L1 – Introduction
L2 – Financial statement analysis
Overview L2
- Financial statements (financial reports) → written records of business activities and
financial performance of a company.
- 3 important financial statements
1. The statement of financial position (balance sheet)
2. The income statement
3. The cash flow statement
The statement of financial position
Non-current assets = fixed assets
-
The statement of financial position (balance sheet) is an accountant's snapshot of a
firm's accounting value on a particular date.
Lists a company's resources (assets) and how they are financed (equity and liabilities)
The Accounting Equation: Assets = Liabilities + Shareholders' equity
Net working capital
- Net working capital = current assets – current liabilities
The income statement
- The income statement (statement of profit and loss) measures performance over a
specific period.
- Revenue − Expenses = Net Income
- Operating expenses:
Cost of goods sold (COGS) ← the direct cost of earning the main revenues (e.g.,
materials, labour, depreciation of PPE used in production)
Other operating costs (e.g., R&D, SG&A)
- Operating income (EBIT) = Revenues - Operating expenses
Corporate taxes
- Marginal tax rate – the tax rate you pay if you earn one more unit of currency.
- Average tax rate – the proportion of the taxable income that goes to pay taxes
The tax rate is 16% for taxable income up to 200,000 and 22.25% for income
above 200,000. → The amount of tax paid is: 16% × 200, 000 + 22.25% × (400,
000 − 200, 000) = 76, 500
The average tax rate is:
Tax paid / Profit before tax = 76, 500 / 400, 000 = 19.125%
The marginal tax rate is 22.25%.
The cash flow statement
-
The statement of cash flows  explains the change in accounting cash and
equivalents.
It shows the firm's cash receipts (inflow) and cash payments (outflow) during a
specified period.
The net cash flow is the sum of cash flows resulting from operating, investing and
financing activities
Comparing performance
Comparing profitability
- Gross (profit) margin = Gross profit/Revenues
Gross profit = Revenues - COGS
- Operating (profit) margin = EBIT/Revenues
- Profit margin = Net income/Revenues
Comparing performance – it is important to compare like for like
Financial ratios
- Financial ratios are traditionally grouped into the following categories:
Short-term solvency or liquidity
o Assess the firm's ability to pay its bills over the short run without undue
stress.
Long-term solvency or financial leverage
o Assess the firm's long-run ability to meet its obligations
Asset management or turnover (kapitalomsättningshastighet)
o Describe how efficiently, or intensively, a firm uses its assets to generate
sales.
Profitability
o Measure performance
Market value
o Involve market-based information (e.g., share price, market value of
equity), applicable for publicly traded firms only
Liquidity measures
Long-term solvency measures
Asset management measures
Profitability measures
Decomposing ROE
DuPont  ROA
Decomposing ROE with The Du Pont identity
-
ROE is affected by
1. Operating efficiency (as measured by profit margin)
2. Asset use efficiency (as measured by asset turnover)
3. Financial leverage (as measured by equity multiplier)
Financial leverage and ROE
- Let´s define operating return on assets
OROA = operating ROA
Also measures how efficiently a firm manages its operations
But unaffected by capital structure
-
ROE can be expressed as
-
When would shareholders prefer more leverage?
A) OROA > interest rate
B) OROA < interest rate
A is the correct answer
-
Let's consider firm U
Total assets =100 million
All equity financed
Corporate tax rate = 40%
Its performance depends on the business cycle as below
OROA = EBIT / Total Assets
Net Income = EBIT – interest rate (0) – Tax = (1-t)(EBIT – interest rate)
ROE = Net Income / Equity
-
Now suppose that firm L that is identical to firm U except for its capital structure
60% equity and 40% debt;
interest rate = 8%
-
Compare the two firms' ROE
When OROA > interest rate  more leverage
Decomposing ROA
Market value Measures
Using financial statement information – choosing a benchmark
- Benchmark can be the firm itself, then you compare over time
- You can also compare across firms
Comparing over time
Comparing across firms
L3 – bond valuation
Overview L3
- Debt financing
Bank loans
Bonds
- Bond valuation
Bank loans
Bonds vs. bank loans
- Bonds
Principal not normally paid until end of bond life
Public
- Bank loans
Repayments normally in the form of annuity
Private
What is a bond? – A brief introduction
- A bond is a legally binding agreement between a borrower and a lender that specifies
the details of the loan and its payment (bond's features)
o Par (face) value
o Coupon rate
o Coupon payment
o Maturity Date
Bond quote – usually as a percentage of face value (102,5 in the chart)
Coupon – coupon amount = coupon rate x face value
How to value bonds
- Primary principle: Value of financial securities = PV of expected future cash flows
- Bond value is, therefore, determined by the present value of the coupon payments and
par value.
- The discount rate is the interest rate prevailing in the market or the bond's rate of
return (YTM).
Different types of bonds
-
Pure discount – no coupon, only principal
Fixed rate – coupon and principal
Consol – coupon, no principal
Principal = face value of the bond
Bond´s cash flow
Pure discount bonds
- Value of a pure discount bond
R = market interest rate
F = face value
T = time for maturity
Coupon bonds – fixed rate bonds (ATR)
- Value of a coupon bond
Two types of rents
Coupon rate = stated in the borrowing contract.
Interest rate = ca styrränta
Consol bonds
- Value of a consol bond
Yield to maturity
- The yield to maturity (YTM) is defined as the discount rate that makes the present
value of a bond's payments equal to its price.
-
It is viewed as a measure of the average rate of return that will be earned on a bond if
it is bought now and held until maturity.
To calculate the YTM, we solve the bond price equation for the interest rate given the
bond's price.
Relationship between YTM and Bond Value
Interest rates and bond prices
-
Higher interest rates  lower bond prices
Lower bond price  higher interest rates
-
At the face value (par or principle) if the coupon rate is equal to the market-wide
interest rate
At a discount if the coupon rate is below the market-wide interest rate
At a premium if the coupon rate is above the market-wide interest rate
-
Why par / premium / discount?
- Par bonds: (coupon rate = YTM)
o The coupons compensate bond investors for exactly what the market is asking
in terms of time value of money. Hence, the bond sells for PAR (the face
value).
o Coupon rate = market interest rate (R) = YTM.
- Premium bonds: (coupon rate > YTM)
o Coupons are fixed and they are over-compensating investors at a rate that is
higher than the market rate of interest.
o Hence the bond price increases above PAR, which makes the YTM decrease
below the coupon rate. Coupon rate > market interest rate = YTM.
- Discount bonds: (coupon rate < YTM)
o The coupons are fixed, but they are not compensating investors sufficiently
compared with the market rate of interest.
o Hence the bond price decreases below PAR, which makes the YTM increase
above the coupon rate. Coupon rate < market interest rate = YTM
Non-annual coupon bonds
Non-coupon paying dates
Pricing between coupon dates
-
If you buy a bond between coupon payment dates, the price you pay is usually more
than the quoted price, because:
o It is a standard convention in the bond market to quote prices net of accrued
interest. This quoted price is called the clean price.
o The price you actually pay includes accrued interest. This price is called the
dirty price (or invoice price)
Why using quoted price?
-
Bond traders want to know the unpredictable effect of market changes on bond prices,
e.g. affect of changes in market interest rates, unemployment, inflation, etc.
Accrued interest affects bond prices in a predictable way. So bond traders remove it
from the quoted price, i.e. ”clean the price of accrued interest”
L4 – stock valuation
Overview
- The present value of equity
- Growth opportunities
- Firm valuation
The present value of equity
Valuing a security
- Primary principle: value of financial securities = PV of expected future cash flows
R = discount rate reflecting the riskiness of the cash flows being valued
-
Valuing bonds
The answer is both.
The dividend-discount model: A one-year investor
- Potential cash flows
o Dividend
o Sale of stock
-
Timeline
-
Today´s price
R = discount rate for equity (required rate of return on equity, cost of equity, market
capitalization rate
The dividend-discount model
- What is the price P1 determined?
-
Substitute the value of P1 from (2) into (1)
-
Repeating this process by the following
 value of equity = PV of expected future dividends
Zero growth DDM
Constant growth DDM
Constant growth DDM
Differential Growth DDM
Differential Growth
Estimates of parameters in the dividend growth model – growth rate
- Consider a business whose earnings next year are expected to be the same as earnings
this year unless a net investment is made.
- Net investment will be positive only if some earnings are not paid out as dividends,
i.e., some earnings are retained.

-
Divide both sides of the previous equation by earnings this year, we get
-
Let b denote the retention ratio, i.e., the ratio of retained earnings
We have the following
-
g defined as in the previous slide is the growth rate in earnings.
When the dividend pay-out ratio is constant, the growth in dividends is equal to the
growth in earnings.
We can estimate the expected return on retained earnings by historical ROE
-
 We can estimate the growth rate in our DDM as:
Estimate growth
Expected returns
- Recall the following
-
What is the expected total returns that the investor will earn for a one-year investment
in the stock?
E(r) = expected total returns
-
Rearranging (1)

R = required return
E(r) = R  The expected total return of the stock should equal the expected return of
other investments available in the market with equivalent risk
Estimates of parameters in the dividend growth model – required return
- Recall the constant growth DDM
-
Under the constant growth DDM, the share price also grows at the same rate as
dividends
P – 0 is wrong, supposed to be P0
Growth opportunities
Dividends vs. investment and growth
- A firm's earnings can be:
1) paid out to shareholders (as dividends), or
2) retained and reinvested in the business
Investing more today can increase future earnings and dividends
-
To increase the share price, should the firm
1) cut its dividends and invest more? or
2) cut its investment and increase dividends?
Cutting the firm's dividend to increase investment will raise the stock price if, and
only if, the new investments have a positive NPV
Growth opportunities
-
Before the campaign: the firm is a no growth firm  it pays out all its earnings as
dividends
-
The share price when the firm acts as a cash cow:
-
Value of the campaign date 1:
Cutting dividends for profitable growth
-
No-growth price  zero growth DDM
Div1=EPS1 because they pay out all their earnings.
-
New policy: pay-out ratio = 75%
 Div1 = Dividend Pay-out Ratio × EPS1 = 0.75 × 6 = $4.5
g = (1 – 0.75) × 12% = 3%
Dividends vs. investment and growth
- Cutting dividends to invest in new stores will increase Crane's share price ($60 
$64.29)
Because new investments are value-creating (positive NPV projects)  rate of
return (12%) > cost of capital (10%)
-
What if growth is unprofitable?
Unprofitable growth
- Growth rate under new policy: g = (1 − 0.75) × 8% = 2%
- Share price under new policy:
-
Crane's share price will fall if it cuts its dividend to make new investments with a
return of only 8% when its investors can earn 10% on other investments with
comparable risk
Unprofitable growth: new investments have negative NPV
NPVGO
Firm valuation
Market multiples
- Rationale: if the financial market is efficient, companies with similar characteristics
will have similar values.
Valuing a firm using market multiples
- Identify comparable firms
o Similar risk, growth potential and cash flows
o Differences in multiples could be result of differences in firm fundamentals
(e.g., growth) rather than mispricing.
-
Calculate the relevant multiples for the comparable firms
o Use forward-looking multiples
o Calculate multiples in a consistent manner
Differences in multiples could be result of differences in measurement or
accounting distortion rather than mispricing
-
Apply these multiples to the corresponding measures for the target firm:
Value = Multiple of comparables × Firm-specific variable.
Price-earnings ratio
- P/E = Market price per share/Earnings per share
- P/E and growth opportunities:
When comparing market multiple it is important to understand what drives these
multiples
-
Deriving fundamentals
-
Determinants of P/E:
o Growth → P/E increases with growth rate
o Risk → P/E decreases with risk
o Pay-out ratio → P/E increases with pay-out ratio
-
P/E increases as ROE increases
L5 – Capital budgeting – Net present value and other investment rules
Overview
- Net present value
- Internal rate of return
- Other investment rules
Payback period
Discounted payback period
Profitability index
Modified IRR
Margin of safety
Net present value
Net present value
- You can evaluate an investment decision by calculating the net present value (NPV) of
the project's cash flows.
- NPV compares the present value of cash inflows (benefits) to the present value of cash
outflows (costs).
Cash inflows may include:
o Receipts from sale of goods and services
o Receipts from sale of physical assets
Cash outflows may include:
o Purchase of materials, expenditure on labour for manufacturing Selling
and administrative
- It represents the surplus economic value of the project.
-
Formula
Cash outflows are denoted with negative numbers
Cash inflows are denoted with positive numbers
Calculating NPV
- Adjusting the expected CFs of a project by their risk and timing to determine how
much they are worth to us today
Independent vs. mutually exclusive projects
- Independent projects:
Independent Projects are investments that have no impact on each other's cash
flows.
The decision to accept or reject one project will have no impact on whether the
other projects are accepted or rejected.
The firm could accept one or more projects or it could reject them all
- Mutually exclusive projects:
Mutually Exclusive Projects are investments in which accepting one project
requires rejecting all others.
This may be due to financial constraints or limitations to available assets.
Projects need to be ranked in order to determine which to undertake
Two examples of mutually exclusive projects
A company has a piece of land and it is debating either to build an o-ce block on
the land or a warehouse. It cannot use the same piece of land for two different
things at the same time. These are mutually exclusive projects
A company has a fixed budget of $20,000 for investment this year. The firm is
considering two projects. The first will take $15,000 to establish and the second
project will require $18,000. Only one project can be carried out this year so
they are mutually exclusive
The NPV decision rule
- Independent projects:
Accept if NPV > 0
Reject if NPV < 0
-
Mutually exclusive projects:
Select the project with highest positive NPV.
-
The NPV method is consistent with the company's objective of maximizing
shareholders' wealth.
A project with a positive NPV will leave the company better off than before the
project and, other things being equal, the value of the company's shares should
increase.
Internal Rate of Return
Internal Rate of Return
- The internal rate of return (IRR) is the discount rate that makes the present value of a
project's net cash flows equal to the initial cash outlay.
IRR is the rate of return that makes NPV=0 (or when NPV=0)
The IRR Decision rule
- The general rule:
Accept the project if IRR > required rate of return,
Reject if IRR < required rate of return
- This is equivalent to accepting positive NPV projects
- Applies to investing-type projects (cash outflow first, followed by cash inflow later)
Calculating IRR
In this case you can also use the rate function, which we use when finding R.
=IR(table consisting CF)
=RÄNTA(period;C;C0)
Problems with the IRR Method – Problems affecting independent and mutually exclusive
projects
Project A – typical investment
Project B – for example borrowing from a bank
Project C – mixture
- Decision rules – investing vs. financing
a) Investing: negative cash flow first; followed by positive cash flows
Number of IRRs: 1
Accept if IRR > R; reject if IRR < R
Accept if NPV > 0; reject if NPV < 0
b) Financing: negative cash flow first; followed by positive cash flows
Number of IRRs: 1
Accept if IRR < R; reject if IRR > R
Accept if NPV > 0; reject if NPV < 0 C
c) Mixture of positive and negative cash ows: cash ows change sign more than once
Number of IRRs: usually more than 1
No valid IRR
Accept if NPV > 0; reject if NPV < 0
-
Mutually exclusive projects – the scale problem
IRR ignores scale – you can not use it alone to decide which one is better when you
have mutually exclusive projects. Instead you have to use the incremental cash flows
Incremental cash flows
-
You calculate the Incremental IRR by the following
Since this is higher than the discount rate (25%) you should choose this project.
The reason that we choose the larger project is because you can apply the general rule
of IRR which is that if the IRR is higher than the discount rule you should choose this
project.
Incremental IRR = IRR of the cash flows
-
Incremental NPV
Should be 1+0,25, not 1+25
-
Investment decision
Mutually exclusive projects – the timing problem
1) Compare the NPVs of the two projects
2) Compare incremental IRR to discount rate, or
3) Calculate NPV on incremental cash flows
IRR ignores timing
-
Mutually exclusive projects
1) Compare incremental IRR to discount rate
Project B is preferred over project A if discount rate R < 10.55% 2
2) Calculate NPV on incremental cash flows.
Project B is preferred over project A if incremental NPV > 0 (i.e., R < 10.55%)
3) Compare the NPVs of the 2 projects:
NPVA = NPVB at 10.55% discount rate (cross-over rate)
R < 10.55%  NPVB > NPVA → select project B
R > 10.55%  NPVA > NPVB → select project A
Other investment rules
The payback period – how long does it take until I earn my money back?
- Consider a project with the following cash flows
-
It takes 2 years for the investor to recover the initial investment.
Payback period = 2 years.
Decision rule:
Accept the project if its payback period is less than your firm's benchmark
Reject if payback period is greater than your firm's benchmark
Fraction = 20/40 = 0,5
Payback period = 2,5 years
Problems with the Payback Method
- Does not consider the timing of the cash flows
- Ignores all cash flows occurring after the payback period
- Arbitrary standard for choosing the cut-off date
The discounted payback period – how long does it takes until the projects creates value?
- First discount the cash flows, then calculate how long it takes for the discounted cash
flows to equal the initial investment
- Decision rule:
Accept the project if the discounted payback period is less than your firm's
benchmark
Reject if discounted payback period is greater than your firm's benchmark
-
Suppose the discount rate is 10%
Discounted payback period = 2,825 years
The profitability Index
- The profitability index (PI) is the ratio of the PV of the future expected cash flows
after the initial investment divided by the amount of the initial investment.
-
Decision rule:
Accept if PI > 1
Reject if PI < 1
Calculating the profitability Index
-
PV of the cash flows after the initial investment is
-
The project’s profitability index is:
The modified Internal Rate of Return
- The IRR method assumes that cash flows earned in the future are reinvested at the
same rate as the IRR.
- When the reinvestment rate is different from the IRR → use the modified IRR (MIRR)
method
Calculating the MIRR
1) Calculating the terminal value of the project cash flows using the reinvestment rate
Terminal cash flow calculation
Year 1  400*1,1^3
Year 2  400*1,1^2
Year 3  300*1,1^1
2) Calculate the MIRR
Margin of safety
- Accept a project only if its present value is a certain percentage above the asking price
or initial investment
PV of future cash flows
The margin of safety
L6 – Making Capital investment decisions
Overview
- Incremental cash flows
- Capital budgeting Analysis
Incremental cash flows
Cash Flows vs. Accounting Income
Weber-Decker just paid 1 million in cash for a building as part of a new capital
budgeting project.
Assume 20% reducing balance depreciation over 20 years, only 200,000 is considered
an accounting expense in the current year (current earnings are reduced by only
200,000).
For capital budgeting purposes, the relevant cash outflow at date 0 is the full 1 million,
not the reduction in earnings of only 200,000.
Incremental Cash flows
- In calculating the NPV of a project, only cash flows that are incremental to the project
should be used.
- Incremental cash flows are the changes in the firm's cash flows that occur as a direct
consequence of accepting the project.
That is, the difference between the cash flows of the firm with the project and the
cash flows of the firm without the project.
Sunk costs
-
A sunk cost is a cost that has already occurred.
Rule: Ignore all sunk costs
Because sunk costs are in the past, they cannot be changed by the decision to
accept or reject the project
Opportunity costs
-
Opportunity costs are lost revenues that you forgo as a result of making the proposed
investment.
Rule: Incorporate opportunity costs into your analysis.
Side effects
- A side effect is classified as either erosion or synergy
Erosion is when a new product reduces the cash flows of existing products.
Synergy occurs when a new project increases the cash flows of existing projects.
- Rule: Include side effects into the analysis.
Allocated costs
- An allocated cost is an accounting measure to reflect expenditure or an asset's use
across the whole company.
- Rule: Should be viewed as a cash outflow only if it is an incremental cost of the
project.
Capital budgeting analysis
How to carry out a capital budgeting analysis
1) Calculate Depreciation
2) Prepare Income Statement
3) Generate Cash Flow Forecast
4) Investment Appraisal
Energy Renewables Ltd: an example
- History:
Established in 2001.
Manufacture and research new solar power technology.
Recently developing towards wind energy.
- Market research:
Wind turbines to provide low-cost energy to manufacturers that have an explicit
environment policy relating to industrial waste.
Cost 250,000
Positive feedback
-
-
-
-
-
The turbines would be manufactured in a large vacant lot owned by the firm. The
vacant lot has been valued by an independent surveyor, who estimates that it could be
sold now for 1,500,000 after taxes.
The technology underlying the wind turbines is expected to be obsolete after five
years, at which point the project will be terminated.
The cost of the manufacturing facilities is 3,000,000. The facilities are expected to
have an estimated market value at the end of five years of 1,000,000. Assume capital
allowances rate on plant and machinery is 20% per annum.
Production of wind turbines by year during the five-year life of the project is expected
to be as follows: 8 units, 12 units, 24 units, 20 units, 12 units.
The price of turbines in the first year will be 200,000. The turbine market is uncertain,
so you expect that the price of turbines will increase at only 2% per year, as compared
to the anticipated general inflation rate of 5%.
The rare metals used to produce wind turbines are rapidly becoming more expensive
 production cash outflows are expected to grow at 10% per year. First-year
production costs will be 100,000 per unit.
Net working capital (i.e., investment in raw materials and inventory) will immediately
(year 0) grow to 100,000. This will remain level until year 2, when it will grow to
-
¿160,000, then increase again to 250,000 in year 3. By year 4 the project will be
winding down and net working capital will be 210,000. At the end of the project, net
working capital will return to zero as all inventory and raw materials are sold of.
Based on Energy Renewables' taxable income, the appropriate incremental corporate
tax rate in the wind turbine project is 20%. The appropriate discount rate for this type
of investment is 12%.
Step 1 – depreciation
- The cost of the manufacturing facilities is 3,000,000.
- The facilities are expected to have an estimated market value at the end of 5 years of
1,000,000.
- Applying reducing balance depreciation of 20% (i.e., the asset is depreciated by 20%
per year)
Step 2 – income statement
- Estimate Sales Revenues:
Production of wind turbines by year: 8 units, 12 units, 24 units, 20 units, 12
units.
Price in the first year will be 200,000. Price will increase at 2% per year.
Price2 = Price1 × 1.02 = 200, 000 × 1.02 = 204, 000
Sales Revenues = Quantity produced × Turbine price
Sales1 = 8 × 200, 000 = 1, 600, 000
-
Estimate Operating Costs
First-year production costs will be 100,000 per unit. These costs will grow at
10% per year.
Cost per unit2 = 100, 000 × 1.1 = 110, 000
Operating costs = Cost per unit × Quantity produced
Operating costs1 = 100, 000 × 8 = 800, 000
Income statement
-
Income before tax = Sales − Operating costs − Depreciation
Tax = Tax rate × Income before tax
Net income = Income before tax – Tax
Step 3 – Cash Flow Forecast
-
-
Capital Investment:
Manufacturing facilities
Cost = 3,000,000 → Cash outflow in year 0 is 3,000,000.
Estimated market value at the end of 5 years = 1,000,000. → Cash inflow in
year 5 is 1,000,000.
Vacant lot
The vacant lot has been valued by an independent surveyor, who estimates that
it could be sold now for 1,500,000 after taxes → Opportunity cost = 1,500,000
-
Net working capital:
Net working capital (i.e., investment in raw materials and inventory) will
immediately (year 0) grow to 100,000.
This will remain level until year 2, when it will grow to 160,000, then increase
again to 250,000 in year 3. By year 4 the project will be winding down and net
working capital will be 210,000.
At the end of the project, net working capital will return to zero as all inventory
and raw materials are sold off.
-
Investment in working capital (∆NWC):
Increases in NWC are viewed as cash outflows.
Decreases in NWC are viewed as cash inflows
-
Investment cash flows
-
Investment cash flows include
Capital investment
Investment in working capital
-
Operating cash flows
-
Incremental cash flows
Step 4 – investment appraisal
L7 – making capital investment decisions
Overview
- Incremental cash flows
- Energy Renewables Ltd: An Example
- Inflation and Capital Budgeting
- Alternative Definitions of Operating Cash Flow
- Investments of Unequal Lives: The Equivalent Annual Cost Method
- The General Replacement Decision
Inflation and capital budgeting – what to do when inflation is high
-
How does inflation affect interest rates?
-
An approximate formula for real interest rates
-
Real and nominal interest rates – an example
-
Nominal cash flows and real cash flows
Nominal cash flows – the actual money in cash to be paid out or received
Real cash flow – the purchasing power of the cash once inflation has been taken into
account
-
What to Discount – nominal or real cash flows?
Be consistent
Nominal cash flows  use nominal discount rate
Real cash flows  use real discount rate
-
Nominal vs. real cash flows: example
Nominal terms
Revenue and cash expenses * inflation because it is given in real terms
Real terms
Depreciation/inflationt because it is given in nominal terms
Alternative definitions of operating cash flow – Three methods
- The bottom-up approach
OCF = Net income + depreciation
-
The top-down approach
OCF = Sales – Costs – Taxes
-
The tax-shield approach
OCF = (sales – costs) x (1 – tc) + Depreciation x tc
-
Example
The bottom up approach
Project net income = EBIT – Taxes = 144
OCF = Net income + Depreciation = 144 + 600 = 744
The top-down approach
OCF = Sales – Cost – Taxes = 1500 – 700 – 56 = 744
The tax shield approach
OCF = (Sales – Costs) × (1 - tc ) + Depreciation × tc= (1500-700) x 0.72 + 600 x 0.28
= 744
Investments of unequal lives
- The equivalent annual cost method – how to compare the Present Value of projects of
different lives
DON´T do the following
Compare like with like – calculate the equivalent annual cost
-
We equate the single payment €798.42 (€916.99) at date 0 with a three (four) year
annuity:
The general decision to Replace
- When to replace a machine?
When the annual cost of keeping the old machine is higher than the EAC for the new
machine
The present value of the cost of the new replacement machine is as follows:
The EAC of a new replacement machine equals:
Cost of old machine:
If BIKE keeps the old machine for one year, the firm must pay maintenance cost of
£1,000 a year from now. BIKE will receive £2,500 at date 1 if the old machine is kept
for one year but would receive £4,000 today if the old machine were sold
immediately.
Therefore, the PV of the costs of keeping the machine one more year before selling it
equals to:
The future value one year from now would be: £2,696 × 1.15 = £3,100
BIKE should replace the old machine immediately to minimize the expense at year 1
L8 – risk analysis, Real options and capital budgeting
Overview
- Sensitivity Analysis, Scenario Analysis and Break-Even Analysis
- Monte Carlo Simulation
- Real Options
Sensitivity Analysis, Scenario Analysis and Break-Even Analysis
- Differentiating between the three methods
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Sensitivity analysis – example
Solar Electronics (SE) has recently developed a solar-powered jet engine and wants to
go ahead with full-scale production. The initial (year 0) investment is £1,500 million,
followed by production and sales over the next 5 years.
Breakdown of revenue assumptions
Assumptions: market share; market size; unit price
Breakdown of cost assumptions
Assumptions: market share; market size; unit cost
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Choose best- and worst- case estimates
Find NPV for each variable outcome
This table shows which variables that are most sensitive and which ones that are the
most important (Market size and Market size)
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What does sensitivity analysis tell us?
Backup – if there are many negative NPVs in the sensitivity analysis, more
investigation is needed
Influential variables – sensitivity analysis identifies influential variables. These
variables must be estimated with more accuracy
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Weakness of sensitivity analysis
If assumptions are wrong, may increase sense of security
Each variable is treated in isolation
Scenario analysis
You can change more than one variable at the same time.
Assume market size is 70% of expectation = 7 000
Assume market share is 2/3 of expectation = 20%
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Scenario analysis – Example
Number of jet engines sold per year = Market share × Market size
1,400 = 0.20 × 7,000
Annual sales revenue = Number of jet engines sold × Price per engine
2,800 = 1,400 × 2
Variable cost per year = Variable cost per unit × Number of jet engines sold per year
1,400 = 1 × 1,400
Recreate cash flows under scenario
Break-even analysis
- Accounting – find input value for a break-even profit over life of project
- Financial – find input value for a zero NPV
Accounting break-even analysis
Break-even point is where blue and green cross
The sales price is £2 million per engine;
The variable cost is £1 million per engine;
Pre-tax contribution margin:
Sales price – variable cost = £2 – £1 = £1
Fixed costs including depreciation:
Fixed costs + Depreciation= £1,791 – £300 = £2,091
As long as annual sales are above 2,091 jet engines, the project will make a
profit.
Financial break-even analysis
You want the NPV to break even.
We look at opportunity cost in financial break-even.
The firm originally invested £1,500 million. This initial investment can be expressed
as a 5-year equivalent annual cost (EAC), determined by dividing the initial
investment by the appropriate 5-year annuity factor:
If we take into account that the £1,500 million could have been invested at 15 per cent,
the true annual cost of the investment is £447.5 million, not £300 million.
Depreciation understates the true costs of recovering the initial investment.
In addition to the initial investment’s equivalent annual cost of £447.5 million, the
firm pays fixed costs each year and receives a depreciation tax shield each year.
After-tax costs, regardless of output, can be viewed like this:
After-tax costs = EAC + Fixed costs × (1-tax rate) – Depreciation × tax rate
After-tax costs = £447.5 + £1,791 (1 – 0.28) – £300 × 0.28 = £1,653
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Thus, 2,296 engine planes is the break-even point from the perspective of present
value.
Break-even analysis – Overview
- Accounting – investments shouldn´t make a loss
- Investments should have a positive NPV
Monte Carlo simulation – random sampling
- How to undertake a monte Carlo simulation
Sensitivity analysis allows only one variable to change at a time.
Scenario analysis cannot cover all sources of variability.
-
Monte Carlo simulation is a further attempt to model real-world uncertainty.
Name comes from the famous European casino
Analyses projects the way one might analyse gambling strategies
Sensitivity analysis allows only one variable to change at a time.
Scenario analysis cannot cover all sources of variability.
Play thousands of hands in a casino, sometimes drawing a third card when your
first two cards add to 16 and sometimes not drawing that third card. You could
compare your winnings (or losings) under the two strategies to determine which
were better.
How to undertake a Monte Carlo simulation
1) Specify the Basic model
2) Specify a distribution for each variable
3) The computer draws one outcome
4) Repeat the procedure
5) Calculate the NPV
Monte carlo simulation – example
Backyard Barbeques (BB), a manufacturer of both charcoal and gas grills, has a
blueprint for a new grill that cooks with compressed hydrogen.
A consultant specializing in the Monte Carlo approach, Lester Mauney, takes the
company through the five basic steps of the method.
Les Mauney breaks up cash flow into three components:
Annual revenue
Annual costs
Initial investment
Real options – the option to expand; the option to abandon; timing options
- What is a Real Option?
An option to adjust operations once a project has started
Three types: option to expand; option to abandon; timing option
Option to expand
- Option to expand – example
Conrad Willig, an entrepreneur, recently learned of a chemical treatment causing
water to freeze at 20 degrees Celsius rather than 0 degrees. Of all the many practical
applications for this treatment, Mr Willig liked the idea of hotels made of ice more
than anything else. Conrad estimated the annual cash flows from a single ice hotel to
be £2 million, based on an initial investment of £12 million. He felt that 20 per cent
was an appropriate discount rate, given the risk of this new venture. The cash flows
would be perpetual.
Option to abandon
Timing options
- Why would anyone pay a positive price for land that has no source of revenue?
Suppose that the land’s best use is: office building
Total construction costs for the building are estimated to be €1 million
Net rents are estimated to be €90 000 per year in perpetuity,
Discount rate is 10 per cent
The NPV of this proposed building would be:
-€1 000 000 + €90 000/0,10 = -€100 000
L9 – externalities and LCA
Overview
- Sustainability and investment appraisal
- Life Cycle Analysis
- Social LCA
- Investment appraisal exemplified
Sustainability and investment appraisal
- When do we add value?
When the sum of all expected incremental cash flows discounted with a risk-adjusted
discount rate exceeds the initial outlay (the price of the investment).
-
Net present value (NPV) – the sum of all future discounted cash flow subtracted by
the initial outlay
-
Private and social costs
Private costs + External costs = Social cost
With regulatory approaches we come closer to Q2 instead of Q1
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Private and social benefits
External benefits – for example a bee keeper that pollinates a farmer´s flowers without
getting any private benefit from it. The bee keeper generates a social benefit that the
bee keeper cannot monetize on. As a society we want to see more of it than what is
produced by the bee keeper because of the positive effects it has on the society.
(Q1Q2)
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Regulatory approach
Taxes – Carbon tax or Alcohol and tobacco
Investment subsidies – Solar power
Cap and trade – EU ETS
Certificates – Green certificates
Bonus-Malus – NOx
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Social preferences – Substituting classical preferences for social preferences
Accepting lower returns
Boost revenues (PQ)
Increased demand
Price premium
Lower costs
Smaller input volumes
Lower reservation prices (e.g. salaries)
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Sustainability and risk management
Sustainability concerns may impact not only the cash flows of an enterprise.
It could also impact the business risk.
Reputation risk
Litigation risk
Political risk
NB: Idiosyncratic risk (the Beta does not capture this risk) and market risk (finance
theory)
LCA – life cycle assessment
- What is LCA?
Assessing all the inputs and outputs of a product, process or service; assessing the
associated wastes and burdens to human health and ecosystems; and interpreting the
results of the assessments for the whole life cycle of the product/process/service under
review.
Cradle-to-grave
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LCA components
Goal Definition and Scoping
Inventory Analysis
Impact Assessment
Interpretation
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Goal Definition and Scoping
1) Define goal(s) – differentiate between primary and secondary goals
2) Determine what data is needed – depends on the goals
3) Determine how data should be organized and displayed – make a functional unit
that makes it possible to compare for example do not define how thick isolation is,
but instead define how well it isolates heat.
4) Determine what to include – depends on the goal. Which part of the production
process should you study? Everything?
5) Determine the required accuracy – a trade-off. Difficult to determine because you
often have to do estimations.
6) Determine ground rules – document assumptions
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Life cycle inventory – The process of quantifying energy and raw material
requirements, emissions wastes and other releases for the entire life cycle of the
product.
-
Develop a flow diagram
System boundaries vary between projects.
Goal definition determines initial boundaries that define what is included.
The more complex, the greater the accuracy
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Life cycle impact assessment
The evaluation of potential human health and environmental impacts that follow
from the resource usage and emissions identified in the inventory.
The impact assessment offers a more precise basis to make comparisons than the
inventory.
What are the impacts of the emissions identified? For global warming? For
ocean acidification? For water depletion? What is less preferable?
May incorporate value judgments.
Key steps
1) Select and define impact categories – global warming, water depletion etc
2) Classification – we relate the items from the inventory to the chosen
categories
3) Characterization – convert and combine the results from the lifecycle
inventory into representative indicators of impacts to human health and
ecological health
4) Normalization – optional from a legal point of view. Here you relate your
result to something else to evaluate its´ relative importance.
5) Grouping – optional from a legal point of view.
6) Weighting - The qualitative or quantitative procedure where the relative
importance of an environmental impact is weighted against all the other
7) Evaluation and reporting
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Impact categories (1), classification (2) and characterization (3)
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Characterization factors (3)
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Weighting (6)
The qualitative or quantitative procedure where the relative importance of an
environmental impact is weighted against all the other. This is difficult since there is
no correct answer to which the best option is.
Weighting factor
Several possible principles (mostly based in social sciences):
Monetarization: Costs of environmental damage and prices of environmental
goods. Value of goods where there is no market, which is very difficult. WTP is
one way to set a value but it is not rock solid
Authorized targets: Based on difference between current pollution levels and
targeted levels.
Authoritative panels: Panels can be made up by scientific experts, government
representatives, company decision makers… Panel methods
Technology abatement: Weighting factors determined by the possibility to use
technological abatement methods. “Distance-to.-technically-feasible-target”
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Life cycle interpretation (Last step)
Based on the findings in previous phases the interpretation is the last phase of the
LCA.
Two objectives for the interpretation is proposed:
1) Analyze results, reach conclusions, explain limitations and provide
recommendations in a transparent manner.
2) Provide a readily understandable, complete and consistent presentation of the
results of an LCA study
Key steps:
1) Identify significant issues
2) Evaluate the completeness, sensitivity and consistency of the data
3) Draw conclusions and recommendations
Social LCA
- S-LCA
The youngest approach, with a growing interest.
Does not provide information on the question of whether a product should be
produced or not – “food for thought”
Investment appraisal exemplified
- An example
Bioenergy combine in Östersund
Joint production of cellulosic ethanol through enzymatic hydrolysis
Supposed to replace the current Bio-CHP utility
L10, L11 & L12 – external