Formulas to Memorise Flashcards
Investment decision making process:
Terminal Value, Present Value and Annuity PV (Cumulative Present Value)
Terminal value is used for compounding the interest earned on a sum.
= (1+r)^n
Present value is used for discounting a future cash inflow to today’s prices.
= (1+r)^-n
Annuity Present Value (when cashflows are constant over multiple periods)
= (1-(1+r)^-n) / r
Investment decision making process:
Profitability Index and Discounted Payback Profitability Index (p.165)
Profitability index is an investment appraisal tool for ranking projects for the allocation of funds. This is particularly important when resources are limited.
Profitability Index:
- This gives a measure of the profitability in relation to the initial investment allowing a range of projects to be ranked when resources are scarce.
= NPV of the project / Initial cash outflows (investment)
Discounted Payback Profitability Index (DPBI)
- This is a measure of the number of times a project recovers the initial funds invested.
= Present value of net cash inflows / Initial cash outflows (investment)
Accounting rate of return (ARR) aka ROCE (p.191)
Accounting rate of return calculates a percentage return provided by the accounting profits of the project.
= [a] Avg Annual Profit / [b] Average value of investment
[a] = Net Cash inflow - Depreciation / Number of periods [b] = Initial Investment + Residual value / 2
Profit maximization model - Algebraic method and tabular method
Algebraic method:
1. Find [a] and [b]
2. Determine [MC]
3. MC = [MR]
4. MR = a - (2b)q
[q] = MR - a / (-2b)
5. [p] = a - bq
6. [TC] = (p-MC)q
Profit = TC - Fixed costs
a = Maximum price that would return zero sales. b - Change in price / change in demand MC - Marginal cost MR - Marginal revenue TC - Target cost P - Optimum price q - Quantity of demand
Profit maximization model - Algebraic method and tabular method
Algebraic method:
1. Find [a] and [b]
2. Determine [MC]
3. MC = [MR]
4. MR = a - (2b)q
[q] = MR - a / (-2b)
5. [p] = a - bq
6. [TC] = (p-MC)q
Profit = TC - Fixed costs
a = The price at which sales are zero b - Change in price / change in demand MC - Marginal cost MR - Marginal revenue TC - Target cost P - Optimum price q - Quantity of demand - trial and error can be used until the quantity used returns MR to = MC.
Investment Appraisal:
Payback Period
The amount of time until the initial investment is repaid.
= Initial Investment / Annual cash inflow
With uneven cash flows use the cumulative cash flow method remembering to calculate the months by:
[a] Payback amount required between months
[b] The next cash inflow / 12.
a / b = The number of months between periods.
Investment Appraisal:
Real rate of return (p.202)
(1+r) = (1+m)/(1+i)
Real rate of return is a tool that is used to deal with the impact inflation has on the NPV of investments that span over multiple period.
Formula
= (1+r) = (1+m)/1+i)
Two methods can be used depending whether there are multiple rates of inflation or tax in the question.
Single rate of inflation (No tax)
- Money / Nominal method
= Inflate each cash flow by its specific inflation rate (i.e convert it to a ‘money flow’)
- # Real method
Pricing Decisions:
Price elasticity of demand
PED is a tool used to measure the change in demand as a result of a change in a products price.
= Percentage change in demand / percentage change in price
Pricing Decisions:
Price elasticity of demand (p.240)
PED is a tool used to measure the change in demand as a result of a change in a products price. A PED < 1 would indicate an INELASTIC demand meaning that demand is not very responsive to changes in price. The opposite would be for a PED >1 indicating an ELASTIC demand.
= Percentage change in demand / percentage change in price
Pricing Decisions:
Profit Maximisation (p.249)
A mathematical model used to determine the optimal selling price. Based on the theory that profit is maximised at the output level there marginal cost is equal to marginal revenue (MR).
MR = a-(2b)q
a = Theoretical price that would result in zero sales.
calculated as:
