (NWC) Return from Capital Gain: Rt + 1 = realized return formula
𝐶 𝐶 𝐶 𝐶 ∆𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 without dividend: (new-old)/old
Present Value of a Cash Flow Stream: 𝑃𝑉 = 𝐶0 + ( (1+𝑟1 ) ) + ( (1+𝑟2 ) + ( (1+𝑟3 ) +..... +( (1+𝑟𝑛 ) 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝐺𝑟𝑜𝑤𝑡ℎ 𝑅𝑎𝑡𝑒 = 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠
= 𝑅𝑒𝑡𝑒𝑛𝑡. 𝑅𝑎𝑡𝑖𝑜 · 𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑛𝑒𝑤 𝑖𝑛𝑣𝑠𝑡𝑚𝑒𝑛𝑡
1 2 3 𝑛
