Discounted Payback Method, Net Present Value, Internal Rate of Return, Profitability Index, and the Weighted Average Profitability Index.
Discounted Payback Method
Represents the amount of time that it takes (in years) for the initial cost of a project to equal to discounted value of expected cash flows.
Discounted payback accounts for time value - Applies discount rate to cash flows during payback period. - But still ignores cash flows after required payback period.
Discounted Payback Method: Pros and Cons
Advantages of discounted payback method:
Easy to calculate
Easy to understand
Focuses on cash flow
Takes into account the time value of money & risk
Disadvantages of discounted payback method:
Cut-off period is arbitrary
Does not lead to value-maximizing decisions
Example with Excel (Exercise 5 - Tecnocampus) (VIDEO - Spanish Version): https://www.loom.com/share/d30b52a3740e441e9eb0bc0e47535a9b
Net Present Value
NPV: The sum of the present values of a project's cash inflows and outflows.
Discounting cash flows accounts for the time value of money.
Choosing the appropriate discount rate accounts for risk.
When the NPV is higher than 0, we accept the project because we are getting more than we invested (Accept projects in NPV>0).
Formula: NPV = CFo + CF1/(1+k)^1 + CF2/(1+k)^2+...+ CFn/(1+k)^n
A key input in NPV analysis is the discount rate. - k represents the minimum rate that the project must earn to satisfy investors. - k varies with the risk of the firm and /or the risk of the project.
Net Present Value: Pros and Cons
Advantages:
NPV is the 'gold standard' of investment decision rules.
Focuses on cash flows, not accounting earnings.
Makes appropriate adjustment for time value of money.
Can properly account for risk differences between projects.
Disadvantages:
Lacks the intuitive appeal of payback.
Example with Excel (Exercise 6 - Tecnocampus) (VIDEO - Spanish Version):
Internal Rate of Return
The IRR, is the point where we will recover our investment. It's the break even point: total costs = income.
It's the discount rate that results in a zero NPV for a project (NPV = 0).
Formula: NPV = 0 = CFo + CF1/(1+r)^1 + CF2/(1+r)^2+...+ CFn/(1+r)^n
The IRR decision rule for an investing project is: - If IRR is greater than the minimum required return, accept the project. - If IRR is less than the minimum required return, reject the project.
Internal Rate of Return: Pros and Cons
Advantages of IRR:
Properly adjusts for time value of money
Uses cash flows rather than earnings
Accounts for all cash flows
Project IRR is a number with intuitive appeal
Disadvantages of IRR:
“Mathematical problems”: multiple IRRs, no real solutions
Scale problem
Timing problem
Example with Excel (Exercise 7 - Tecnocampus) (VIDEO - Spanish Version):
It is also possible to find multiple internal rate of return, this situation happens when a project has cash flows with multiple changes in signs. The question here is, which IRR do we use?
The answer is that there is no real solution. Sometimes, projects do not have a real IRR solution, because there is no real number that will make NPV = 0.
The scale problem
The scale problem appears when the NPV and the IRR do not agree when raking competing projects.
For example: if we have two different projects:
European project: IRR = 28,2% and the NPV = €85,6m
US project: IRR = 46,7% and the NPV = €35,7m
The US project has a higher IRR, but doesn't increase shareholder's wealth (NPV) as much as the European project. Therefore, a higher NPV is more attractive than a higher IRR, because the opportunities to make a larger investment is more attractive.
Profitability Index
It is calculated by dividing the PV of a project's cash inflows by the PV of its initial cash flows.
Formula:
A project is accepted when PI > 1,0, or equal to NPV > 0. The highest, the better.
For example: Project PV of CF (years 1 to 5) Initial Outlay PI EU project € 425,7 million € 350 million 1,2 US project € 85,9 million € 60 million 1,4 Answer: PI has been calculated dividing PV of CF by the Initial Outlay (|CFo|). Both PI are bigger than 1, so both are acceptable if independent. However, the highest the better.
Like IRR, PI suffers from the scale problem.
Example with Excel (Exercise 8 - Tecnocampus) (VIDEO - Spanish Version):
Weighted Average Profitability Index (WAPI)
The WAPI is calculated when we know the maximum amount of EUR that we can invest in one or more projects.
For example:
If we only have 400,000 EUR to invest. Which project to we select? Project PV Investment PI A 240.000,00€ 210.000,00€ 1,14 B 151.350,00€ 135.000,00€ 1,12 C 198.450,00€ 180.000,00€ 1,10 D 172.000,00€ 160.000,00€ 1,08
WAPI project A + C = 1,14 x (210/400) + 1,10 x (180/400) + 0 x (10/400) = 1.09 WAPI project A + B = 1,14 x (210/400) + 1,12 x (135/400) + 0 x (55/400) = 0.98
WAPI project A + D = 1,14 x (210/400) + 1,08 x (160/400) + 0 x (30/400) = 1.03
WAPI project B + C = 1,12 x (135/400) + 1,10 x (180/400) + 0 x (85/400) = 0.87 WAPI project B + D = 1,12 x (135/400) + 1,08 x (160/400) + 0 x (105/400) = 0.81 WAPI project D + C = 1,08 x (160/400) + 1,10 x (180/400) + 0 x (60/400) = 0.93
Answer: After trying all the possible combinations, we have to select the project with the highest Weighted Average PI. In this example, the highest WAPI is Project A + C with 1.09, which means that we will invest in those two projects because they have the highest weighted average profitability index.
Example with Excel (Exercise 9 - Tecnocampus) (VIDEO - Spanish Version):
*Information and Loom exercises have been gathered from Tecnocampus' slides and own knowledge.
Comentários