A company wishes to buy new equipment for $85,000.The equipment is expected to generate an additional $35,000 in cash inflows for four years.All cash flows occur at year-end.A bank will make an $85,000 loan to the company at a 10% interest rate so that the company can purchase the equipment.Use the table below to determine break-even time for this equipment. $$\begin{array} { c c }
\text { Year } & \text { Present Value } \
& \text { of 1 at } 10 \% \
0 & 1.0000 \
1 & 0.9091 \
2 & 0.8264 \
3 & 0.7513 \
4 & 0.6830
\end{array}$$

Question

A company wishes to buy new equipment for $85,000.The equipment is expected to generate an additional $35,000 in cash inflows for four years.All cash flows occur at year-end.A bank will make an $85,000 loan to the company at a 10% interest rate so that the company can purchase the equipment.Use the table below to determine break-even time for this equipment. $$\begin{array} { c c } 
\text { Year } & \text { Present Value } \
& \text { of 1 at } 10 \% \
0 & 1.0000 \
1 & 0.9091 \
2 & 0.8264 \
3 & 0.7513 \
4 & 0.6830
\end{array}$$

Quizplus · Accepted Answer

To calculate the break-even time, we need to find the point at which the total present value of the cash inflows equals the present value of the cost of the equipment and the loan.

The present value of the cost of the equipment and the loan is simply $85,000, since that's how much the company will receive from the bank.

To find the total present value of the cash inflows, we can use the table provided. We multiply the cash inflow for each year by the present value of 1 at 10% for that year and sum the results:

Year 1: $35,000 x 0.9091 = $31,818.50 
Year 2: $35,000 x 0.8264 = $28,924 
Year 3: $35,000 x 0.7513 = $26,296.50 
Year 4: $35,000 x 0.6830 = $23,905

Total present value of cash inflows: $31,818.50 + $28,924 + $26,296.50 + $23,905 = $110,944

Now we need to find the point at which the total present value of the cash inflows equals the present value of the cost of the equipment and the loan:

$110,944 = PV of $85,000 + PV of interest payments

Using the present value table, we can calculate the present value of four annual interest payments of $8,500:

Year 1: $8,500 x 0.9091 = $7,727.85 
Year 2: $8,500 x 0.8264 = $7,013.40 
Year 3: $8,500 x 0.7513 = $6,386.05 
Year 4: $8,500 x 0.6830 = $5,795.50

Total present value of interest payments: $7,727.85 + $7,013.40 + $6,386.05 + $5,795.50 = $26,922.80

So now we can rewrite the equation as:

$110,944 = $85,000 + $26,922.80

Solving for the break-even time gives us:

$25,021.20 = PV of cash inflows for break-even year

Looking at the table, we can see that this occurs between years 2 and 3, so the break-even time is between 2 and 3 years.

A Company Wishes to Buy New Equipment for $85,000 A)Break-Even Time Is Longer Than 4 Years