We will use examples. In the following examples, you are the treasurer, and must make decisions about financial investments in various projects. All the decisions you make will rest on the assumption that the investment money is raised through a bank loan bearing 10% interest.
In most of the cases, the amount that you can raise from the bank for investment purposes is limited, while on the other hand you are offered a number of projects. You must decide which project to choose.
Before we present these examples, we will first say that the decision-making technique is simple: We will invest only in a project when the present value of the flow of income that it generates is greater than the sum that is necessary to invest in the project.
When our money is limited, we will choose the projects that are the most profitable. The meaning of “most profitable” will be described in the examples.
Example 1:
You are offered three projects, which are described in the table.
Each project involves an oil well that will produce oil for only a limited number of years, as indicated in the table. The investment required for each of the projects is $1 million. In which of the projects will you invest assuming that you can raise only $1 million?
Table 2.4
| Project 1 | Project 2 | Project 3 | |||
| 1 | 1 | 2 | 3 | 4 | |
| 2 | Amount of investment | $1.0 million | $1.0 million | $1.0 million | |
| 3 | Income | End of Year 1 | $0.3 million | $0.4 million | $0.5 million |
| 4 | End of Year 2 | $0.4 million | $0.4 million | $0.4 million | |
| 5 | End of Year 3 | $0.3 million | $0.3 million | $0.1 million | |
| 6 | End of Year 4 | $0.3 million | $0.3 million | Oil runs out | |
| 7 | End of Year 5 | $0.1 million | Oil runs out | — | |
| 8 | End of Year 6 | Oil runs out | — | — | |
| 9 | Present value of the flow of income | $1.10 million | $1.12 million | $0.86 million | |
| 10 | Profitability of the project (line 9 minus line 2) | $0.10 million | $0.12 million | $0.14 million (loss) | |
The Choice:
Project no. 2.
The explanation:
You should pick project no. 2 which has a present value of $1.12 million. (Project no. 2 provides a gain of $0.12 million in present value since $1 million would be invested to recieve a value of $1.12 million.)
Example 2:
You have two investment proposals, and you can choose only one. The source of financing is a bank loan bearing 15% interest. Which of the proposals will you choose?
Table 2.5
| Investment Proposal No. 1 | Investment Proposal No. 2 |
| You are offered the opportunity to purchase a new machine for $600,000. The machine will increase the annual profit by $360,000 a year for three years. | You are offered the opportunity to purchase an industrial building for $1,200,000. The building is leased to the AB company and yields an annual net profit of $200,000. |
| Assume that: | Assume that: |
| 1) The profit is received at the end of each year. | 1) The profit is received at the end of each year. |
| 2) The machine is completely worn out at the end of the third year. | 2) AB Company resumes owndership of the building at the end of 25 years. |
| 3) The capitalization interest is 15%. | 3) The capitalization interest is 15%. |
Table 2.6 contains the data necessary to make a decision about each of the proposals.
The data includes:
- The sum of the investment
- The present value of the flow of income (we calculate the amount)
- The percentage of profit on the investment
Table 2.6
| Proposal No. 1 | Proposal No. 2 | ||
| 1 | Sum of the investment | $600,00 | $1,200,000 |
| 2 | Present value of the flow of income (we calculated the sum for you) | $684,968 | $1,292,830 |
| 3 | Percentage of profit on the investment (row 2 divided by row 1) | 14% | 7.7% |
In conclusion:
Both proposals are profitable, but proposal no. 1 is more profitable. More profitable means that for each $1 of investment, proposal no. 1 earns 14%, while under proposal no. 2, you would earn only 7.7%.
The Standard Interest Rate Used for Examining Investment Proposals
A distinction is usually made between these two situations:
- The source of financing for the investment is a loan from banks.
- The source of financing is money belonging to us (equity).
When the source is a bank loan, the rate of interest that the bank charges for the loan is usually used to calculate the present value. Alternatively, the present value of equity is calculated using a rate that is used to discount similar risky equity investments, such the stock of a competing company.
Conclusions
We see clearly in the table that the viability of the investment decreases when the capitalization interest rises from 10% to 15%.
According to the first alternative, it is worthwhile investing $1 million in projects no. 1 and no. 2. when the level of certainty falls (alternative 2), however it is no longer worthwhile to invest more than $0.98 million in project no. 1, $1.02 million in project no. 2, and $0.80 million in project
Use of Present Value VS Future Value
Future value is almost never used to calculate profitability. Present value is the main tool for evaluating the profitability of investments.
