Summary Extra notes for finance with all important formulas
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Vak
Finance (FINANCE)
Instelling
Syddansk Universitet
Boek
Corporate Finance
This document contains all important formulas, theory explained and notes for the finance book. It also has templates that can be used to easily create capital budgeting, graphs,...
Market Value of Equity Shares Outstanding Market Price per [2.2] 𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦=𝑆ℎ𝑎𝑟𝑒𝑠 𝑂𝑢𝑡𝑠𝑡
𝑀𝑎𝑟𝑘𝑒𝑡 𝑡𝑜 𝐵𝑜𝑜𝑘 𝑅𝑎𝑡𝑖𝑜=(𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦)/
Market to Book Ratio Market Value of Equity Book Value of E [2.3]
Enterprise Value Market value of Equity Debt Cash [2.4] 𝐸𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 𝑉𝑎𝑙𝑢𝑒=𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞
𝐸𝑃𝑆=(𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒)/(𝑆ℎ𝑎𝑟𝑒𝑠 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔)
EPS Earnings per share Net Income Shares Outstanding [2.5]
𝑅𝑒𝑡𝑎𝑖𝑛𝑒𝑑 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠=𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒−𝐷𝑖𝑣𝑖𝑑𝑒
Retained Earnings Net Income Dividends [2.6]
Change in Stockholder's Equity Retained Earnings Net sales of[2.7] 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑆𝑡𝑜𝑐𝑘ℎ𝑜𝑙𝑑𝑒𝑟𝑠^′ 𝐸𝑞𝑢𝑖𝑡𝑦=
𝑔𝑟𝑜𝑠𝑠 𝑚𝑎𝑟𝑔𝑖𝑛=(𝑔𝑟𝑜𝑠𝑠 𝑝𝑟𝑜𝑓𝑖𝑡)/𝑠𝑎𝑙𝑒𝑠
Gross margin gross profit sales [2.8]
𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑚𝑎𝑟𝑔𝑖𝑛=(𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑖𝑛𝑐𝑜𝑚𝑒)/𝑠𝑎𝑙𝑒
operating margin operating income sales [2.9]
𝑛𝑒𝑡 𝑝𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛=(𝑛𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒)/𝑠𝑎𝑙𝑒𝑠
net profit margin net income sales [2.10]
𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑟𝑎𝑡𝑖𝑜=(𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑎𝑠𝑠𝑒𝑡𝑠)/(𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒
current ratio current assets current liabilities [no number]
𝑐𝑎𝑠ℎ 𝑟𝑎𝑡𝑖𝑜=𝑐𝑎𝑠ℎ/(𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠)
cash ratio cash current liabilities [no number]
𝑎𝑐𝑐𝑜𝑢𝑛𝑡𝑠 𝑟𝑒𝑐𝑒𝑖𝑣𝑎𝑏𝑙𝑒 𝑑𝑎𝑦𝑠=(𝑎𝑐𝑐𝑜𝑢𝑛𝑡𝑠 𝑟𝑒𝑐𝑒𝑖𝑣𝑎𝑏𝑙𝑒)/(𝑎
Accounts receivable days Accounts receivable average daily s [2.11]
𝑎𝑐𝑐𝑜𝑢𝑛𝑡𝑠 𝑝𝑎𝑦𝑎𝑏𝑙𝑒 𝑑𝑎𝑦𝑠=(𝑎𝑐𝑐𝑜𝑢𝑛𝑡𝑠 𝑝𝑎𝑦𝑎𝑏𝑙𝑒)/(𝑎𝑣𝑒𝑟
accounts payable days accounts payable average daily cost of[2.12]
𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 𝑡𝑢𝑟𝑛𝑜𝑣𝑒𝑟=(𝑎𝑛𝑛𝑢𝑎𝑙 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠)/𝑖𝑛
Inventory turnover [2.13]
𝐸𝐵𝐼𝑇𝐷𝐴=𝐸𝐵𝐼𝑇+𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑛𝑑 𝐴𝑚𝑜𝑟𝑡
EBITDA EBIT Depriciation and Amortization [2.14]
𝐷𝑒𝑏𝑡−𝐸𝑞𝑢𝑖𝑡𝑦 𝑅𝑎𝑡𝑖𝑜=(𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡)/(𝑇𝑜𝑡𝑎𝑙 𝐸𝑞𝑢𝑖𝑡
Debt Equity Ratio [2.15]
𝐷𝑒𝑏𝑡−𝑡𝑜−𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑅𝑎𝑡𝑖𝑜=(𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡)/(𝑇𝑜𝑡𝑎
Debt to Capital Ratio [2.16]
Net Debt Total Debt Excess Cash and Short term Investments [2.17] 𝑁𝑒𝑡 𝑑𝑒𝑏𝑡=𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡−𝐸𝑥𝑐𝑒𝑠𝑠 𝐶𝑎𝑠ℎ 𝑎𝑛𝑑
𝐷𝑒𝑏𝑡−𝑡𝑜−𝐸𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 𝑉𝑎𝑙𝑢𝑒 𝑅𝑎𝑡𝑖𝑜=(𝑁𝑒𝑡 𝑑𝑒𝑏𝑡)/(𝑀𝑎
Debt to Enterprise Value Ratio Net debt Market Value of Equi[2.18]
𝑃/𝐸 𝑅𝑎𝑡𝑖𝑜=(𝑀𝑎𝑟𝑘𝑒𝑡 𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑠𝑎𝑡𝑖𝑜𝑛)/(𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒)=(𝑆𝑎ℎ𝑟
P/E Ratio Market Capitalisation Net income Share Price Earni [2.19]
, 𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝐸𝑞𝑢𝑖𝑡𝑦=(𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒)/(𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸
Return on Equity Net income Book Value of Equity [2.20]
𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝐴𝑠𝑠𝑒𝑡𝑠=(𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒+𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐸𝑥𝑝𝑒𝑛𝑠𝑒)/(𝐵
Return on Assets Net income interest expense Book Value of [2.21]
𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝐼𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝐶𝑎𝑝𝑖𝑡𝑎𝑙=(𝐸𝐵𝐼𝑇∗(1−𝑇𝑎𝑥 𝑟𝑎𝑡𝑒))/(𝐵
Return on Invested Capital EBIT tax rate book value of Equity [2.22]
No Arbitrage Price of a Security [3.3] 𝑃𝑟𝑖𝑐𝑒(𝑆𝑒𝑐𝑢𝑟𝑖𝑡𝑦)=𝑃𝑉(𝑎𝑙𝑙 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤𝑠 𝑝𝑎𝑖𝑑
𝑅𝑒𝑡𝑢𝑟𝑛=(𝐺𝑎𝑖𝑛 𝑎𝑡 𝐸𝑛𝑑 𝑜𝑓 𝑌𝑒𝑎𝑟)/(𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑐𝑜𝑠𝑡)
Return Gain at the End of Year Initial cost [3.4]
Value Additivity Price(C) Price(A+B) Price(A) Price(B) Law of o [3.5] 𝑃𝑟𝑖𝑐𝑒(𝐶)=𝑃𝑟𝑖𝑐𝑒(𝐴+𝐵)=𝑃𝑟𝑖𝑐𝑒(𝐴)+𝑃𝑟𝑖𝑐𝑒
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑓 𝑎 𝑟𝑖𝑠𝑘𝑦 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡=(𝐸𝑥𝑝𝑒
Expected Return of a risky investment expected gain at end of[3A.1]
FVn C Future Value of Cash Flow [4.1] 𝐹𝑉_𝑛=𝐶∗(1+𝑟)^𝑛
𝑃𝑉=𝐶/(1+𝑟)^𝑛
Present Value of a Cash Flow PV C 1+r [4.2]
𝑃𝑉=𝑐_0+𝑐_1/((1+𝑟) )+𝑐_2/((1+𝑟) )+…+𝐶_𝑁/(
Present Value for a stream of cash flows PV C [4.3]
𝑃𝑉=∑129_(𝑛=0)^𝑁▒𝑃𝑉 (𝐶_𝑛 )=∑129_(𝑛=0)^𝑁▒𝐶_𝑛/(1+
Present Value of a stream of Cash flows PV C [4.4]
Future Value of a Cash Flow stream with a Present Value of PV[4.5] 𝐹𝑉_𝑛=𝑃𝑉∗(1+𝑟)^𝑛
NPV net present value PV(benefits) PV(costs) [4.6] 𝑁𝑃𝑉=𝑃𝑉(𝑏𝑒𝑛𝑒𝑓𝑖𝑡𝑠)−𝑃𝑉(𝑐𝑜𝑠𝑡𝑠)
𝑃𝑉(𝐶 𝑖𝑛 𝑝𝑒𝑟𝑝𝑒𝑡𝑢𝑖𝑡𝑦)=𝐶/𝑟
Present Value of a Perpetuity PV(C in perpetuiuty) C r [4.7]
𝑃𝑉(𝑎𝑛𝑛𝑢𝑖𝑡𝑦 𝑜𝑓 𝐶 𝑓𝑜𝑟 𝑁 𝑝𝑒𝑟𝑖𝑜𝑑𝑠 𝑤𝑖𝑡ℎ 𝑖𝑛𝑡𝑒𝑟
PV(Annuity of C for N periods with interest rate r) Present Val[4.9]
𝐹𝑉(𝑎𝑛𝑛𝑢𝑖𝑡𝑦)=𝑃𝑉∗(1+𝑟)^𝑁=𝐶/𝑟∗(1−1/
Future Value of an Annuity FV(Annuity) PV C r N (1+r)N [4.10]
𝑃𝑉(𝑔𝑟𝑜𝑤𝑖𝑛𝑔 𝑝𝑒𝑟𝑝𝑒𝑡𝑢𝑖𝑡𝑦)=𝐶/(𝑟−𝑔)
Present Value of a growing perpetuity PV(growing perpetuity)[4.11]
𝑃𝑉=𝐶∗1/(𝑟−𝑔)∗(1−((1+𝑔)/(1+𝑟))^𝑁 )
Present Value of a growing annuity PV C r-g [4.12]
𝑁𝑃𝑉=𝑃𝑉+𝑃𝑀𝑇∗1/𝑅𝐴𝑇𝐸∗(1−1/(1+𝑅𝐴𝑇𝐸)^𝑁𝑃
Using a spread sheet NPV RATE PMT FV [4.13]
𝐶=𝑃/(1/𝑟∗(1−1/(1+𝑟)^𝑁 ) )
Loan or Annuity Payment C P r (1+r) N 1/r [4.14]
𝐼𝑅𝑅 𝑤𝑖𝑡ℎ 𝑡𝑤𝑜 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤𝑠=(𝐹𝑉/𝑃)^(1/𝑁)−1
IRR with two cash flows FV/P 1/N [4.15]
𝐼𝑅𝑅 𝑜𝑓 𝑔𝑟𝑜𝑤𝑖𝑛𝑔 𝑝𝑒𝑟𝑝𝑒𝑡𝑢𝑖𝑡𝑦=(𝐶/𝑃)+𝑔
IRR of growing perpetuiuty C/P g [4.16]
Chapter 7
𝑃𝑟𝑜𝑓𝑖𝑡𝑎𝑏𝑙𝑖𝑡𝑦 𝐼𝑛𝑑𝑒𝑥=(𝑉𝑎𝑙𝑢𝑒 𝐶𝑟𝑒𝑎𝑡𝑒𝑑)/(𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒 𝐶𝑜𝑛
Profitability Index Value Created Resource Consumed NPV [7.2]
, Chapter 5
𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑛 𝑃𝑒𝑟𝑖𝑜𝑑 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑟𝑎𝑡𝑒=(1+
Equivalent n-Period discount rate (1+r) N [5.1]
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝑝𝑒𝑟 𝐶𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑃𝑒𝑟𝑖𝑜𝑑=𝐴
Interest rate per compounding period APR k Periods/year [5.2]
1+𝐸𝐴𝑅=(1+𝐴𝑃𝑅/𝑘)^𝑘
Converting APR to EAR 1+EAR APR/k k [5.3]
𝐺𝑟𝑜𝑤𝑡ℎ 𝑖𝑛 𝑃𝑢𝑟𝑐ℎ𝑎𝑠𝑖𝑛𝑔 𝑃𝑜𝑤𝑒𝑟=1+𝑟_𝑟=(1+𝑟)/(1+𝑖)=(
Growth in purchasing power 1+rr real interest rate [5.4]
𝑟_𝑟=(𝑟−𝑖)/(1+𝑖)
The real interest rate rr r i [5.5]
𝑃𝑉=𝐶_𝑛/(1+𝑟_𝑛 )^𝑛
Present Value of a cash flow in period n PV Cn rn n [5.6]
𝑃𝑉=∑129_(𝑛=1)^𝑁▒𝐶_𝑛/(1+𝑟_𝑛 )^𝑛
PV C r1 r2 Cn rn Present Value of a Cash Flow stream using a [5.7]
After tax interest rate r T r [5.8] 𝐴𝑓𝑡𝑒𝑟 𝑡𝑎𝑥 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒=𝑟−(𝑇∗𝑟)=𝑟∗(1−
The EAR for continuously compoundet APR e [5A.1] 1+𝐸𝐴𝑅=𝑒^𝐴𝑃𝑅
Continuously Compoundet APR for an EAR APR ln(1+EAR) [5A.2] 𝐴𝑃𝑅=ln(1+𝐸𝐴𝑅)
𝑃𝑉=𝐶/(𝑟_𝑐𝑐−𝑔_𝑐𝑐 )
Present value of continuously growing perpetuity rcc gcc C [5A.3] 𝑟_𝑐𝑐=ln(1+𝑟)
𝐶/(𝑟_𝑐𝑐−𝑔_𝑐𝑐 )≈𝐶 ̅_1/(𝑟−𝑔)∗(1+𝑟)^(1⁄2)
Mid year convention [5A.4]
Chapter 6
𝐶𝑃𝑁=(𝐶𝑜𝑢𝑝𝑜𝑛 𝑟𝑎𝑡𝑒∗𝑓𝑎𝑐𝑒 𝑉𝑎𝑙𝑢𝑒)/(𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑢𝑝𝑜𝑛 𝑝
Coupon Payment CPN Coupon rate face Value Number of Cou[6.1]
𝑃=𝐹𝑉/(1+𝑌𝑇𝑀_𝑛 )^𝑛
Price of a zero Coupon bond with ytm and face value P FV YT [6.2]
𝑌𝑇𝑀_𝑛=(𝐹𝑉/𝑃)^(1/𝑛)−1
Yield to Maturity of an n-Year Zero-Coupon Bond YTMn FV P [6.3]
Default free zero coupon bond risk free interest rate YTM yiel[6.4] 𝑟_𝑛=𝑌𝑇𝑀_𝑛
𝑃=𝐶𝑃𝑁∗1/𝑦∗(1−1/(1+𝑦)^𝑁 )+𝐹𝑉/(1+𝑦)^𝑁
Price of a coupon bond YTM y CPN y N FV [6.5]
𝑃=𝑃𝑉(𝐵𝑜𝑛𝑑 𝐶𝑎𝑠ℎ 𝑓𝑙𝑜𝑤𝑠)=(𝐶𝑃𝑁_1)/((1+𝑌𝑇𝑀_1 ) )+(𝐶𝑃𝑁_2
Price of a Coupon bond P PV(Bond cash flows) YTM CPN FV [6.6]
The YTM of a defaultable Bond exceeds the expected Return of investing in the bond
The Bond's expected return, which is equal to the firm's debt cost of capital is less than the YTM if there is risk of default. A
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