This chapter has described different tools to help MBA to make business decisions. (Information from link: http://encyclopedia.thefreedictionary.com - this is easier to understand than the ones in the book). To understand the following popular tools is important:
1) Decision Trees
A decision tree is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm. Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal. Another use of decision trees is as a descriptive means for calculating conditional probabilities.
Example
Decision trees can be used to optimize an investment portfolio. The following example shows a portfolio of 7 investment options (projects). The organization has $10,000,000 available for the total investment. Bold lines mark the best selection 1, 3, 5, 6, and 7, which will cost $9,750,000 and create a payoff of 16,175,000. All other combinations would either exceed the budget or yield a lower payoff.
2) Net Present Value (NPV) – The total present value of all cash flows “discounted” to today’s dollars.
Net present value (NPV) is a standard method for the financial appraisal of long-term projects. Used for capital budgeting, and widely throughout economics, it measures the excess or shortfall of cash flows, in present value (PV) terms, once financing charges are met. It is also called net present worth (NPW)[1]. By definition,
NPV = Present value of net cash flows. For its expression, see the formula section below.
Formula
Each cash inflow/outflow is discounted back to its present value (PV). Then they are summed. Therefore
Where
t - the time of the cash flow
N - the total time of the project
r - the discount rate (the rate of return that could be earned on an investment in the financial markets with similar risk.)
Ct - the net cash flow (the amount of cash) at time t (for educational purposes, C0 is commonly placed to the left of the sum to emphasize its role as the initial investment.).
The following sums up the NPVs in various situations.
If... | It means... | Then... |
NPV > 0 | the investment would add value to the firm | the project may be accepted |
NPV < 0 | the investment would subtract value from the firm | the project should be rejected |
NPV = 0 | the investment would neither gain nor lose value for the firm | We should be indifferent in the decision whether to accept or reject the project. This project adds no monetary value. Decision should be based on other criteria, e.g. strategic positioning or other factors not explicitly included in the calculation. |
3) Internal Rate of Return (IRR) – The discount rate that makes the net present value of the cash flows equal zero in today’s dollars.
The internal rate of return (IRR) is a capital budgeting metric used by firms to decide whether they should make investments. It is an indicator of the efficiency of an investment, as opposed to net present value (NPV), which indicates value or magnitude.
The IRR is the annualized effective compounded return rate which can be earned on the invested capital, i.e., the yield on the investment.
A project is a good investment proposition if its IRR is greater than the rate of return that could be earned by alternate investments (investing in other projects, buying bonds, even putting the money in a bank account). Thus, the IRR should be compared to any alternate costs of capital including an appropriate risk premium.
Mathematically the IRR is defined as any discount rate that results in a net present value of zero of a series of cash flows.
In general, if the IRR is greater than the project's cost of capital, or hurdle rate, the project will add value for the company.
To find the internal rate of return, find the value(s) of r that satisfies the following equation:
t - the time of the cash flow
N - the total time of the project
r - the discount rate (the rate of return that could be earned on an investment in the financial markets with similar risk.)
Ct - the net cash flow (the amount of cash) at time t (for educational purposes, C0 is commonly placed to the left of the sum to emphasize its role as the initial investment.).
Example
Calculate the internal rate of return for an investment of 100 value in the first year followed by returns over the following 4 years, as shown below:
Year | Cash Flow |
0 | -100 |
1 | 39 |
2 | 59 |
3 | 55 |
4 | 20 |
Solution:
We use an iterative solver to determine the value of r that solves the following equation:
The result from the numerical iteration is .
Joyce...very impressive!
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