The Oakley-Brown, a frozen food processor, requires an additional refrigeration unit. The company is considering a premium model at a cost of $52,000. Expected life for the unit is five years with a residual value of $18,500. The incremental income before depreciation is expected to be $14,500 a year. The company's cost of capital is 14%. Using 14% and 25% as trial values, what increase in the cost of capital will eliminate the unit from consideration?

Question

Quizplus · Accepted Answer

To determine the increase in cost of capital that would eliminate the unit from consideration, we need to calculate the present value of the incremental income before depreciation, deduct the present value of the cost of the unit, and compare this to zero. If the result is negative, the unit should not be purchased. We can then use trial and error to find the increase in the cost of capital that just makes the result equal to zero.

Using a financial calculator or spreadsheet, we can calculate that the present value of the incremental income before depreciation is:

PV(income) = $14,500 * (1 - 1 / (1 + 0.14)^5) / 0.14 = $49,840.27

And the present value of the cost of the unit is:

PV(cost) = $52,000 - $18,500 / (1 + 0.14)^5 = $33,634.68

Therefore, the net present value (NPV) of the investment is:

NPV = PV(income) - PV(cost) = $49,840.27 - $33,634.68 = $16,205.59

If the cost of capital increases, the present value of the income will be reduced more than the present value of the cost, leading to a lower NPV. We can use trial and error to find the increase in the cost of capital that just makes the NPV equal to zero:

- With a 14% cost of capital, the NPV is positive, which means the investment is profitable.
- With a 25% cost of capital, the NPV is negative, which means the investment should not be made.
- To find the required increase in cost of capital, we can try a value between 14% and 25%, such as 20%.

With a 20% cost of capital, the present value of the income is reduced to:

PV(income) = $14,500 * (1 - 1 / (1 + 0.20)^5) / 0.20 = $39,085.03

And the present value of the cost is still:

PV(cost) = $33,634.68

Therefore, the NPV is:

NPV = PV(income) - PV(cost) = $39,085.03 - $33,634.68 = $5,450.35

To make the NPV equal to zero, we need an increase in the cost of capital that reduces the NPV by $5,450.35. The required increase can be calculated as:

Increase in cost of capital = $5,450.35 / $16,205.59 = 0.3361 = 33.61%

Therefore, a 33.61% increase in the cost of capital would eliminate the unit from consideration. The closest option to this result is D) 5.1%, which represents a lower percentage than what is truly required.

The Oakley-Brown, a Frozen Food Processor, Requires an Additional Refrigeration