thanks a lot :)
my pleasure..
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my pleasure..anum...
i have checked ur file that is good effort to make it but it covers lesson 01 to 45.. if u have any file that cover whole course i.e. leson 01 to lesson 45.. plz share with us...
BUISNESS FINANCE FORMULAS 1-22
By IQRA JAHANGIR
The Balance Sheet Identity is:
Assets ≡ Liabilities + Stockholder’s Equity
Net Working Capital ≡ Current Assets – Current Liabilities
– NWC > 0 when Current Assets > Current Liabilities
– NWC < 0 when Current Assets < Current Liabilities
– NWC = 0 when Current Assets = Current Liabilities
The Income Statement
Revenue – Expenses ≡ Income
Average vs. Marginal Tax Rates
Suppose a Corporation has a taxable income of $200,000. So the Tax calculation will be:
$ 50,000 x 15% = $ 7,500
($ 75,000 – 50,000) x 25% = 6,250
($ 100,000 – 75,000) x 34% = 8,500
($ 200,000 – 100,000) x 39% = 39,000
$ 61,250
Cost of a Tax Deductible Expense
Corporation A Corporation B
Earnings before interest and taxes $400,000 $400,000
- Interest Expense 100,000 0
Earning before taxes (taxable income) 300,000 400,000
- Taxes @35% 105,000 140,000
Earning after taxes $195,000 $260,000
Difference in earning after taxes $65,000
It can also be computed as: Interest Expense (1 – Tax rate)
$100,000 (1 – 35%) = $65,000
Depreciation as a Tax Shield
Corporation A Corporation B
Earnings before interest and taxes $400,000 $400,000
- Interest Expense 100,000 0
Earning before taxes (taxable income) 300,000 400,000
- Taxes @35% 105,000 140,000
Earning after taxes $195,000 $260,000
+ Dep. charged without cash outlay 100,000 0
Cash flow $295,000 $260,000
Difference $35,000
It can also be computed as: Depreciation x Tax rate
$100,000 x 35% = $35,000
Cash flow from Assets = Cash Flow to creditors + Cash flow to Stockholders
Cash flow from assets = Operating Cash Flow- Net Capital Spending- Change in Net Working Capital
Where,
Operating cash flow = Earnings before Interest and taxes+ Depreciation – Taxes
Net Capital Spending = Ending Net Fixed Assets- Beginning Net Fixed Assets +Depreciation
Change in NWC = Ending NWC – Beginning NWC
Cash flow to creditors = Interest paid – Net new borrowings
Cash flow to stockholders = Dividends Paid
– Net new equity raised
Current Ratio
Current Assets
Current Ratio= ------------------------
Current Liabilities
Quick (or Acid-Test) Ratio
Current Assets – Inventory
Quick Ratio= ------------------------------------
Current Liabilities
Cash Ratio
Cash
Cash Ratio= -----------------------
Current Liabilities
Total Debt Ratio
Total Assets – Total Equity
Total Debt Ratio= ------------------------------------
Total Assets
Total Debt Ratio
Total Debt Ratio
Debt–Equity ratio = Total Debt / Total Equity
Equity Multiplier = Total Assets / Total Equity
Interest Coverage Ratio
Earning before Interest & Taxes
Interest Coverage ratio = -----------------------------------------
Interest
Cash Coverage Ratio
EBIT + Depreciation
Cash Coverage ratio = -----------------------------------------
Interest
Inventory Turnover Ratio
Cost of goods Sold
Inventory Turnover ratio = --------------------------------
Inventory
Days’ Sales in Inventory
365 days
Days’ Sales in Inventory = --------------------------------
Inventory Turnover
Receivables Turnover
Sales
Receivables Turnover = -------------------------------
Accounts Receivables
Days’ Sales in Receivables
365 days
Days’ Sales in Receivables = -------------------------------
Receivables Turnover
A Variation: Payables Turnover
Cost of Goods Sold
Payables Turnover = -------------------------------
Accounts payables
Capital Intensity Ratio
Total Assets
Capital Intensity Ratio = --------------------
Sales
Profit Margin
Net income
Profit Margin= --------------------
Sales
Return on Assets
Return on Assets (ROA) is a measure of profit per dollar of assets:
Net income
Return on Assets = --------------------
Total Assets
Return on Equity
Net income
Return on Equity = --------------------
Total Equity
Earnings Per Share
Net income
EPS = ---------------------------
Shares Outstanding
Price-Earning Ratio
Price-earnings or PE ratio is defined as:
Price per share
PE ratio = --------------------------
Earnings per share
Book Value per share
Total equity
Book Value = ------------------------------------
No. of shares outstanding
Market-to-Book ratio
Market value per share
Mark-to-Book ratio = ------------------------------------
Book value per share
The Du Pont Identity
Net Income
ROE = --------------------
Total Equity
Net Income Net Income Assets
ROE = -------------------- = ---------------- x -----------
Total Equity Total Equity Assets
Net Income Assets
= ---------------- x ----------------
Assets Total Equity
The Du Pont Identity
Net Income Assets
ROE = ---------------- x ----------------
Assets Total Equity
ROE = ROA x Equity multiplier
= ROA x (1 + Debt-Equity ratio)
The Du Pont Identity
Sales Net Income Assets
ROE = -------- x ---------------- x ----------------
Sales Assets Total Equity
Net Income Sales Assets
ROE = --------------- x ----------- x ----------------
Sales Assets Total Equity
ROE =Profit Margin x Total Assets Turnover x Equity Multiplier
The Du Pont Identity
ROE =Profit Margin x Total Assets Turnover x Equity Multiplier
Dividend Payout
Cash Dividends
Dividend Payout ratio = -----------------------
Net Income
Retention Ratio
Retained Earnings
Retention ratio = -----------------------
Net Income
Payout and Retention
A: If payout ratio is 40%, retention ratio is
1 – 40% = 60%
A: Dividends are $800 x 40% = $320
Internal Growth Rate
ROA x b
Internal Growth rate = ------------------
(1 – ROA) x b
Where ROA is return on assets and b is the retention ratio
Sustainable Growth Rate
ROE x b
Sustainable Growth rate = ------------------
(1 – ROE) x b
Simple interest.
I = P x r x t
Where
P => principal amount
r => interest rate
t => time periods (years)
I => simple interest
Compound interest.
I = P x rt
Future Value
FV = P(1 + rt)
In the one-period case, the formula for FV can be written as:
FV = C0× (1 + r)
Where C0 is cash flow today (time zero) and r is the appropriate interest rate.
Generalizing the future value of an investment over many periods:
FV = C0× (1 + r)t
Where
C0 is cash flow at date 0,
r is the appropriate interest rate, and
t is the number of periods over which the cash is invested.
The expression (1 + r)t is the future value interest factor.
Present Value
•
FV
PV = ----------------
(1+rt)
In the one-period case, the formula for PV can be written as:
Where
C1 is cash flow at date 1 and
r is the appropriate interest rate or discount rate
General formula for calculating present value of C cash flow in t periods time is:
Present Value vs. Future Value
What we called the present value factor is just the reciprocal of the future value factor.
If we let FVt stand for the future value after t periods, then the relationship between the future value and the present value is:
PV x (1 + r)t = FVt
PV = FVt / (1 + r)t = FVt x [1/ (1 + r)t]
Finding the Number of Periods: Rule of 72
t = 72 / r%
t = 72 / 10 = 7.2 years
Time Value Calculations
PV = Present value, what future cash flows are worth today
FVt = Future value, what cash flows are worth in the future
r = Interest rate, rate of return, or discount rate per period
t = number of periods
C = cash amount
FVt = C* (1 + r)t
The term (1 + r)t is called the future value factor.
PV = C/(1 + r)t
The term 1/(1 + r)t is called the present value factor.
IV. The basic present value equation giving the relationship between present and future
value is:
PV = FVt/ (1 + r)t
Present Value for Annuity cash flows
PV=C *(1 - Present value factor)/r = C *[1 - 1/(1 + r)t ]/r
Where
C = Periodic payment or annuity
r = rate of interest
t = number of periods
The term in the parenthesis is called present value interest factor of an annuity (PVIFAr,t).
PVIFA = (1 – Present value factor)/r
Future Value for Annuities
FVt = C (Future value factor - 1)/r
= C [(1 + r)t - 1]/r
Perpetuities
The present value of perpetuity is:
Perpetuity PV = C / r
Summary of Annuity and Perpetuity
PV = Present value, what future cash flows bring today
FVt = Future value, what cash flows are worth in the future
r = Interest rate, rate of return, or discount rate per period
t = Number of time periods
C = Cash amount
II. FV of C per period for t periods at r percent per period:
FVt = C [(1 + r)t - 1] / r
III. PV of C per period for t periods at r percent per period:
PV = C (1 - [1/ (1 + r)t]) / r
IV. PV of perpetuity of C per period:
PV = C / r
Effective Annual Rates
$1 x 1.10 = $1.10
$1 x 1.052 = $1.1025
Effective Annual Rates
EAR is computed in three steps
So
EAR = (1 + Quoted rate / m)m – 1
Where m is the number of times the interest is compounded
Annual Percentage Rates
A typical credit card agreement quotes an interest rate of 18% APR. Monthly payments are required. What is the actual interest rate you pay on such a credit card?
So,
EAR = (1 + 0.18/12)12 – 1
= 10.1512 – 1 = 19.56%
Valuing a Bond
If a bond has
– a face value of F paid at maturity
– a coupon of C paid per period
– t periods to maturity
– a yield of r per period
Its value is
Bond value = C x [1 – 1/(1+r)t]/r + F/ (1+r)t
Valuing Bonds
Bond value = C x [1 – 1/(1+r)t]/r + F/ (1+r)t
= Present value of coupons + Present value of face amount
Summary of Bond Valuation
I. Finding the value of a bond
Bond value = C x [1 - 1/(1 + r)t]/r + F/(1 + r)t
Where:
C = the promised coupon payment
F = the promised face value
t = number of periods until the bond matures
r = the market’s required return, YTM
II. Finding the yield on a bond
Given a bond value, coupon, time to maturity, and face value, it is possible to find the implicit discount rate, or yield to maturity, by trial and error only. To do this, try different discount rates until the calculated bond value equals the given bond value. Remember that increasing the rate decreases the bond value.
The Fisher Effect
• The relationship between real and nominal returns is described by the Fisher Effect.
Let:
R = the nominal return
r = the real return
h = the inflation rate
• According to the Fisher Effect:
1 + R = (1 + r) *(1 + h)
Rearranging the fisher effect
1 + R = (1 + r) *(1 + h)
R = r + h + r x h
• It tells that nominal rate has three components
– Real rate on investment r
– Compensation for the decrease in value of original investment because of inflation h
– Compensation for the decrease in value of income earned on investment due to inflation
• Dropping the third component (being very small), nominal rate gives us then approximately equal to:
R ≈ r + h
Cash Flows
Generalizing this valuation, let
– P0 => current price of stock
– P1 => price in one period
– D1 => Dividend paid at the end of the period
• So
P0
= (D1 + P1)/(1 + R)
– Where R is the market rate of return
• But this possible only if we know P1, making the problem more complicated
• So, if we want to know the price in one year i.e. P1 and we somehow know the price in two years P2 with D2 dividend expected in two years, then
P1
= (D2 + P2)/(1 + R)
• Now substituting this expression for P1 into our previous expression for P0 , we would have the following equation:
If we continue the substitution for 2 periods:
Note that no matter what the stock price is, the present value is essentially zero if we push the sale of stock far enough away.
• So, the current price of stock can be written as the present value of the dividends beginning in one period and extending out forever
• Alternatively, we can say that the price of stock today is equal to the present value of all of future dividends.
Zero Growth Stocks
A share of common stock in a company with a constant dividend is termed as zero growth type of stocks. This implies:
D1 = D2 = D3 = D = constant
• So the value of the stock is:
Since dividend is always the same, the stock can be viewed as an ordinary perpetuity with a cash flow equal to D every period.
• So the per share value is
P0 = D/R
Where R is the required rate of return
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