Formulas Flashcards
Abnormal ROE Valuation of Firm in Steady State
If ROE is expected to remain constant and dividend policy constant (so Sustainable Growth Rate is constant)
MVE = BVE + BVE(ROE – re)/re – g
If all other forecast ratios are held constant, forecast growth rate for year t
forecast growth rate for year t will be the SGR for year t-1.
All relevant forecasting ratios (sales growth, profit margin, operating assets / sales, debt ratio etc) for the current year must have the same value as those ratios for the previous year for this generalisation to be true.
Sustainable Growth Rate
ROE x (1 - Dividend Rate)
Cost of Debt
Net Interest Expense / Average Net Debt
must be net of taxes b/c after tax cash flows are discounted
Forecast Abnormal Earnings in in particular year
Net Income - Cost of Equity x Opening BVE
Value of Firm with Forecast Abnormal earnings
Value of Firm =
BVE + PV(Abn Earn 1-10) + PV of Terminal Abn Earn Stream
Abnormal ROE
ROE - Cost of Equity
Growth BVE
Opening BVEt / Opening BVE in Year One (Beginning of Year 1/ day we are valuing the firm)
Valuation using Abnormal ROE
Terminal Value Under Abnormal ROE Method
3% terminal sales growth with persistent profit margin means
3% terminal sales growth with persistent profit margin means that Abnormal ROE stays the same, but BVE Growth Factor increases by 3% each year, so (Abn ROE x BVE Growth Factor) is growing by 3% forever
PV10 = 0.0185 / (0.0896 – 0.03) =0.3112
total value multiplier is
Multiplier (Years 1- 10) + Multiplier (Terminal)
ROE
Value of Equity is
BVE0 + 0.2233 (multiplier) x BVE0
Value per share =
FCFE / cost of equity
Given the assumed constant dividend policy and constant ROE,
Book value of equity will grow at the sustainable growth rate (SGR).
(Terminal)
for deferred tax effects what happens if the net effect on current profit is an increase?
If the net effect of adjustments is an increase in net profit,
Higher accounting profit = higher tax expense to be recorded
– Higher tax expense = lower current net profit after tax
– Change in After Tax Profit = -$2202 x Eff. Tax Rate = -$2202 x 29.5%
- Decrease Current Profit $649
- Decrease Deferred Tax Assets $649
for deferred tax effects what happens if the net effect on current profit is a decrease?
If the net effect of adjustments is an decrease in net profit,
Lower accouting profit = lower expense to be recorded
– lower tax expense = higher current net profit after tax
– Change in After Tax Profit = $2202 x Eff. Tax Rate = $2202 x 29.5%
- Increase Current Profit $649
- Increase Deferred Tax Assets $649
for deferred tax effects what happens if the net effect on opening retained earnings is a decrease?
Lower retained profits = lower prior period tax expenses
Lower tax expense = higher accumulated profits (retained earnings)
– Change in Accumulated After Tax Profit = $60,355 x 29.5% (Eff. Tax Rate) = $17,789
• Increase Opening Retained Earnings $17,789 • Increase Deferred Tax Assets $17,789
Reclassify Lease Liability - current v
non current
what this involves
PV of lease payments due within one year
Increase current liability
Decrease non current liability
Capitalise Closing Lease Liability and Asset
Increase Non-current assets
Increase non current liabilities
Add back rent expense associated with current year lease payments
if operating leases are brought onto the balance sheet, the rent expense associated with them should be removed. Eliminating an expense makes profit go up.
Lease payment at the end of pervious year = beginning of this year
Increase current profit
Decrease retained earnings
Recognise interest
PV of future payments at the end of last year/beginning of this year
Decrease current profit
Increase retained earnings
Recognise depreciation
PV of lease payments at the end of this year - adjustment for lease assets / remaining years
Reduce the asset value to 0 in remaining years
Decrease current profit
Increase retained earnings
OR cost of asset - 0 / useful life
net effect on current year profit of all of our adjustments is -$44.92 (Rent Adj + Int Adj + Dep Adj + Tax Adj), logically the opening retained earnings for next year (2017) should be adjusted
the net effect on current year profit of all of our adjustments is -$44.92 (Rent Adj + Int Adj + Dep Adj + Tax Adj), logically the opening retained earnings for next year (2017) should be adjusted by the same amount (-$44.92).
Dupont System
ROA
profit before leverage/ average total assets
ROE
Dupont System
Net Profit – Pref. Divs) / Average Ordinary shareholders’ equity
ROE
Forecasting in Abnormal ROE Valuation
Net income/ Opening BVE
If ROE > cost of equity, and current ROE is a good predictor of future ROE,
he market value of the firms equity > book value of the firm’s equity
ROA
Dupont
Profit before leverage (Net Profit + + Gross Interest expense x 1 - effective tax rate + minority) interest
/ average total assets
ROA
Dupont
Profit before leverage (+ Gross Interest expense x 1 - tax rate)
/ average assets
Effective tax rate
Tax Expense/Net Profit Before Tax
Common earnings leverage
Capital Structure Leverage
Average Total Assets / Average Ordinary Equity
ROE =
Adj ROA x Common earnings leverage x Capital structure leverage
ROA breakdown
Dupont
- Profit Margin: Average $ profit per $ of sales
– Asset Turnover: $ Sales for Each $ of Assets
ROA
profit margin
ProfitB4Leverage/
Sales
ROA
asset turnover
Sales / average total assets
Breakdown of Profit margin
Profit margin = coverage x EBIT/sales
Breakdown of Profit margin
EBIT/ sales
Gross Profit / Sales (gross profit margin) is described as a measure of
production efficiency, because this is where efficiencies achieved in the cost of producing/acquiring goods for sale will be reflected
EBIT/Gross Profit is described as a measure of
operating efficiency because it capture any economies achieved in SG&A type expenses.
difference between NOPAT margin and Dupon net profit margin
NOPAT Margin adds back the after-tax value of NET Interest Expense
Dupont adds back the after-tax value of GROSS Interest Expense.
Cost of Doing Business
Expenses from Core Activities excl. COGS, Depn & Impairment. Sales /
Sales
Alternative Approach to Decomposing ROE
ROE =
ROE = Operating ROA + Spread x Net Fin. Leverage + Unexpected ROE
Alternate ROE
Net Profit
Net Operating Profit + Net Unusual Profit (both including Profit to Minority Interests)
Alternate ROE
Net Interest Expense After Tax
Interest Exp – Interest Rev.) x (1 - Effective Tax Rate)
Alternate ROE
Net Operating Profit After Tax (NOPAT)
Net Operating Profit + Net Interest Exp. After Tax
Alternate ROE
Operating Working Capital
(Curr. Assets – Cash Equiv) – (Curr. Liab – S.T. Debt and Curr Portion of L.T. Debt)
Alternate ROE
Net Long-Term Operating Assets
Total Long-Term Operating Assets – Non-Interest Bearing Liabilities
Alternate ROE
Net Debt
Total Interest-Bearing Liabilities – Cash & Cash Equiv.
Alternate ROE
Total Net Operating Assets
Operating Working Capital + Net Long-term Operating Assets
Alternate ROE
Net Capital
Net Debt + Shareholders Equity
Alternate ROE
Operating ROA
NOPAT / Total Net Operating Assets
Alternate ROE
Net Financial Leverage
Net Debt / Equity
net debt/ opening equity (opening BVE)
Alternate ROE
Unexpected ROE
NUP / Equity
Alternate ROE
Spread
Operating ROA – Effective Interest Rate After Tax
Alternate ROE
Net Op. Asset T/O
Net operating assets / sale
Spread
Operating ROA - effective interest rate after tax
Find Effective Interest Rate after tax
Net Interest Expense After Tax / Net Debt
Value per share =
FCFE / cost of equity
After tax cost of debt
pre-tax cost of debt x (1-0.3)
FCFE
Net Debt
Net Debt Ratio x Total Net Operating Assets
FCFE
Net Income
= NOPAT – Net Interest Expense After Tax
FCFE
Net Interest Expense After Tax
After Tax Cost of Debt x Opening Net Debt
FCFE
New Investment 2016
Total Net Operating Assets at Beginning of 2017 - Total Net Operating Assets at Beginning of 2016
FCFE
Increase in Net Debt 2016
Net Debt at Beginning of 2017 – Net Debt at Beginning of 2016
Dividend Payout Ratio
Dividends paid / net income to common
Dividend Payout Ratio = Dividends Paid/ Opening Equity
Debt Ratio
Debt Ratio = Net Debt/ Net Total Operating Assets
Opening Equity
Total Net Operating assets - Net Debt
Net Interest Expense after Debt (with net Debt)
Net Debt x After Tax Cost of Debt
Net income
for valuation
NOPAT + Net Interest Expense After Tax
Net income to shareholders
Net Income - Preference Dividends
What is the implicit interest rate for Lease adjustments
Interest Exp / Ave Total Debt
or net interest expense / ave total debt
under consolidated accounting, all of the assets of subsidiary companies are
added to the ‘group’ assets, even if the parent owns less than 100% of the subsidiary
When to adjust minority interest
Adj ROA = net profit + gross interest exp (1 - effec tax rate) + minority interest / average total assets
If minority interests have already been deducted when calculating Net Profit in the Consolidated accounts:
- Add the ‘profit to minority interests’ to your numerator
• If minority interests have not been deducted in the calculation of Net Profit, there’s no need to make an adjustment.
If cost of doing business ratio of 14.92%, what does this mean
For each $1 of sales, 14.92 cents is spent on things like: employee wages, power, rent, cleaning, stationery etc
– These are the direct costs of being open for business
Common Size Analyses
State all Income Statement items as percentages of Sales
• State all Balance Sheet items as percentages of total assets
Net Unusual Profit After Tax
Sum of one-off items (e.g. discontinued ops.) after effect of tax is deducted.
Treatment of Preference Shares Under Alternate ROE Breakdown
- Preference Share Capital is treated as Long-Term Debt
- Preference Dividends are treated as interest expense.
Key ratios useful for analysing the management of working capital include:
– Operating Working Capital to Sales
- Accounts receivable turnover
– Inventory turnover
– Accounts Payable Turnover
Key working capital ratio alternate ROE
– Accounts receivable turnover
Expressed alternately as Days Sales in Receivables (‘Days Receivables) = Average Receivables / Average Sales per Day
Key working capital ratio alternate ROE
Inventory turnover
Expressed Alternately as ‘Days in Inventory’ (‘Days Inventory’) = Average Inventory / Average COGS per day
Key working capital ratio alternate ROE
Accounts Payable Turnover
Expressed Alternately as ‘Days in Payables’ (‘Days Payables’) =
Average Payables / Average COGS per day
Operating Cycle:
ave. number of days between purchasing goods and collecting the cash from our customers
Calculate operating cycle
Days receivables + days inventory
net operating cycle calculation
Days receivables + days inventory - days payables
net operating cycle
: ave no. of days between when *WE* pay cash for inventories and when our customers pay us cash for those goods (also known as ‘cash conversion cycle’)
– The shorter the net operating cycle, the lower the cost of financing our investment in working capital
Large increase in Days in Receivables
• Indicate
channel stuffing, heavy discounting to boost revenues at year end
Large increase in Days in Inventory
• Suggests either:
– Expected growth in sales next year
– Trouble selling this year’s stock
– Overproduction at year end to split fixed production costs across a greater number of units of inventory
Is Net Operating Cycle Always Positive?
No….firms with considerable power (particularly over suppliers) may have negative net operating cycles
Alternate ROE
Net Long-Term Operating Assets to Sales
(Total Long-Term Assets – Non-Interest Bearing Liabilities) / Sales
Average Asset Age
Average Age = Accumulated Depreciation / Depreciation Expense
Average Asset age
provide information about the likelihood that a firm will need to replace/repair assets, or explain cross-firm differences in actual maintenance expenses
– ROE = ROA x CEL x CSL (DuPont Breakdown)
– What if NPAT (ROA) is negative?
Capital Structure Leverage multiplies the effect of the losses.
• ROE much more sensitive to small variations in ROA if CSL is large.
Current ratio
current assets / current liabilities
Quick ratio
Cash + Short-term investments + Accts. receivable / Current liabilities
Cash ratio
Cash + Marketable securities / Current liabilities
Operating cash flow ratio
Cash flows from operations / Current liabilities
Liquidity of the same item may vary across firms
how
A firm that runs a very strict credit policy may have much more liquid receivables than does a firm who grants credit very easily
Debt and Coverage Ratios
Liabilities-to-equity ratio
Total liabilities / Shareholders’ equity
Debt and Coverage Ratios
Debt-to-equity ratio
Short-term debt + Long-term debt / Shareholders’ equity
Debt and Coverage Ratios
Net-debt-to-equity ratio
Short-term debt + Long-term debt – Cash and marketable securities/
Shareholders’ equity
Debt and Coverage Ratios
Debt-to-capital ratio =
Debt and Coverage Ratios
Net-debt-to-net-capital ratio =
A key point to remember when analysing a firm’s solvency ratios is the means by which the firm arrived at its present position
example
A successful firm that has increased debt levels to finance expansion is very different to a firm that has reached a D/E ratio of 5:1 due to making repeated financial losses (and thus reducing Equity each year).
Two ratios that try to address the ability to pay interest on debts are:
Interest coverage ratio (earnings basis)
Interest coverage ratio (cash flow basis)
Two ratios that try to address the ability to pay interest on debts are:
Interest coverage ratio (earnings basis)
Two ratios that try to address the ability to pay interest on debts are:
Interest coverage ratio (cash flow basis)
Sustainable growth rate
rate at which a firm can grow given the current level of profitability and current financing policies
– Function of the periodic profits re-invested in the firm’s operations
Dividend payout ratio
Cash dividends paid/
Net income
JB’s sustainable growth rate for 2013 is 25%
what does this mean
This is a historical measure…the current year’s profits and dividends have resulted in an increase in shareholder’s equity of 25% of the book value of equity
JB’s sustainable growth rate for 2013 is 25%
Could theoretically
grow their shareholder’s equity by 25% next year, without external financing, if ROE stays the same
assuming that the opportunity for growth exists…i.e. there will be growth in demand for JB’s products
Change in Equity
Change in Net Op. Assets – Change in Net Debt
Change in Equity = Chg(Sales x 1/ATO) + 0
Asset Turnover = Sales / Net Op Assets
Components of change in equity
any meaningful growth in equity has to reflect either
– Growth in sales
– Growth in net operating assets required to support each dollar of sales (i.e. decrease in ATO)
Change in equity
What if retains some of its earnings rather than paying dividends, but leaves this lying around in spare cash
This changes ‘Net Debt’ NOT ‘Net Operating Assets’
Assume Asset Turnover = 1
this means
Need $1 of Net Operating Assets to support each $1 of sales
In 2012, XYZ has no debt, Opening Equity of $100, earns an ROA and ROE of 20% and has Div Payout Ratio of 40%
closing equity
ROE = net income / opening BVE
net income = 20
Dividend payout ratio = dividends paid / net income
0.4 = x/ 20
x = 8
Closine equity = opening equity + 20 - 8 = 112 = amount of growth if sustainable growth rate
In 2012, XYZ has no debt, Opening Equity of $100, earns an ROA and ROE of 20% and has Div Payout Ratio of 40%
– SGR = 20% * (1-40%) = 12%p.a.
– Closing Equity is $112 ($100 + $20 - $8).
• Can they grow in 2013?
– Assume Asset Turnover = 1 and never changes (i.e. Need $1 of Net Operating Assets to support each $1 of sales)
XYZ can support Sales growth of 12% in 2013, without having to borrow more, or change dividend policy
In 2012, XYZ has no debt, Opening Equity of $100, earns an ROA and ROE of 20% and has Div Payout Ratio of 40%
SGR = 20% * (1-40%) = 12%p.a.
What if Sales only grows by 7%, and Profit Margin and ATO do not change??
– Change in Net Operating Assets = 7%
– ROA stays at 20%
– Net Debt is Decreased by an amount equal to 5% of opening equity (rather than being invested in operating assets needed to support sales, this part of 2012 retained earnings are represented by ‘cash’ not an operating asset)
– Chg Equity = Chg NOA – Chg Net Debt
– 12% = 7% - (-5%)
– 2013 ROE < 20%
In 2012, XYZ has no debt, Opening Equity of $100, earns an ROA and ROE of 20% and has Div Payout Ratio of 40%
SGR = 20% * (1-40%) = 12%p.a.
What if Sales only grows by 7%, and Profit Margin and ATO do not change??
Why is ROE in 2013< 20%
if actual sales growth < last period SGR what happens to ROE
ROE will keep falling assuming profit margin and asset turnover held constant)
A number of questions can be answered through analysis of the statement of cash flows.\
operating activities
How strong is the firm’s internal cash flow generation?
How well is working capital being managed?
A number of questions can be answered through analysis of the statement of cash flows
Investing activities
How much cash did the company invest in long-term operating assets?
A number of questions can be answered through analysis of the statement of cash flows.
Financing activities
What type of external financing does the company rely on?
Didthecompanyuseinternallygeneratedfundsforinvestments?
Didthecompanyuseinternallygeneratedfundstopaydividends?
CFO B4 WC tells us
bout the (expected) cash flows resulting from sales, COGS and operating expenses that affect cash
- During rapid growth, WC eats cash (Receivables + Inventory increase faster than payables)
- During declines in sales, WC releases cash
what is needed in cash flow analysis
Adjust value of lease asset to reflect difference between depreciation and principal reduction
Asset/liability ratio is 88.7%.
Adjustment = - (1- 0.887) x PV of lease asset this year
Adjustment -21.496357
Decrease non-current assets, decrease retained earnings
current ratio measures
company’s ability to pay short-term and long-term obligations
The higher the ratio, the more able a company is to pay off its obligations.
current ratio
if over 1 and below
A ratio under 1 implies that a company would be unable to pay off its obligations if they become due at that point in time
quick ratio
interpretation
The higher the ratio, the more financially secure a company is in the short term.
quick ratio of greater than 1.0 are sufficiently able to meet their short-term liabilities
quick ratio
pay liabilities when due with quick assets - can easily converted to cash within 90 days or in the short-term.
cash ratio
company’s ability to pay current liabilities using only cash and cash equivalents on hand. If
the company is forced to pay all current liabilities immediately, this metric shows the company’s ability to do so without having to sell or liquidate other assets.
interpretation of cash ratio
If a company’s cash ratio is equal to 1, the company has exactly the same amount of current liabilities as it does cash and cash equivalents to pay off those debts.
If a company’s cash ratio is less than 1, there are more current liabilities than cash and cash equivalents. In this situation, there is insufficient cash on hand to pay off short-term debt.
If a company’s cash ratio is greater than 1, the company has more cash and cash equivalents than current liabilities. In this situation, the company has the ability to cover all short-term debt and still have cash remaining.
too high liquidity can be bad because
company is inefficient in the utilization of cash or not maximizing the potential benefit of low-cost loans.
why is inventory, receivable, prepaid assets excluded from cash ratio
These items may require time and effort to find a buyer in the market
money received from the sale of any of these items may be indeterminable.
operating cash flow ratio measures
how well current liabilities are covered by the cash flow generated from a company’s operations.
