An investment project has annual cash inflows of $4,300 , $5,500, $6,400, and $7,800, and a discount rate of 13 percent. What is the discounted payback period for these cash flows if the initial cost is $9,000? What if the initial cost is $12,000? What if it is $16,000?

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To solve this problem, we need to calculate the **discounted payback period**. The discounted payback period accounts for the time value of money by discounting future cash flows before determining the payback period.

### Key Concepts and Formulas

1. **Discount Factor**:
   The discount factor is calculated using the formula:
   \[
   \text{Discount Factor} = \frac{1}{(1 + r)^t}
   \]
   where:
   - $ r $ is the discount rate (13% in this case, or 0.13).
   - $ t $ is the year number (1, 2, 3, etc.).

2. **Discounted Cash Flow (DCF)**:
   The discounted cash flow for each year is calculated as:
   \[
   \text{Discounted Cash Flow} = \text{Cash Inflow} \times \text{Discount Factor}
   \]

3. **Cumulative Discounted Cash Flow**:
   The cumulative discounted cash flow is the

Learn how to calculate the discounted payback period for investment projects with annual cash inflows of $4,300, $5,500, $6,400, and $7,800 at a 13% discount rate. Includes solutions for initial costs of $9,000, $12,000, and $16,000.

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