FORMULAS TO LEARN Flashcards
total cost of a semi variable cost (high low method)
Total costs = Total fixed costs + (Variable cost per unit × Activity level)
calculate vc per unit using the high low method
VCPU = cost at high activity - cost at low activity/high level activity - low level activity
total annual holding costs
Total annual holding cost = holding cost per unit of inventory (Ch) × average inventory (Q/2).
Where average inventory held is equal to half of the order quantity Q.
Toal annual ordering cost
Total annual ordering cost = cost of placing an order (Co) × number of orders (D/Q).
Where the number of orders in a year is expected annual demand D divided by the order quantity Q.
total annual cost of inventory
Total annual cost = PD + (Co × D/Q) + (Ch × Q/2)
The Total Annual Costs (TAC) is the total of purchasing costs P multiplied by annual demand D plus total ordering costs (Co × D/Q) and total holding costs (Ch × Q/2)
reorder level
Reorder level = Maximum usage × Maximum lead time
EOQ
GIVEN
D = Demand per annum
Co = Cost of placing one order
Ch = Cost of holding one unit for one year
EBQ
GIVEN
Q = Batch size
D = Demand per annum
Ch = Cost of holding one unit for one year
Co = Cost of setting up one batch ready to be produced
R = Annual replenishment rate
min/max inventory level
Minimum level = Re-order level – (Average usage × Average lead time)
Maximum level = Re-order level + Re-order quantity – (Minimum usage × Minimum lead time)
closing inventory valuation
Closing inventory valuation = Opening inventory + receipts – issues
AVCO cumulative weighted average price
cumulative weighted average price = total costs before issue/total number of units before issue
total wages
total wages = (total hours worked x basic rate of pay ph) + (overtime hours worked x overtime premium pay ph)
piecework wages
total wages = units produced x rate of pay per unit
premium bonus plans
if an employee receives 50% of time saved
bonus = (time allowed - time taken)/3 x time rate
employee is paid based on ratio of time taken to time allowed
bonus = time taken/time allowed x time rate x time saved
labour turnover
number of leavers who require replacement/average number of employees x 100
labour efficiency ratio
standard hours for actual output/actual hours worked to produce output x 100
idle time ratio
idle hours/total hours x 100
labour capacity ratio
actual hours worked to produce output/total budgeted hours x 100
labour production volume ratio (activity ratio)
standard hours for actual output/total budgeted hours x 100
Overhead absorption rate
OAR = budgeted production overhead/budgeted total of absorption basis
The absorption basis is most commonly units of a product, labour hours, or machine hours.
calculate under/over absorption
calculate OAR
OAR = budgeted overheads/budgeted level of activity
calculate overhead absorbed by actual activity
overheads absorbed = OAR x actual level of activity
compare absorbed to actual
if absorbed are less Han actual overheads then there is an under absorption
reconcile absorption/marginal costing profits
absorption costing profit >
(opening inv - closing inv) x OAR >
marginal costing
total contribution
contribution = sales price - all variable costs
batch costing (cost per unit in batch)
total production cost of batch/number of units in batch
process costing (average cost per unit)
average cost per unit = net costs of inputs/expected output
average cost per unit (normal loss and scrap value)
average cpu = (total cost of inputs - scrap value of normal loss)/input unit - normal loss units
balancing equation for abnormal gains and losses
input units + abnormal gain = output units + normal loss
expected output (process costing)
output = input units - normal loss units
normal loss units
normal loss units = % normal loss x input
cost per unit for by products
(process costs materials & conversion - scrap value of normal loss - sales value of by product)/ (input units - normal loss units - by products)
net costs of inputs/expected outputs
cost per service unit
cost per service unit = total costs for providing the service/number of service units used to provide the service
coefficient of variation
standard deviation/mean
expected value
EV = sum of PX
P = probability of outcome
X = the outcome
standard normal distribution
z = (x - u)/o
z = the score
x = value being considered
u = the mean
o = the standard deviation
formula for a (y intercept)
a = sum of y/n - (b x sum of x)/n
y = dependent variable
n = number of pairs of data
b = gradient
x = independent variable
simple price/quantity index
simple price index = p1/p0 x 100
simple quantity index = q1/q0 x 100
0 = price/quantity at time 0
1 = price/quantity at time 1
chain base index
chain base index = this years value/last years value x100
Laspeyre index
price index = sum of (current year price x base year quantity)/sum of (base year price x base year quantity)
quantity index = sum of (current year quantity x base year price)/sum of (base year quantity x base year price) x100
paasche index numbers
price index = sum of (current year price x current year quantity)/sum of (base year price x current year quantity) x100
quantity index = sum of (current year quantity x current year price)/sum of (base year quantity x current year price) x100
budgeted production levels
forecast sales - opening inv + closing inv = budgeted production in units
material purchases budget
forecast material usage - opening inv of raw material + closing inv of raw material = material purchases budget
formula for compounding
v = X(1+ r)^n
v = future value
x = initial investment (present value)
r = interest rate (decimal)
n = number of time periods
formula for effective interest rate
r = (1 + I/n)^n -1
r = effective interest rate
I = nominal interest rate
n= number of time periods
formulas for discounting
present value = future value x discount factor
discount factor = 1/(1+r)^n or (1+r)^-n (GIVEN)
r = the interest rate as a decimal
n = number of time periods
payback period
initial investment/annual cash inflow
internal rate of return IRR
IRR = L + NL/(NL - NH) X (H-L)
L= lower rate of interest
H = higher rate of interest
NL = NPV at lower rate of interest
N = NPV at higher rate of interest
NPV using annuity factor AF
PV = annual cash flow x AF
AF = (1-(1+ r)^-n)/r
can also find using the table in exam, find the DF at the % rate column
NPV and IRR formula using perpetuities
PV = cashflow/r
or
PV = cash flow x 1/r
IRR of a perpetuity = annual inflow/initial investment x 100
sale volume variance
(actual q sold - budget q sold) x standard margin
standard margin is the standard cpu (marginal), or standard profit pu (absorption)
sales price variance
(actual price - budget price) x actual q sold
material price/usage variance
material price variance = (actual q bought x actual p) - (actual q bought x standard price)
material usage variance = (actual q used x standard p) - (standard q used for actual production x standard price)
Labour/overheads/materials total variance
total of rate and efficiency variances
rate variance = (actual hours x actual rate) - (actual hours x standard rate)
efficiency variance = (actual hours x standard rate) - (standard hours x standard rate)
fixed overhead expenditure variance in absorption costing
fixed overhead expenditure variance = actual expenditure - budget expenditure
fixed overhead volume variance - (actual units x OAR) - budgeted expenditure
fixed overhead capacity and efficiency variances
capacity variance = (actual hours x OAR per hour) - budget expenditure
efficiency variance = (standard hours for actual production x OAR per hour) - (actual hours x OAR per hour)
ROCE
= operating profit/(non current liabilities + equity)
ROS
return on sales = operating profit/revenue
gross margin
= gross profit/revenue
asset turnover
= revenue/capital employed
ROCE/ROS/Asset turnover formula
ROCE = ROS x Asset turnover
current ratio
= current assets/current liabilities
acid test (quick ratio)
= (current assets - inventory)/current liabilities
inventory holding period
= inventory/cost of sales x 365
receivables collection period
= receivables/credit sales x 365
payable payment period
= payables/credit purchases x 365
capital gearing (leverage)
= non current liabilities (debt)/ordinary shareholders funds (equity)
or
= non current liabilities/(non current liabilities +equity)
interest cover (income gearing)
= operating profit/finance cost
ROI
= controllable profit/controllable capital employed x 100
residual income RI
= controllable profit - notional interest on capital
production volume ratio
= actual output measured in standard hours/budgeted production hours x 100
capacity ratio
= actual production hours worked/budgeted production hours x 100
efficiency ratio
= actual output measured in standard hours/actual production hours worked x 100
