Principle Finance Summary Notes
Investment Appraisal
Time value of money: interest rates, compound FV = CF (1+r)n, continuous compound FV = CF x ert ,
continuous compound also FV = CF (1 + r/m)mt where monthly is 1/12, weekly is 1/52 and daily is 1/365
Discounting: moving backwards to work out a present value, PV = CF/(1+r)n , or conts PV = CF/ert
Perpetuities: constant stream of cash flows that never ends, PV = CF/r, growing: PV = CF/(r-g)
Annuity: stream of equal cash flows that lasts for a fixed # of periods, PV = CF x Annuity Factor (use tables)
Delayed Annuity: work out as if a normal annuity, then discount back to present time
Investment Decisions
NPV: net present value, NPV = PV(benefits) – PV(costs) = PV(all cash flows), decision is to take all
projects with a positive NPV, or the highest if choosing, reject negative NPV projects
𝑪𝑭𝒏
IRR: internal rate of return, discount rate that gives a project an NPV=0, NPV = ∑𝒕𝒏=𝟎 = 0, use of
(𝟏+𝑰𝑹𝑹)𝒏
𝑁𝑃𝑉1 (𝑟2 − 𝑟1 )
similar triangles for NPV/IRR graphs, IRR = 𝑟1 + 𝑁𝑃𝑉1 − 𝑁𝑃𝑉2
, issues: delayed payments, multiple IRRs,
non-existent IRRs
Risk and Uncertainty
States of Knowing: known knowns, knowns unknowns, unknown unknowns, unknown knowns
Sensitivity Analysis: looks at a project’s viability, and how a slight change in each variable could make
the project a failure. By setting the NPV=0 (breakeven) and looking at how much each variable would
need to change by, then calculating the percentage change in each needed for failure, we can see how
close the project is to become unviable
NPV = - I + [ V x ( S – ( L + M ) ) ] x AFn r
where: I = original investment, V = annual sales volume, S = sales revenue/unit, L = labour cost/unit, M =
material cost/unit, r = cost of capital, n = life of project, AF = annuity factor at cost of capital for a period
of time
issues are that is does not evaluate risk, it assumes the variables are independent
Scenario Planning: best, worst and base case scenarios, stress testing and risk mitigation, lets an
informed decision be made, limits on imagination, a supportive government and correctness in planning
Expected Value: a weighted average (probability of it happening * cost/units/etc)
Tree diagram: can look at probabilities for multiple possible scenarios
issues with EV: doesn’t look at individual probs (esp. bad in -NPV outcomes), doesn’t highlight the most
likely outcome
Monte Carlo Simulation: define cash flows, calculates NPV in each case, analyse a range of outcomes,
specify a distribution for each cash flow, BUT might create unrealistic scenarios, may not fully
acknowledge risks when placing inputs
Real Options:
financial options, buy/sell, commodity/stock, real option refers to the flexibility in some investment
decisions, true value may not be captured beforehand
Embedded options: discounted cash flow (DCF) can underestimate value of options
Option to delay/wait/defer: invest later? will tech change? let uncertainty clear? value added = NPV
after – NPV before
, Option to Abandon: less risky from an investors POV, option to review a project after the first period,
option to abandon and therefore have a lower possible loss, adds value to an NPV project
Human Behaviour: loss aversion, risk adversity, planning fallacy (humans don’t learn), overconfidence
(overestimation of NPV or cash flows, underestimate risk, too many -NPV projects get taken, however
benefits of more risk takers and possible entrepreneurs), project entrapment
Correcting Biases: behavioural view (hard to correct if people/managers believe they are doing the right
thing), managers invest in self-interest (may cause staff to rise up, which might lead to bad investments),
awareness, practical advice, sensitivity/scenario analysis, probability forecast > discount rate, involve
other decision makers, at the end of the day – nobody can predict everything
Long Term Financing
Cost of capital: cost of funds that a company raises and uses for investments, r.o.r for investors, a
minimum return, measured by looking a returns required by investors, used as the discount rate for
investment appraisal
Risk-free rate of return + Premium for business risk + Premium for financial risk = Cost of Capital
(base rate i.e govnt bonds)
Sources of funding: Internal (retained earnings, shareholders still need returns), debt, equity, hybrid
(characteristics of D & E)
D vs E
Cash Flows Tax Deductible Liquidation Life Management
Debt Fixed Yes High priority Finite maturity No role
Equity Residual No Low priority Infinite life Controlled
Private equity financing: eg. Angel investors, the entrepreneur themselves, family or friends
Initial Public Offering (IPO): selling stock to the public for the first time. Advantages: greater liquidity,
better access to capital, shares can be used in acquisitions. Disadvantages: equity holders become
widely dispersed, must satisfy all public company requirements, cost of going public (around 7%),
shareholder expectations, financial transparency and business scrutiny
Debt: bank loans (low legal costs, quick and simple, fixed rates above floating rates, interest rates),
corporate bonds (long term contract, annual interest, large variety) [callable bonds: allows issuer to
repurchase at predetermined price, may retire all outstanding bonds, these bonds are cheaper for
investors, usually if interest rate fall it will lead to a call-back], loan stock with warrants (long term
[years], the right to buy equity/stock at a particular date and price)
Hybrid Securities: Convertible debt (benefits of both debt and equity, issued cheaper, require careful
judgement, pre-determined price), Preference shares/Preferred stock (fixed collar dividend, do not
have a share of control in the firm, not tax-deductible/equity, does not have a maturity date, can be
designed, possible to not give out a regular cash dividend, convertibility, usually has preferential
divided and seniority in any liquidation), Option-Linked Bonds (ex1. linking the principle and even
interest payments to the price of the commodity, ex2 principle reduced in the case of a specific
catastrophe)
Cost of Debt: (irredeemable) cost is the post-tax interest as a % of the ex M.V of the bonds or preferred
shares, (redeemable) cost is IRR of the cash flows involved
kd = I / B0,XI = cash flow / current ex interest price; PV = cashflow / r ; bond price = interest / Kd
Redeemable debt capital: P = 1/(1+Kd) + … + (1+pn)/(1+Kd)n , pn amount payable on redemption in yrn
Cost of Equity:
• Dividend Valuation Model: stock price = div(annual cash flow)/r ;P0 = div/Ke ;Ke = div/P0 +
g
Investment Appraisal
Time value of money: interest rates, compound FV = CF (1+r)n, continuous compound FV = CF x ert ,
continuous compound also FV = CF (1 + r/m)mt where monthly is 1/12, weekly is 1/52 and daily is 1/365
Discounting: moving backwards to work out a present value, PV = CF/(1+r)n , or conts PV = CF/ert
Perpetuities: constant stream of cash flows that never ends, PV = CF/r, growing: PV = CF/(r-g)
Annuity: stream of equal cash flows that lasts for a fixed # of periods, PV = CF x Annuity Factor (use tables)
Delayed Annuity: work out as if a normal annuity, then discount back to present time
Investment Decisions
NPV: net present value, NPV = PV(benefits) – PV(costs) = PV(all cash flows), decision is to take all
projects with a positive NPV, or the highest if choosing, reject negative NPV projects
𝑪𝑭𝒏
IRR: internal rate of return, discount rate that gives a project an NPV=0, NPV = ∑𝒕𝒏=𝟎 = 0, use of
(𝟏+𝑰𝑹𝑹)𝒏
𝑁𝑃𝑉1 (𝑟2 − 𝑟1 )
similar triangles for NPV/IRR graphs, IRR = 𝑟1 + 𝑁𝑃𝑉1 − 𝑁𝑃𝑉2
, issues: delayed payments, multiple IRRs,
non-existent IRRs
Risk and Uncertainty
States of Knowing: known knowns, knowns unknowns, unknown unknowns, unknown knowns
Sensitivity Analysis: looks at a project’s viability, and how a slight change in each variable could make
the project a failure. By setting the NPV=0 (breakeven) and looking at how much each variable would
need to change by, then calculating the percentage change in each needed for failure, we can see how
close the project is to become unviable
NPV = - I + [ V x ( S – ( L + M ) ) ] x AFn r
where: I = original investment, V = annual sales volume, S = sales revenue/unit, L = labour cost/unit, M =
material cost/unit, r = cost of capital, n = life of project, AF = annuity factor at cost of capital for a period
of time
issues are that is does not evaluate risk, it assumes the variables are independent
Scenario Planning: best, worst and base case scenarios, stress testing and risk mitigation, lets an
informed decision be made, limits on imagination, a supportive government and correctness in planning
Expected Value: a weighted average (probability of it happening * cost/units/etc)
Tree diagram: can look at probabilities for multiple possible scenarios
issues with EV: doesn’t look at individual probs (esp. bad in -NPV outcomes), doesn’t highlight the most
likely outcome
Monte Carlo Simulation: define cash flows, calculates NPV in each case, analyse a range of outcomes,
specify a distribution for each cash flow, BUT might create unrealistic scenarios, may not fully
acknowledge risks when placing inputs
Real Options:
financial options, buy/sell, commodity/stock, real option refers to the flexibility in some investment
decisions, true value may not be captured beforehand
Embedded options: discounted cash flow (DCF) can underestimate value of options
Option to delay/wait/defer: invest later? will tech change? let uncertainty clear? value added = NPV
after – NPV before
, Option to Abandon: less risky from an investors POV, option to review a project after the first period,
option to abandon and therefore have a lower possible loss, adds value to an NPV project
Human Behaviour: loss aversion, risk adversity, planning fallacy (humans don’t learn), overconfidence
(overestimation of NPV or cash flows, underestimate risk, too many -NPV projects get taken, however
benefits of more risk takers and possible entrepreneurs), project entrapment
Correcting Biases: behavioural view (hard to correct if people/managers believe they are doing the right
thing), managers invest in self-interest (may cause staff to rise up, which might lead to bad investments),
awareness, practical advice, sensitivity/scenario analysis, probability forecast > discount rate, involve
other decision makers, at the end of the day – nobody can predict everything
Long Term Financing
Cost of capital: cost of funds that a company raises and uses for investments, r.o.r for investors, a
minimum return, measured by looking a returns required by investors, used as the discount rate for
investment appraisal
Risk-free rate of return + Premium for business risk + Premium for financial risk = Cost of Capital
(base rate i.e govnt bonds)
Sources of funding: Internal (retained earnings, shareholders still need returns), debt, equity, hybrid
(characteristics of D & E)
D vs E
Cash Flows Tax Deductible Liquidation Life Management
Debt Fixed Yes High priority Finite maturity No role
Equity Residual No Low priority Infinite life Controlled
Private equity financing: eg. Angel investors, the entrepreneur themselves, family or friends
Initial Public Offering (IPO): selling stock to the public for the first time. Advantages: greater liquidity,
better access to capital, shares can be used in acquisitions. Disadvantages: equity holders become
widely dispersed, must satisfy all public company requirements, cost of going public (around 7%),
shareholder expectations, financial transparency and business scrutiny
Debt: bank loans (low legal costs, quick and simple, fixed rates above floating rates, interest rates),
corporate bonds (long term contract, annual interest, large variety) [callable bonds: allows issuer to
repurchase at predetermined price, may retire all outstanding bonds, these bonds are cheaper for
investors, usually if interest rate fall it will lead to a call-back], loan stock with warrants (long term
[years], the right to buy equity/stock at a particular date and price)
Hybrid Securities: Convertible debt (benefits of both debt and equity, issued cheaper, require careful
judgement, pre-determined price), Preference shares/Preferred stock (fixed collar dividend, do not
have a share of control in the firm, not tax-deductible/equity, does not have a maturity date, can be
designed, possible to not give out a regular cash dividend, convertibility, usually has preferential
divided and seniority in any liquidation), Option-Linked Bonds (ex1. linking the principle and even
interest payments to the price of the commodity, ex2 principle reduced in the case of a specific
catastrophe)
Cost of Debt: (irredeemable) cost is the post-tax interest as a % of the ex M.V of the bonds or preferred
shares, (redeemable) cost is IRR of the cash flows involved
kd = I / B0,XI = cash flow / current ex interest price; PV = cashflow / r ; bond price = interest / Kd
Redeemable debt capital: P = 1/(1+Kd) + … + (1+pn)/(1+Kd)n , pn amount payable on redemption in yrn
Cost of Equity:
• Dividend Valuation Model: stock price = div(annual cash flow)/r ;P0 = div/Ke ;Ke = div/P0 +
g
