To calculate the Discounted Payback Period (DPP):
\[ DPP = -\frac{\ln \left( \frac{I \times R}{CF} \right)}{\ln (1+R)} \]
Where:
The Discounted Payback Period is a financial metric used to determine the time it takes for an investment to recoup its initial cost while considering the time value of money. Unlike the traditional Payback Period, which ignores the concept of interest rates, the Discounted Payback Period considers the present value of future cash flows by discounting them to their current value.
This metric is essential because it helps investors evaluate the profitability and risk associated with an investment project. By incorporating the time value of money, the Discounted Payback Period provides a more accurate assessment of an investment's potential return. It considers the opportunity cost of tying up capital in a project and allows investors to compare different investment options more effectively.
Let's assume the following values:
Using the formula:
Step 1: Convert the discount rate to a decimal:
\[ R = \frac{10}{100} = 0.10 \]
Step 2: Calculate the ratio:
\[ \frac{I \times R}{CF} = \frac{100000 \times 0.10}{20000} = 0.5 \]
Step 3: Calculate the natural logarithm of the ratio:
\[ \ln(0.5) = -0.6931 \]
Step 4: Calculate the natural logarithm of (1 + R):
\[ \ln(1 + 0.10) = \ln(1.10) = 0.0953 \]
Step 5: Divide the natural logarithms:
\[ DPP = -\frac{-0.6931}{0.0953} \approx 7.27 \text{ years} \]
The Discounted Payback Period is approximately 7.27 years.
Let's assume the following values:
Using the formula:
Step 1: Convert the discount rate to a decimal:
\[ R = \frac{5}{100} = 0.05 \]
Step 2: Calculate the ratio:
\[ \frac{I \times R}{CF} = \frac{50000 \times 0.05}{10000} = 0.25 \]
Step 3: Calculate the natural logarithm of the ratio:
\[ \ln(0.25) = -1.3863 \]
Step 4: Calculate the natural logarithm of (1 + R):
\[ \ln(1 + 0.05) = \ln(1.05) = 0.0488 \]
Step 5: Divide the natural logarithms:
\[ DPP = -\frac{-1.3863}{0.0488} \approx 28.42 \text{ years} \]
The Discounted Payback Period is approximately 28.42 years.
