Kara, Incorporated, imposes a payback cutoff of three years for its international investment projects. Assume the company has the following two projects available.

Year: 0
Cash Flow (A): −$ 53,000
Cash Flow (B): −$ 98,000

Year: 1
Cash Flow (A): 21,000
Cash Flow (B): 23,000

Year: 2
Cash Flow (A): 27,800
Cash Flow (B): 28,000

Year: 3
Cash Flow (A): 23,000
Cash Flow (B): 31,000

Year: 4
Cash Flow (A): 9,000
Cash Flow (B): 242,000


A. What is the payback period for each project? 
B. Which, if either, of the projects should the company accept?

Note: Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.

### A. Payback Period Calculation:

The **payback period** is the time it takes for an investment to recover its initial cost from the cash inflows. To find the payback period, we accumulate the cash flows until the initial investment is fully recovered. 

Let's calculate this for **Project A** and **Project B**.

---

#### **Project A**:

- **Year 0**: Cash flow = -$53,000
- **Year 1**: Cash flow = +$21,000
- **Year 2**: Cash flow = +$27,800
- **Year 3**: Cash flow = +$23,000
- **Year 4**: Cash flow = +$9,000

Cumulative cash flows:
- **Year 0**: -$53,000
- **Year 1**: -$53,000 + $21,000 = -$32,000
- **Year 2**: -$32,000 + $27,800 = -$4,200
- **Year 3**: -$4,200 + $23,000 = $18,800

At the end of Year 2, Project A has not yet paid back its initial investment (there's still -$4,200 to recover). But during Year 3, it crosses into positive cash flows.

To calculate the exact payback point during Year 3:
\[
\text{Payback in Year 3} = 2 + \frac{\$4,200}{\$23,000} \approx 2 + 0.18 = 2.18 \text{ years}
\]

Thus, the payback period for **Project A** is **2.18 years**.

---

#### **Project B**:

- **Year 0**: Cash flow = -$98,000
- **Year 1**: Cash flow = +$23,000
- **Year 2**: Cash flow = +$28,000
- **Year 3**: Cash flow = +$31,000
- **Year 4**: Cash flow = +$242,000

Cumulative cash flows:
- **Year 0**: -$98,000
- **Year 1**: -$98,000 + $23,000 = -$75,000
- **Year 2**: -$75,000 + $28,000 = -$47,000
- **Year 3**: -$47,000 + $31,000 = -$16,000
- **Year 4**: -$16,000 + $242,000 = $226,000

At the end of Year 3, Project B has still not paid back the initial investment. The payback happens in Year 4.

To calculate the exact payback point during Year 4:
\[
\text{Payback in Year 4} = 3 + \frac{\$16,000}{\$242,000} \approx 3 + 0.07 = 3.07 \text{ years}
\]

Thus, the payback period for **Project B** is **3.07 years**.

---

### B. Which project should Kara, Incorporated accept?

Kara, Incorporated imposes a **payback cutoff of 3 years**. This means that any project that has a payback period longer than 3 years will not be accepted.

- **Project A** has a payback period of **2.18 years**, which is within the 3-year cutoff.
- **Project B** has a payback period of **3.07 years**, which is slightly beyond the 3-year cutoff.

Therefore, **only Project A** should be accepted based on the company's payback cutoff criteria.

---

### Summary:
- **Payback period for Project A**: **2.18 years**
- **Payback period for Project B**: **3.07 years**
- **Recommendation**: Accept **Project A** only, as it meets the 3-year payback cutoff criterion.

Would you like any more details on these calculations or explanations? 

Here are some related questions to deepen your understanding:
1. How is the payback period different from other capital budgeting methods like NPV or IRR?
2. What are the advantages and disadvantages of using the payback period as a decision criterion?
3. Could the timing of large future cash flows (like in Year 4 for Project B) affect the decision-making process even if they fall outside the payback period?
4. How might different discount rates affect decisions if Kara Incorporated also considered NPV or IRR?
5. What additional factors might a company consider when choosing between projects besides the payback period?

**Tip**: The payback period is simple but ignores the time value of money, so it’s often used alongside other methods like NPV to give a more complete picture.

Kara, Incorporated, imposes a payback cutoff of three years for its international investment projects. Assume the company has the following two projects available:

Year: 0
Cash Flow (A): −$ 53,000
Cash Flow (B): −$ 98,000

Year: 1
Cash Flow (A): 21,000
Cash Flow (B): 23,000

Year: 2
Cash Flow (A): 27,800
Cash Flow (B): 28,000

Year: 3
Cash Flow (A): 23,000
Cash Flow (B): 31,000

Year: 4
Cash Flow (A): 9,000
Cash Flow (B): 242,000

A. What is the payback period for each project?
B. Which, if either, of the projects should the company accept?
Note: Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.

Learn how to calculate the payback period for two investment projects at Kara, Incorporated. This problem covers key finance concepts, including cash flow accumulation and the payback period formula. We explain the steps to calculate the exact payback year and compare the projects based on Kara's 3-year cutoff criterion. Suitable for undergraduate finance students.

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