Equations for Final
ROA =
From Exam 1
Liquidity Ratios
ROE =
current ratio =
quick ratio =
current assets
curent liabilities
ROCE = EBIT(1-T)/Total Assets
Market Value Ratios
Asset Management Ratios
inventory turnover =
net income
equity
BEP = EBIT/Total Assets
current assets−inventory
current liabilities
accounts receivable
ACP = DS0 = average daily sales
accounts receivable
x 360
sales
net income
total assets
=
P/E 𝑟𝑎𝑡𝑖𝑜 =
cost of goods sold
inventory
ICP = Inventory/(COGS/360) = 360/ITO
fixed asset turnover =
sales
fixed assets
total asset turnover =
sales
total asset
= TAT
Debt Management Ratios
𝑠𝑡𝑜𝑐𝑘 𝑝𝑟𝑖𝑐𝑒
𝐸𝑃𝑆
𝑚𝑎𝑟𝑘𝑒𝑡 𝑡𝑜 𝑏𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑟𝑎𝑡𝑖𝑜 =
𝑠𝑡𝑜𝑐𝑘 𝑝𝑟𝑖𝑐𝑒
𝑏𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒
Book value = common equity/# of shares
EPS = Net Income/ # of shares
DuPont Equations
ROA = ROS*TAT
ROE = ROS*TAT*EM, where
Other
debt ratio = TL/TA
Sales x profit margin = net income
EM = TA/Equity = [1/(1- (TL/TA))]
Net income x retention rate = retained earnings
TIE =
EBIT
interest
Cost ratio = COGS/sales
cash coverage =
EBIT + depreciation
interest
𝑓𝑖𝑥𝑒𝑑 𝑐ℎ𝑎𝑟𝑔𝑒 𝑐𝑜𝑣𝑒𝑟𝑎𝑔𝑒 =
𝐸𝐵𝐼𝑇 + 𝑙𝑒𝑎𝑠𝑒 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠
𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 + 𝑙𝑒𝑎𝑠𝑒 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠
Profitability Ratios
ROS = PM =
Cash Conversion Cycle
CCC = ICP + DSO – AP deferral
AP deferral = Accounts Payable/(COGS/360) =
(Accounts Payable/COGS) x 360
Operating cycle = ICP + DSO
net income
sales
From Chapter 5:
k = kPR + INFL + DR + LR + MR
INFLn = (I1+I2+….+In)/n
1
Two simplified or “textbook” income statement
formats used this semester.
sales
-COGS
Gross margin
-Expenses
EBIT
- Int.
EBT
- Tax
NI
-DIV
RE
sales
-VC
Gross margin
-FC
EBIT
- Int.
EBT
- Tax
NI
-DIV
RE
is dividends. RE is the contribution to retained
earnings this accounting period.
EBIT is
operating
income. Int. is
interest
expense not
the interest
rate. Taxes
are income
taxes and DIV
Simplified Balance Sheet as used this semester
Assets
Cash
Accounts receivable
Inventory
Current Assets
1000
3000
2000
6000
Fixed assets:
Gross PP&E
Accumulated dep.
Net Fixed Assets
$4000
(1000)
$3000
Total Assets
9000
Liabilities and Owner’s Equity
Accounts payable
1000
Accruals
500
Notes payable
1000
Current Liabilities
2500
Long term debt
Total Liabilities
5000
7500
Stockholder Equity
1500
Total Liab. & Equity
9000
Current Assets= gross working
capital
Net Working Capital = CA-CL
PP&E is property plant and
equipment. Equity is usually
divided into at least Stock and
accumulated Retained Earnings.
Stock is sometimes divided into
Par Value and Paid in Excess.
Sometimes equity is called net worth. Paid in Excess is also called surplus.
From Exam 2
8. Contribution margin = CM = (P-V)/P
1. BEP = EBIT/Total Assets
9. Operating breakeven quantity:
2.
ROCE =
EBIT 1 - tax rate 
debt + equity
ROCE = BEP (1- tax rate)
3. After-tax cost of debt = Kd(1- tax rate)
4. ROE = NI/Equity
5. EPS = NI/ #shares
6. NI = [EBIT – interest exp.](1- tax rate)
7. Contribution = P – V
QB/E = FC / (P – V)
10. Financial breakeven quantity:
QBE= (FC+I)/(P - V)
11. SB/E = QB/E(P)
SB/E = FC / CM
12. 𝐷𝑂𝐿 =
𝑆−𝑉𝐶
𝑆−𝑉𝐶−𝐹𝑐
=
𝐺𝑟𝑜𝑠𝑠 𝑃𝑟𝑜𝑓𝑖𝑡
𝐸𝐵𝐼𝑇
13. %ΔEBIT = DOL x %ΔSales
2
𝑛
EBIT
14. DFL =
EBIT - Interest
2
𝜎 = ∑ 𝑝𝑖 (𝑘𝑖 − 𝑘̂ )
2
𝑖=1
24. Standard deviation: 𝜎 = √𝜎 2
15. %ΔEPS = DFL x %ΔEBIT
16.
DTL 
𝜎
25. CV = ̂
𝑘
Sales  VC
 DOLxDFL
EBIT  Interest
26. Portfolio beta:
𝑛
17. %ΔEPS = DTL x %ΔSales
𝛽𝑝 = ∑ 𝛽𝑖 𝑤𝑖
𝑖=1
18. PV of a perpetual annuity:
PV = PMT
27. Portfolio expected return:
𝑛
K
𝑘̂𝑝 = ∑ 𝑘̂𝑖 𝑤𝑖
19. Constant growth model:
P0 
D1
D (1  g)
 0
Ks  g
Ks  g
𝑖=1
28. Effective Annual interest rate:
n
i

EAR  1    1
 n
In general, if the constant growth model is applied
after time zero then:
PN 1 
DN
Ks  g
29. current yield on a bond = (annual coupon
interest)/ (current bond price)
20. SML: Ks = KRF + (KM – KRF)s
30. YTM = current yield + capital gains yield
(If you know the YTM and the current yield on a
bond, you can subtract to get the expected
capital gains.)
31. The required return on a stock is equal to the
dividend yield plus expected capital gains yield.
32. capital gains yield = (Pt - Pt-1)/Pt-1
33. Dividend yield = D1/P0
21. MRP = KM – KRF
n
22. Mean:
k̂   p i k i
i 1
23. Variance:
Chapter 13 Equations:
n
1.
WACC   wi sourcei ; (weights, w, and cost of source)
i 1
2. Cost of debt: Kd × (1 - tax rate)
3. Cost of preferred stock:
K PF 
Dp
(1  f )PP
or = kp / (1 - f)
4. Cost of retained earnings from SML: Kx = KRF + bX (Km - KRF)
5. Cost of retained earnings from constant growth model:
6. Cost of new stock:
Ke 
D 0 (1  g)
g
(1  f )P0
Ke 
D 0 (1  g)
g
P0
3
“Equation” Sheet for AGEC 424 Exam 3
Net Salvage Value (NSV) Calculation
Adjusted Basis:
Tax on SV:
NSV:
Initial Basis
-Accumulated dep.
Adjusted Basis
Selling Price
-Adjusted Basis
Taxable gain (loss)
x tax rate
Tax (tax “credit” if neg.)
Selling price
-Tax on SV
NSV
Replacement Investmenta (we will do the third column)
Buy a new machine
Keep your old machine
Replacement = Buy new
minus keep oldb
a. Initial outlay items
-Cost of new machine
-/+ NWC
- Current NSV old machine
-Cost of new machine
- /+NWC
+ Current NSV old machine
b. Operating cash flow items of note
Depreciation new machine
Depreciation old machine
c. Terminal Cash Flow items
+ NSV new machine
+/-NWC offset
+ ending NSV old machine
Change in depreciation is
used in the modified income
statement to get operating cash
flow
+ NSV new machine
- ending NSV old machine
+/-NWC offset
a
In AGEC 424 we always do replacement problems where the life is the same for the new and for the old. If the
life is different one needs to take the net present values of “new machine” and “keep old” separately and then
compute the equivalent annual annuity before comparing.
b
There are three items in bold. These are the three differences between a new investment problem and a
replacement investment problem.
1. SML: ks = kRF + s (kM – kRF)
n
2. Mean or expected value:
k̂   p i k i
i 1
3. ∆NWC = ∆CA - ∆CL = ∆Inv. + ∆ AR - ∆AP - ∆Accruals [we omit cash and notes payable from
working capital for problems in this section of the course]
4