Formulas Flashcards
Present Value (PV)
Present Value -
The value today of future cash flows.
PV = FV / (1 + r)n
FV = future value
r = interest rate
n = number of time periods
Example: what is present value of $300,000 received 3 years from now if we expect the interest rate to be 10%?
Answer: $225,394
Payback / Break Even Period
Payback / Break Even Period -
Amount of time required to recuperate costs incurred on a project - to reach the break even point.
Exam: when choosing between two project, select the one with the fastest payback period, regardless of the investment!
Example: what is the payback period if the cost of project is $200,000 and revenue is $50,000 per year,
Answer: the payback period will be 4 years.
Internal Rate of Return (IRR) / Discount Rate
Internal Rate of Return (IRR) / Discount Rate -
Exam: when comparing projects always select project with the highest IRR, meaning better positive return. The durations are already part of the IRR calculations and therefore irrevelant!
The rate at which an investment will yield returns.
- Also called discount rate that makes NPV=0.
- Similar to bank’s interest rate.
- Normally expressed as a percentage.
- The higher the IRR, the more lucrative the project will be.
So when the IRR is 5%, it means that for every $100 you invest, the return on investment will be $105.
Example: Project A with a projected duration of 3 years has an IRR of 9%. Project B would take 2 years and has an IRR of 6%. Which project would you select?
Answer: Project A since it has a higher IRR, meaning better positive return. Durtion is irrevelant!
Net Present Value (NPV)
Net Present Value (NPV) -
The sum of PVs of the expected inflows minus the outflows (investment or cost).
Exam: always select project with highest NPV, regardless of number of years!
Higher NPV is better:
> 0 = project is lucrative
= 0 = project is neither profitable nor unfavorable
< 0 = project is unfavorable
Return on Investment (ROI) / Marginal Analysis
Return on Investment (ROI) -
A return ratio that compares the net benefits of a project with its total cost. Subtracts costs from benefits.
Net Benefits / Total Costs
Example: project total cost was $150,000 and is expected to bring in $350,000 (total benefit) this year.
Answer: the ROI is $200,000 / $150,000 = 1.33 = 133%
Net Benefits: $350,000-150,000 = 200,000;
Cost = 150,000.
Example: Acme widget produced widgets at total cost of $50,000 and sold them for $1,200 each, for a total revenue of $60,000.
If Acme Widget produces a 51st widget at a cost of $1,500, its total cost will be $51,500 and its total revenue will be $61,200.
Should the firm produce the 51st widget?
Answer:
First 50 widgets:
Marginal benefit = $1,200 (marginal revenue) - $1,000 (marginal cost) = $200
ROI = $200 / $1,000 = 20%
Starting with 51st widget:
Marginal benefit = $1,200 (marginal revenue) - $1,500 (marginal cost) = -300
ROI = $-300 / $1,500 = -20%!
Answer is NOPE!
Discounted Cash Flow (DCF)
Discounted Cash Flow (DCF) -
PV of an investment’s future cash flows.
Just take the highest number; no math involved.
Lifecyle Cost (TCO)
Lifecycle Cost (total cost of ownership) -
Developmental Cost + Maintenance & Operational
Applies to products.
Exam: when comparing projects, select project that has LOWER lifecycle costs!
Example 1:
product development cost = $30,000
operations & maint cost = $70,000
product lifecycle cost = $100,000
Example 2:
Project A started with investment of $300,000 and has lifecycle cost of $700,000. Project B started with investment of $200,000 and has lifecycle cost of $850,000. Which project would you select?
Answer:
Project A = $300,000 + $700,000 = $1,000,000
Project B = $200,000 + $850,000 = $1,050,000
Select Project A because it has lower lifecycle cost, regardless of the investment!
Opportunity Cost
Opportunity Cost -
Economic value of the next best alternative forgone or given up
Example: PMTI had 3 project opportunities. PMTI chose a $4M project over a $2M project and $3M projects. PMTI’s opportunity cost was $3M.
Depreciation
Depreciation -
A decline in value of property
Benefit-Cost Ratio (BCR)
Benefit-Cost Ratio (BCR) -
Benefit / Cost
Exam: when comparing multiple projects, select the one with the highest BCR regardless of the investment!
Compares revenue (benefit) of project to its cost.
If ratio is > 1, project is profitable.
If ratio is = 1, project will break even.
If ratio is < 1, costs are higher than benefit
Example: benefits = $350,000; costs = $150,000
Answer: 2.33
Example:
Project Investment BCR Ratio
Project A $200,000 8 : 4
Project B $700,000 5 : 3
Project C $1,000,000 5 : 2
Answer:
Project C.
Scoring Models
Scoring Models -
Point based system using known facts to predict future outcomes. Used to examine “project worthiness” and compare it to other projects.
Weights are assigned to factors to calculate weighted average project score.
Example (see screenshot)
Answer:
Project A since it has the highest score
Future Value (FV)
Future Value -
The value today of future cash flows.
FV = PV / (1 + r)n
To do this math, you need to use PV in the numerator, which is the missing element. Then do algebra to multiply the denominator by FV.
FV = future value
PV = present value
r = interest rate
n = number of time periods
Example: A project manager wants to invest money into a project. What is the future value after 2 years if the present value is $100,000 and the rate of return is 5%?
Answer:
Present value = future value / (1 + interest rate)n
$100,000 = future value / (1 + .05)2
Then do the algebra thing (multiply denominator by PV)
Future value = $110,250
