Discounted payback: KML Co. has bought some new machinery at a cost of $1,250,000. The impact of the new machinery will be felt in the additional annual cash flows of $375,000 over the next five years. The company's cost of capital is 10 percent. What is the discounted payback period for this project? If their acceptance period is three years, will this project be accepted?

To solve this problem, we'll calculate the **Discounted Payback Period (DPP)** for KML Co.'s project. The **Discounted Payback Period** is the time it takes for a project to recover its initial investment in present value terms, considering the cost of capital.

### Steps:
1. **Determine the Cash Flows:**
   - The initial investment is $1,250,000$.
   - Annual cash inflows are $375,000$ for 5 years.
   - The cost of capital (discount rate) is 10%.

2. **Discount the Cash Flows:**
   - Each cash flow will be discounted using the formula:
     \[
     \text{PV of Cash Flow} = \frac{\text{Cash Flow}}{(1 + r)^t}
     \]
     where $r$ is the discount rate (10%), and $t$ is the year number.

3. **Calculate the Cumulative Discounted Cash Flows:**
   - We will sum the discounted cash flows year by year until the initial investment is recovered.

Let's proceed with the calculations.Here are the calculations:

1. **Discounted Cash Flows:**
   - Year 1: \$340,909.09
   - Year 2: \$309,917.36
   - Year 3: \$281,743.05
   - Year 4: \$256,130.05
   - Year 5: \$232,845.50

2. **Cumulative Discounted Cash Flows:**
   - Year 1: \$340,909.09
   - Year 2: \$650,826.45
   - Year 3: \$932,569.50
   - Year 4: \$1,188,699.54
   - Year 5: \$1,421,545.04

The **Discounted Payback Period** is **5 years**, as it takes this long for the cumulative discounted cash flows to exceed the initial investment of \$1,250,000.

### Project Acceptance:
Since KML Co.'s acceptance period is 3 years, the project **will not be accepted** because the discounted payback period (5 years) exceeds their required time frame.

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Do you have any questions or want further details?

Here are 5 related questions for further learning:
1. How does the discounted payback period differ from the regular payback period?
2. What are the advantages of using the discounted payback period over other methods?
3. How would a change in the cost of capital affect the discounted payback period?
4. What are some limitations of the discounted payback period method?
5. How does the discounted payback period impact investment decisions compared to NPV or IRR?

**Tip:** The discounted payback period provides a better perspective on the time it takes to recover an investment because it accounts for the time value of money, unlike the simple payback period.

Learn how to calculate the discounted payback period for KML Co.'s $1,250,000 machinery investment, considering cash flows of $375,000 over five years and a 10% cost of capital. Explore detailed steps and assess if the project will be accepted based on a 3-year acceptance period.

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