Download NI/Sales ROA

MSBC 5060
Chapter 3
Financial Statement Analysis
and Financial Models
1
Chapter Outline
1.
2.
3.
4.
5.
6.
Financial Statements Analysis
Ratio Analysis
The Du Pont Identity
Financial Models
External Financing and Growth
Some Caveats
2
Key Concepts and Skills
• Know how to standardize financial statements
for comparison purposes
• Know how to compute and interpret
important financial ratios
• Be able to develop a financial plan using the
percentage of sales approach
• Understand how capital structure and
dividend policies affect a firm’s ability to grow
• Relate corporate loan criteria to personal loan
criteria
3
Common-Size Financial Statements
The basic idea: Divide Everything on the page by
the main number on the page
• Balance Sheet:
– The main number is Total Assets
• which equals Liabilities plus Equity
– So all values are reported as a percentage of Total
Assets
• Income Statement
– The largest number is Sales
– So all values are reported as a percentage of Sales
(also called Total Revenue)
4
Common-Size Balance Sheet
(Tables 3.1 and 3.2) Prufrock corporation
5
Common-Size Income Statement
(Tables 3.4 and 3.5)
Some other stuff we will need later for the Ratio Analyses:
• EBIT = NI + Int Exp + Tax Exp = 363 + 141 + 187 = $691
• EBITDA = NI + Int Exp + Tax Exp + Dep Exp = 691 + 276 = $967
6
Review of Earnings numbers (Table 3.3 page 47)
7
Ratio Analysis
Instead of values, show as fractions of other values (ratios)
Ratio Categories:
1. Short-Term Solvency
– Firm’s ability to pay current bills
2. Long-Term Solvency
– Firm’s ability to meet LT debt obligations
3. Asset Management
– aka Turnover Ratios (Efficiency measures)
4. Profitability Ratios
5. Market Value Ratios
8
Some things to think about as we look at ratios:
1. Definition of the Ratio
– How is it computed? Is it always the same?
(It will be for us)
– Use the Beginning, Ending or Average B-S value?
2. What is the unit of Measure?
– dollars, years, dollars per dollars of assets…
3. What are HIGH values? What are LOW values?
–
–
–
–
High or low for the company over time
for the industry
for the sector
for all companies…
9
Category 1: Short-Term Solvency
First Some Notation:
• Current Assets = CA
• Current Liabilities = CL
• Total Assets = TA = A
• Total Liabilities = TL = L = Total Debt = TD = Debt =D
• Total Equity = TE = E
[3.1] Current Ratio = CA/CL = 708/540 = 1.31
[3.2] Quick Ratio = (CA – Inv)/CL = (708 – 442)/540 = 0.53
• Inventory is the least liquid current asset
[3.3] Cash Ratio = Cash/CL = 98/540 = 0.18
• Cash is the most liquid current asset
10
Review Question
Current Assets
2013
2014
Cash
$84
$98
A/R
$165
$188
Inventory
$393
$422
$642
$708
Total
Current Liabilities
2013
2014
A/P
$312
$344
Notes Payable
$231
$196
$543
$540
Total
Did the firm’s short-term solvency improve or
deteriorate?
Ratio
Current Ratio = CA/CL
Quick Ratio = (CA – Inv)/CL
Cash ratio = Cash/CL
2013
2014
642/543 = 1.18
708/540 = 1.31
(642-393)/543 = 0.46
(708-442)/540 = 0.53
84/543 = 0.15
98/540 = 0.18
11
Category 2: Long-Term Solvency and Leverage
Balance Sheet:
[3.4] Total Debt Ratio = Debt to Assets = D/A = 997/3,588 = 0.28
Equity to Assets = E/A = 2,591/3,588 = 0.72
[3.5] Debt to Equity = D/E = 997/2,591 = 0.38
= 0.28/0.72 = 0.39 ≈ 0.38
[3.6] Equity Multiplier (EM) = A/E = 3,588/2,591 = 1.38
= 1/(E/A) = 1/0.72 = 1.38
= 1 + D/E = 1 + 0.38 = 1.38
Note: EM = A/E = (D + E)/E = E/E + D/E = 1 + D/E
• All these are also called Financial Leverage Measures
• In general, the more levered, the less likely a firm is to repay its debt
12
Category 2: Long-Term Solvency (Continued)
Coverage Ratios:
Income Statement:
[3.7] Times Interest Earned (TIE) = EBIT/In Exp
= 691/141 = 4.9 times
[3.8] Cash Coverage = EBITDA/In Exp
= 967/141 = 6.9 times
13
Review Question
Current Assets
2013
2014
Liab. and Equity
2013
2014
ST Assets
$100
$150
ST Liabilities
$300
$300
LT Assets
$900
$1,050
LT Liabilities
$500
$700
Equity
$200
$200
Did the firm’s Long-term solvency improve or deteriorate?
Ratio
Debt to Assets
2013
2014
$800/$1,000 = 0.80 $1,000/$1,200 = 0.83
Debt to Equity
$800/$200 = 4
$1,000/$200 = 5
Equity Multiplier = A/E
$1,000/200 = 5
$1,200/200 = 6
• The firm borrowed $200 and bought new assets
• LT solvency deteriorated since Leverage increased
14
Category 3: Asset Management or Efficiency
[3.9] Inventory Turnover = COGS/Inventory = 1,344/422 = 3.2 times
• This is the value of inventory sold during the year (COGS) divided by
the amount of inventory on hand at the end of the year
• So during the year, the firm sold 3.2 times amount of inventory on
hand at year’s end
[3.10] Days’ Sales in Inventory = 365/Inventory Turnover
= 365/3.2 = 114 days
• Since the firm sold the current amount of inventory 3.2 times over the
last year, the current inventory will be sold in 1/3.2 years or 114 days
15
Cat 3: Asset Management or Efficiency (Continued)
[3.11] Receivables Turnover = Sales/(A/R) = 2,311/188 = 12.3 times
• Really should be “Credit Sales” not total Sales. We don’t have that.
• Would be number of times in the year credit was extended and then
collected
• Often Average A/R is used as opposed to Ending A/R
[3.12] Days’ Sales in Receivables = 365/Receivables Turnover
= 365/12.3 = 30 days
• Credit was extended and collected 12.3 times over the last year or
1/12.3 years or 30 days
16
Cat 3: Asset Management or Efficiency (Continued)
[3.13] Asset Turnover = Sales/Assets = 2,311/3,588 = 0.64
• For each dollar of assets, the firm generated $0.64 in sales
• This is the amount of sales the firm was able to generate
from asset in place
Capital Intensity = Assets/Sales = 3,588/2,311 = 1.56
• It takes $1.56 in Assets to generate $1 in Sales
• A way to think about this ratio:
• If Sales are going to increase by 25%
• Then assets must also increase by 25%
• Unless the firm can somehow generate more sales from each unit of
assets
• Which means increase Asset Turnover or lower Capital Intensity
• Which means an increase in operating efficiency
17
Review Question
Account
Sales
$10,000
COGS
$5,000
Inventory
$1,000
A/R
Assets
$500
Calculate:
(1) Inventory Turnover (IT)
(2) Days’ Sales in Inventory (DSI)
(3) Asset Turnover (AT)
$25,000
• IT = Inv sold/Inv on hand
IT = COGS/Inv = $5,000/$1,000 = 5
• DSI = Days per year/ # of times Inv turned in per year
DSI = 365/IT = 365/5 = 73
• AT = Amount sold/Amount “employed” to generate sales
AT = Sales/Assets = $10,000/$25,000 = 0.4
18
Category 4: Profitability (Really Efficiency)
[3.14] Profit Margin (PM)
PM = NI/Sales = 363/2,311 = 15.7%
•
•
•
•
Income Statement “Bottom Line” divided “Top Line”
Accounting Profit per Dollar of Sales
Think of PM as a measure of Efficiency not Profitability
Measures the expenses needed to generate sales (Sales – Expenses = NI)
[3.15] Return on Asset (ROA)
ROA= NI/Assets = 363/3,588 = 10%
• This is the (accounting) profit per unit of Assets
• Compare with Asset Turnover Ratio (AT) = Sales/Assets = 2,311/3,588 =
0.64
• Sales are 64% of Assets and Profits are 10% of Assets
• PM = ROA/AT = 0.10/0.64 = 15.7%
• Think of ROA as a measure of Efficiency not Profitability
• Think of assets as some number of trucks. How much profit is generated
from these trucks? The more you generate, the more efficient the
business.
• It is a function of sales (more is better) and expenses (less is better)
19
Category 4: Profitability
[3.16] Return on Equity (ROE)
ROE = NI/Equity = 363/2,591 = 14%
•
•
•
•
•
This measures the (accounting) profit per unit of Equity
ROE = ROA x EM = NI/Assets x Assets/Equity
So Profit (ROE) is a function of Efficiency (ROA) and Leverage (EM)
So increase profit by increasing efficiency or increasing leverage
Remember Efficiency has two components:
Increasing Sales and Decreasing Expenses
• So Increase Efficiency by Increasing Sales or Decreasing Expenses
20
Important Relationship:
ROE = NI/Equity (Profitability)
ROA = NI/Assets (Efficiency)
EM = Assets/Equity (Leverage)
Profitability = Efficiency X Leverage
ROE = ROA X EM
NI/Equity = NI/Assets X Assets/Equity
21
Category 5: Market Value Measures
But First: # of Shares Outstanding is 33m and Price is $88 per share
[3.17] Earnings per Share (EPS) = NI/Shares = $363/33 = $11/Share
• So each owners’ share earned $11
[3.18] Price-Earnings Ratio (PE or P/E) = Price/EPS = $88/$11 = 8 times
• So pay $8 for $1 of earnings
• PE (and EPS) can be compared across different stocks
• Why pay more for a dollar of earnings?
[3.19] Market-to-Book = Price per Share/Book Val of Equity per Share
•
•
•
•
Book Value of Equity per Share = $2,591/33 = $78.52
Market-to-Book = $88/$78.52 = 1.12
Sometimes called Price-to-Book
Some contexts use Book-to-Market (BM), the inverse
22
Category 5: Market Value Measures
[3.20] Enterprise Value (EV) = Mkt Cap + Mkt Val Debt – Cash
= Shares x Price + Notes + LTD – Cash
= 33 m x $88 + $196 + $457 – $98 = $3,465
• Note the use of book value of debt instead if market value of debt. This is
common since they are often very close.
• This is cost to acquire all claims on the firm’s assets
[3.21] Enterprise Value Multiple = EV/EBITDA
= $3,465/$967 = 3.6 times
• The EV Multiple is especially useful because it allows comparison
across firms even if there are differences in capital structure.
• Since EBITDA is before interest expense, taxes, or capital spending
(depreciation)
23
Review Question
Price Share
(6/22 Close)
EPS
(ttm)
Book Val of
Equity (mrq)
# of Shares
(mrq)
Nike (NKE)
$106.79
$3.50
$12,368 m
860 m
Wal-Mart (WMT)
$72.79
$4.98 $76,574 m
Stock
Stock
PE Ratio
NKE
$106.79/$3.50 = 30.51
WMT
Book Val of
Equity Per share
3,227 m
Market-to-Book
$12,368/860 = $14.38
$106.79/$14.38 = 7.43
$72.79/$4.98 = 14.62 $76,574/3,227 = $23.73
$72.79/$23.73 = 4.50
• NKE has a greater PE and Market-to-Book.
• So “the market” is paying more for a dollar of NKE’s earnings
and more for a dollar of its equity.
• Why?
24
One More Efficiency Measure…
EBITDA Margin = EBITDA/Sales = $967/$2,311 = 41.8%
Compare EBITDA Margin to Profit Margin:
Profit Margin (PM) = NI/Sales = $363/$2,311 = 15.7%
• What is the difference in the numerators?
EDITDA – Dep – Amort – Int Exp – Taxes = NI
25
Recap: Table 3.6 page 56
Remember:
Think of ROA and PM as Efficiency Ratios, not Profitability Ratios
26
Problems with Ratio Analysis
• No good way to know which ratios are most
important
• Benchmarking is difficult for diversified firms
• Globalization and international competition
makes comparison more difficult because of
differences in accounting regulations
• Firms use varying accounting procedures
• Firms have different fiscal years
• Extraordinary, or one-time, events can confuse
the results
27
DuPont Identity
• A method of calculating the contribution of different parts
to overall profitability
• Also called Profitability decomposition
or ROE Decomposition
• Profitability is measured by ROE = NI/E
The Du Pont Identity:
[3.22] ROE = AT x PM x EM
NI/E = Sales/A x NI/Sales x A/E
Profit = Sales Efficiency x Expense Efficiency x Leverage
28
DuPont Analysis (Continued)
First:
Decompose Profitability (ROE) into broad measures of
Efficiency (ROA) and Leverage (EM)
• Efficiency  ROA = NI/A
• Leverage  EM = A/E
• ROE = ROA x EM  NI/E = NI/A x A/E
Profit = Efficiency X Leverage
29
DuPont Analysis (continued)
Second:
Decompose Efficiency into
Sales generated from Assets (AT) and
Expenses needed to generate the sales (PM)
• Sales Generated from Assets (Asset Turnover)
AT = Sales/A
• Earnings kept from each dollar of sales
PM = NI/Sales
NI/A = Sales/A x NI/Sales
ROA = AT x PM
Total Efficiency is a function of Sales and Expenses
30
DuPont Analysis (continued)
Third:
Decompose AT (Sales/A) into different types of Sales
•
•
•
Manufactured Products, Servicing, Consulting…
AT  Product Sales/A, Servicing/A, Consulting/A,
What break-down categories are appropriate? Depends on
the company and its business
Fourth:
Decompose PM (NI/Sales) into different expenses
•
•
COGS/Sales, SG&A/Sales, Int Exp/Sales, Tax Exp/Sales, Dep
Exp/Sales
PM = NI/Sales = (Sales – Expenses)/Sales
31
DuPont Analysis (continued)
Equip Sales/A
EM = A/E
(Leverage)
ROE = NI/E
AT = Sales/A
(Profit)
(Revenues)
Servicing/A
Consulting/A
ROA = NI/A
(Efficiency)
PM = NI/Sales
COGS/Sales
(Expenses)
SG&A/Sales
Int Exp/Sales
Tax Exp/Sales
Dep Exp/Sales
32
Review Question
Account
Firm 1
Firm 2
Assets
$10,000
$20,000
Equity
$5,000
$5,000
NI
$1,000
$2,000
Sales
$5,000
$8,000
For both firms calculate:
(1) ROE = NI/E
(2) ROA = NI/A
(3) EM = A/E
(4) AT = Sales/A
(5) PM = NI/Sales
Why is Firm 2 more profitable?
Ratio
Firm 1
Firm 2
ROE = NI/E
0.2
0.4
ROA = NI/A
0.1
0.1
EM = A/E
2.0
4.0
AT = Sales/A
0.5
0.5
PM = NI/Sales
0.2
0.2
• ROE greater for Firm 2 because
EM is bigger.
• EM measures leverage
33
Financing Growth
• For a firm to Grow, Assets must grow (almost by definition)
1.
2.
External Growth: Sell stocks or bonds (talk about this later)
Internal Growth: Retain Earnings (talk about this now)
• Internally Financed Growth is a function of:
1.
2.
•
The Earnings (aka NI) as a percentage of Assets
The Earnings Retained by the business as a percentage of NI
So: How much did you make and how much did you keep?
First some definitions:
[3.23] Dividend Payout Ratio = Div/NI = 121/363 = 33% = 1/3
• Payout 1/3 of Accounting Profits
Retention Ratio (aka Plowback Ratio) = RE/NI = 242/363 = 2/3
• Also equal to 1 - Div/NI
• Often denoted as “b”
• Note: The text Switches from Prufrock to Rosengarten for these ratios.
• I’ll stay with Prufrock for the lecture
34
External Financing and Growth
• Let b = RE/NI
• ROA = NI/A
(Plowback Ratio)
(Accounting profits per unit of assets)
[3.25] Internal Growth = (ROA x b)/(1 – ROA x b)
For the example company
• ROA = 363/3,588 = 10.12% and b = 242/262 = 0.6667
– (How many digits after the decimal point? It depends.)
• Internal Growth = (0.1012 x 0.6667)/(1 – 0.1012 x 0.6667)
= 0.0724 = 7.24%
• If the company plows back 2/3 of NI (which increases assets) and
ROA is 10.12%, then the firm grows at 7.24% (without external
financing).
– Note that growth can be improved if ROA is improved
– How can ROA be improved? Increase Sales or Decrease Expenses
– Which parts of sales or expenses are best suited for improvement?
How do you breakdown sales and expenses into different categories? 
35
Internal and Sustainable Growth (continued)
• Note that retaining earnings increases…
• Retained Earnings (the Equity account on the B-S)
– But this does not increase Debt (liabilities)
– So over time, the D/E ratio decreases
• So to maintain the same D/E ratio, the firm must sell some debt
This leads to the Sustainable Growth Rate:
[3.26] Sustainable Growth = (ROE x b)/(1 – ROE x b)
• ROE = 14.01%
• Sustainable Growth = (0.1401 x 0.6667)/(1 – 0.1401 x 0.6667)
= 0.1030 = 10.30%
• Internal Growth Rate = 7.24%
• Sustainable Growth = 10.30%
– Sustainable growth implies borrowing to maintain the same D/E ration
– Borrowing means increasing leverage
36
Internal and Sustainable Growth (continued)
• So Growth is determined by four things:
1. Sales generated from Assets in place
–
Assets Use Efficiency: AT = Sales/Assets
2. NI (aka Earnings) kept from those sales
–
Operating Efficiency: PM = NI/Sales = (Sales – Expenses)/Sales
3. Portion of NI Retained
–
Plowback Ratio: b = RE/NI
4. Financing Policy
–
–
How much more is borrowed (relative to earnings retained)
Leverage: Equity Multiplier (EM) = A/E
37
Recap: Table 3.16
38
A note about SGR and IGR Calculations
If we use Ending Equity or Assets (at Time 1):
• SGR = (ROE1 x b)/(1 – ROE1 x b)
• IGR = (ROA1 x b)/(1 – ROA1 x b)
If we use Beginning Equity or Assets (at Time 0):
• SGR = ROE0 x b
• IGR = ROA0 x b
See “SGR and IGR Begin or End Values.xlsx”
39
How to use Ratio Analysis:
• Compare to same firm over time
• Compare to firms within industry
– SIC codes
– North American Industry Classification System
– NAICS or “Nakes”
• But use your own common sense and knowledge
about the company or industry
40
Financing Growth
• Given a Sales Growth Forecast
• How much new money will the firm need to raise to finance
the forecast growth?
• The text uses the Rosengarten example to develop the
formula to calculate External Financing Needed (EFN)
EFN is:
• The money that needs to be raised (through new equity or
new borrowing) if sales increase by a certain percent
• Assuming no other relationships or ratios change
– A simplifying assumption
– So no change in EM, or ROA
• Which means no change in AT (or its inverse CIR) or PM
– No change in asset or liability “mix”
41
Financing Growth
• For a given change in sales (sales growth)
• With other relationships fixed…
– Capital Intensity Ratio (Assets/Sales) is fixed
• This is “assets as a percentage of sales”
• So if sales increase, assets must increase
proportionately
• Also the mix of assets does not change
– A/P as a percentage of sales is fixed
• This is the only liability ratio we assume fixed
• We’ll see why in a minute
• This is why we consider A/P a “Spontaneous Liability”
42
Financing Growth
• How much more in assets are needed to
generate this forecast sales increase?
• How much more in liabilities will
automatically result from the increase in
sales?
• How much more earnings will the firm retain
from the increase in sales?
43
The EFN formula:
𝐴𝑠𝑠𝑒𝑡𝑠
[3.24] 𝐸𝐹𝑁 =
× ∆𝑆𝑎𝑙𝑒𝑠
𝑆𝑎𝑙𝑒𝑠
𝑆𝑝𝑜𝑛𝑡𝑎𝑛𝑒𝑜𝑢𝑠 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠
−
× ∆𝑆𝑎𝑙𝑒𝑠
𝑆𝑎𝑙𝑒𝑠
− PM × 𝑃𝑟𝑜𝑗𝑒𝑐𝑡𝑒𝑑 𝑆𝑎𝑙𝑒𝑠 × 1 − 𝑑
Where:
• Spontaneous Liabilities = liabilities that automatically result
from increased sales (in this case it is only A/P)
• d = the div payout ratio = Divs/NI
• (1 – d) = the Retention Ratio
But we will look at the formula slightly differently 
44
EFN
EFN = ΔSales x Capital Intensity Ratio
- ΔSales x Spontaneous Liabilities/Sales
- Retention Ratio x Profit Margin x Projected Sales
• Can rewrite it this way:
EFN = ΔSales x Assets/Sales
- ΔSales x Accts Payable/Sales
- Retention Ratio x NI/Sales x Projected Sales
• Or in words:
EFN = Assets Needed to Generate New Sales
- Liabilities Automatically Created by New Sales
- Increase Retained Earnings from New Sales 45
EFN Example from Text (Page 63)
Text Example:
Sales = $1,000, Sales Growth = 25%  ΔSales = $250
Assets = $3,000  Cap Intensity Ratio = $3,000/$1,000 = 3.00
A/P = $300  (A/P)/Sales = $300/$1,000 = 0.30
NI = $132  PM = NI/Sales = $132/$1,000 = 0.132
Divs = $44  Retention Ratio = 1 - $44/$132 = 0.6667
EFN = ΔSales x Capital Intensity Ratio
- ΔSales x Spontaneous Liabilities/Sales
- Retention Ratio x Profit Margin x Projected Sales
•
•
•
ΔSales x Capital Intensity Ratio = $250 x 3.00 = $750 (in new assets)
ΔSales x Spontaneous Liabilities/Sales = $250 x 0.30 = $75 (in new A/P)
Retention Ratio x PM x Proj Sales = 0.67 x 0.132 x $1,250 = $110 (in new RE)
EFN = $750 - $75 - $110 = $565
• The firm needs to $565 in External Financing to pay for the $750 in
new assets needed to finance 25% sales growth
46
Recap:
• Increase Sales by 25% or $250?  Need $750 in new Assets
– Why? Because Cap Intensity Ratio = Assets/Sales = 3.00
– $250 in new sales requires 3.00 x $250 = $750 in assets
• If Sales increases by $250  A/P will increase by $75
– Why? Because (A/P)/Sales is fixed at = 30%
– So $250 in new sales requires 0.30 x $250 = $75 in new A/P
• If Sales increases to $1,250  RE will be $110
– Why? Because PM = NI/Sales = 13.20% so NI will be $165
– And the firm keeps 66.66% of NI so RE = 0.6667 x $165 = $110
So the firm needs to finance $750 in new Assets
• $75 will be finance though new A/P
• $110 will be financed though RE
• $565 will be finance externally (EFN)
47
So the firm will need to raise $565 to finance forecast growth
– It can’t do it without External Financing
– How do we know? Because EFN > 0
– But just to be sure, check the IGR for Rosengarten:
Internal Growth Rate = (ROA x b)/(1 – ROA x b)
• ROA = NI/Assets = $132/$3,000 = 0.044
• b = Retention Ratio = 1 - $44/$132 = 0.6667
• Internal Growth = (ROA x b)/(1 – ROA x b)
= (0.044 x 0.6667)/(1 – 0.044 x 0.6667) = 0.0302 = 3.02%
• Rosengarten can only grow at 3.02% if it uses only internal financing (RE).
• So it must sell $565 of stocks and bonds in order to finance 25% sales
growth
• But how much of the $565 should be stock and how much should be
bonds?
• Easy if we assume constant EM (leverage)
• We’ll get to that when we cover capital structure in Chapter 14
48
Some Other Return Measures
ROI = Return on Investment = Gain / Cost
= (Value – Cost)/Cost = (P1 – P0)/P0 = P1/P0 - 1
• So an “investment measure”, not really a corporate profitability measure
ROC = Return on Capital
= EBIT( 1 – T)/(Book Value of Debt + Book Value of Equity – Cash)
ROIC = Return on Invested Capital
= EBIT( 1 – T)/(Book Value of Debt + Book Value of Equity)
Some Notation:
• NOPAT = Net Operating Profit After Taxes = EBIT(1 – T)
• K = Invested Capital = Book Value of Debt + Book Value of Equity
ROC = NOPAT/(K – Cash)
ROIC = NOPAT/K
49
One More We’ll Revisit Later…
EVA = (Return Earned on Invested Capital) - (Cost of Invested Capital)
= (r x K) – (c x K)
= (r – c) x K
= (NOPAT/K – c) x K
= NOPAT – c x K
Where:
r = NOPAT/K = ROIC = EBIT( 1 – T)/(Book Value of Debt + Book Value of Equity)
c = WACC = Weighted Average Cost of Capital
50
What’s Next?
• Time Value of Money (TVM)
– Present Value
– Future Value
• Interest Rate Conventions
– APR
– EAR
• Payment (and Repayment) Conventions
– Annuities
– Perpetuates
– Amortization…
51