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A company wishes to buy new equipment for [tex]\$9,000[/tex]. The equipment is expected to generate an additional [tex]\$2,800[/tex] in cash inflows for six years. All cash flows occur at year-end. A bank will make a [tex]\$9,000[/tex] loan to the company at a [tex]10\%[/tex] interest rate so that the company can purchase the equipment. Use the table below to determine the break-even time for this equipment:

[tex]\[
\begin{array}{cc}
\text{Year} & \text{Present Value of 1 at } 10\% \\
0 & 1.0000 \\
1 & 0.9091 \\
2 & 0.8264 \\
3 & 0.7513 \\
4 & 0.6830 \\
5 & 0.6209 \\
6 & 0.5645 \\
\end{array}
\][/tex]

A. This project will never break-even.
B. Break-even time is between five and six years.
C. Break-even time is between two and three years.
D. Break-even time is between four and five years.
E. Break-even time is between three and four years.

Sagot :

GinnyAnswer
To determine the break-even time for this equipment purchase, we will calculate the present value (PV) of the cash inflows for each year and compare the cumulative PV to the initial equipment cost of \[tex]$9,000. Given: - Equipment cost: \$[/tex]9,000
- Annual cash inflow: \[tex]$2,800 - Interest rate: 10% - Present value factors for each year are provided We will use the formula for present value: \[ PV = \frac{\text{Cash inflow}}{(1 + \text{interest rate})^n} \] where \(n\) is the year. However, for simplicity, we will directly use the present value factors provided for each year to calculate the present value of the cash inflows. 1. Year 0: \[ PV_0 = \$[/tex]2,800 \times 1.0000 = \[tex]$2,800 \] 2. Year 1: \[ PV_1 = \$[/tex]2,800 \times 0.9091 = \[tex]$2,545.48 \] 3. Year 2: \[ PV_2 = \$[/tex]2,800 \times 0.8264 = \[tex]$2,314.00 \] 4. Year 3: \[ PV_3 = \$[/tex]2,800 \times 0.7513 = \[tex]$2,103.64 \] 5. Year 4: \[ PV_4 = \$[/tex]2,800 \times 0.6830 = \[tex]$1,912.40 \] 6. Year 5: \[ PV_5 = \$[/tex]2,800 \times 0.6209 = \[tex]$1,738.52 \] To find the year in which the total present value of the cash inflows equals or exceeds the equipment cost (\$[/tex]9,000), we calculate the cumulative present value for each year:

- Cumulative PV for Year 1:
[tex]\[ \text{Total PV} = \$2,800 + \$2,545.48 = \$5,345.48 \][/tex]
- Cumulative PV for Year 2:
[tex]\[ \text{Total PV} = \$5,345.48 + \$2,314.00 = \$7,659.48 \][/tex]
- Cumulative PV for Year 3:
[tex]\[ \text{Total PV} = \$7,659.48 + \$2,103.64 = \$9,763.12 \][/tex]

At this point, we compare the cumulative PV to the equipment cost:
[tex]\[ \text{Total PV} = \$9,763.12 \][/tex]
This is more than \[tex]$9,000. Therefore, the break-even occurs between the beginning of Year 4 and the end of Year 3. But since cumulative calculation for Year 3 is greater than \$[/tex]9,000, the exact break-even time would be between the accrual point of Year 3 and Year 4.

Hence:
[tex]\[ \text{Break-even time is between four and five years.} \][/tex]

Therefore, the correct answer is:
[tex]\[ \text{Break-even time is between four and five years.} \][/tex]
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