In the previous article, we have covered the future value of a mixed stream cash flow. In this article, we cover the present value of a mixed stream cash flow. The calculation is similar except for the use of the discounting factor in order to discount each cash flow to year zero.
In this article, we will illustrate how to calculate the present value of a mixed stream cash flow by using either tabular format or Excel Spreadsheets. In addition, we cover also how to get the present value interest factors table.
So let’s dive in!
What is Present Value of a Mixed Stream Cash Flow?
As has been covered in the previous article, a mixed stream cash flow refers to a stream of unequal periodic cash flows over a certain period of time. Additionally, this type of cash flow has no particular pattern.
Thus, the PV of a mixed stream cash flow is the sum of the expected current value of future periodic unequal cash flow over a certain period of time at a given discount rate.
How to Calculate the Present Value of a Mixed Stream Cash Flow?
We can calculate the present value of a mixed stream cash flow by using tabular format or by using an Excel spreadsheet.
Similar to the future value of a mixed stream of cash flow calculation, in the tabular format, we need to know the present value interest factors (PVIF). These present value interest factors can be obtained from the present value interest factors table.
Therefore, upon getting the present value interest factors of each year at a given interest (or discount) rate, we just simply multiply each stream of cash flow with the present value interest factors.
Hence, we can summary the formula of the present value of a mixed stream cash flow as follows:
PV of a mixed stream cash flow = C1 × PVIF1 + C2 × PVIF2 + C3 × PVIF3 +……. + Cn × PVIFn
Or we can also rewrite the formula in full as follows:
PV of a mixed stream cash flow = C1 × (1+i)-1 + C2 × (1+i)-2 + C3 × (1+i)-3+ …….. + C1 × (1+i)-n
Where:
C = Is each cash flow
i = Interest rate
We can obtain the future value interest factors by looking at the future value interest factors table. Alternatively, we can calculate the future value interest factors for each year at a given interest rate by using the formula below:
PVIFn = (1+i)-n
Example
Let’s continue with the example in the previous article on the future value of a mixed stream cash flow. Suppose ABC Co has been offered an opportunity to receive the future cash flow for the next 5 years as follows:
| End of year | Cash Flow |
|---|---|
| 1 | 11,000 |
| 2 | 12,000 |
| 3 | 14,000 |
| 4 | 16,000 |
| 5 | 15,000 |
The relevant discount rate is at 8%. So calculate how much is the present value of this stream of cash flow?
Solution:
By looking at the present value interest factors table, we can calculate the PV of a mixed stream cash flow as follows:
| Year | Cash flow [1] | PVIF8% [2] | Present value [3 = (1) × (2)] |
|---|---|---|---|
| 1 | 11,000 | 0.926 | $10,185 |
| 2 | 12,000 | 0.857 | $10,288 |
| 3 | 14,000 | 0.794 | $11,114 |
| 4 | 16,000 | 0.735 | $11,760 |
| 5 | 15,000 | 0.681 | $10,209 |
| Present value of mixed stream | $53,556 |
From the tabular calculation above, the PV of mixed stream cash flow is US$53,556. This means that the sum of the present value of each stream of cash flow at a given discount rate is US$53,556.
The PV of this mixed stream of cash flow can be depicted as follows:
As you can see, the sum of the present value of each cash flow to year 0 is $53,556. Alternatively, we can also calculate the PV of the mix stream cash flow by using Excel Spreadsheets as follows:
sample Excel spreadsheet above, the result is the same as the tabular calculation. Thus, whatever methods you use, the PV of the mixed stream is at the same value.
You can use the sample formula of the present value calculation above to develop your own calculation.
Present Value Interest Factors Table
The Present value interest factors table is commonly used in order to calculate the present value of a mixed stream cash flow. So how to get this table?
You can generate your own present value interest factors table by using the below formula and then you just need to develop the data table in the Excel Spreadsheets.
PVIFn = (1+i)-n
By using the PVIF formula above, you can generate the present value interest factors by simply copy the screenshot formula above and then paste it into each cell so that you will get the present value interest factors the same as above.
Conclusion
The present value of a mixed stream cash flow is simple and easily calculated by using either tabular format or Excel Spreadsheets. In the tabular format, you will need to look at the present value interest factors table.
Additionally, you can also generate your own present value interest factors table by yourself by using the PVIF formula.
