ANOPAT* - Cost of Capital % X (Adjusted Total Assets - Current Liabilities)

*ANOPAT  means the Adjusted Net Operating Profit After Taxes

Risk-Free Rate of Return + (Avg. Market Return Rate - Risk-Free Rate) X Beta

Payment Required to be Received Forever / Required Rate of Return

D/(K-g)

D = Annual Dividends per Share

K = Discount Rate or Required Rate of Return

g = Annual Dividend Growth Rate

NPV of Future Cash Flows/Initial Investment

Borrowing Rate x (1 - Tax Rate)

[K_d(1-t)(Market Value of Debt)/Total Debt and Equity ]+ [Ke(Market Value of Equity)/Total Debt and Equity]

t = tax rate

K_d = cost of debt

K_e = cost of equity

Annual Dividend / Market Price Per Share

Annual Dividend / Net Income

Terminal Cash Flow / (Discount Factor^* - Growth)

^{*Discount Factor = WACC} 

K_e = R_f + (K_m - R_f)Beta

_{Rt = Risk Free Treasury Rate}

_{Km - Rt = Risk Premium}

Quick Ratio

or 

Acid Test

Liquid Assets/Quick Liabilities

or

Cash and Cash Equivalent + Marketable Securities + Accounts Receivable/Current Liabilities

($ *. 90) + ($ * .19) = EMV*

*Useful in Decision Trees

($ today) x (1 + Reinvestment Rate)^{Number of Periods}

($ in Future) x (1 + Discount Rate)^{-Number of Periods}

0 = P₀ + P₁/(1+IRR) + P₂/(1+IRR)^₂ + P₃/(1+IRR)^₃ + . . . +P_n/(1+IRR)^_n

^{where P₀, P₁, . . . P_n equals the cash flows in periods 1, 2, . . . n, respectively; and
IRR equals the project's IRR}

[(Point of Interest) - Mean] / SD*

*Standard Deviation

r = number of successes

n = number of trials

p = probability of success.

Please refer to a binomial distribution table.

1 = .3413

2 = .4772

3 = .49865

4 = .4999683

A form of the normal distribution that shows the probability of being less than or equal to all possible outcomes

Queuing Questions

_{A = Average number of random arrivals per unit of time}

_{S = Average number of services provided per channel per unit of time}

_{M = Number of available channels}

• Utilization factor of the System = A/MS
  
  
• Average Number Waiting = Total Number in Line - (A/S)
  
  
• Expected Waiting Time in Line = Average # Waiting / A

Economic Order Quantity (EOQ)

EOQ = Optimal inventory order Quantity

_{R = Annual unit requirements (Demand)}

_{O = Cost of placing an order}

_{C = Cost of carrying a unit of inventory per period}

Square Root √(2 X R X O / C)

Upper Control Limits (UCL)

A measurement of how the process is actually performing as opposed to a specification limit.  Typically within 3 standard deviations above or below the Median.

Lower Control Limits (LCL)

A measurement of how the process is actually performing as opposed to a specification limit.  Typically within 3 standard deviations above or below the median.

X Bar Control Chart

R (Range Chart) Control Chart

Shows any tendency of a process to behave more or less randomly over time.

Learning Curve

_{Many learning curves exist.}

Cost Per Unit X Curve

Unit 1              = $10       

$10 x .8

Unit 2,097,152 = $.09      $10 x  (.8)²¹

Gross National Product (GNP)

_{C = Personal Consumption}

_{I = Private Investment}

_{G = Government Purchases}

_{X = Net of Exports over Imports}

Spending Multiplier

_{MPC = Marginal Propensity to Consume}

Nominal GNP

M X V = P X Q

Money x Velocity =Price Level x Real GNP

Money Supply = Nominal GNP

CAC (Cost to Acquire a Customer)

MRR¹ Per Customer

Churn Rate %

Margin %

LTV = MRR/(Churn Rate X Margin)

LTV:CAC = LTV/CAC

1 _{^{Monthly Recurring Revenue}}