Question

Butler Corporation is considering the purchase of new equipment costing $45,000. The projected annual after-tax net income from the equipment is $1,700, after deducting $15,000 for depreciation. The revenue is to be received at the end of each year. The machine has a useful life of 3 years and no salvage value. Butler requires a 12% return on its investments. The present value of an annuity of 1 for different periods follows: Periods 12 Percent 1 0.8929 2 1.6901 3 2.4018 4 3.0373What is the net present value of the machine?a. $45,000. b. $(4,890). c. $36,027. d. $5,100. e. $40,110.

Answer 1

The net present value (NPV) is calculated by subtracting the initial cost of the equipment from the present value of the projected annual after-tax net income. However, there is a mistake in using the presented annuity factor, which should be applied yearly. Correct calculation reveals that the NPV does not match any of the provided answer options.

Step-by-step explanation:

To determine the net present value (NPV) of the equipment, we need to calculate the present value of the projected after-tax net income for each year and then subtract the initial cost of the equipment. Using the present value of an annuity formula, we will apply the provided annuity factors for the 12 percent discount rate.

Here are the steps for the NPV calculation:

1. Calculate the present value of the annual net income for the three years using the given annuity factor:
   
   $1,700 × 2.4018 = $4,083.06
2. Subtract the initial cost of the equipment from the present value of the net income to determine the NPV:
   
   $4,083.06 - $45,000 = $(35,916.94).

There seems to be a mismatch between the annuity factor and the number of years. To correctly calculate the NPV, we should use the annuity factor corresponding to each year:

1. Year 1: $1,700 × 0.8929 = $1,517.93
2. Year 2: $1,700 × 1.6901 = $2,873.17
3. Year 3: $1,700 × 2.4018 = $4,083.06

The sum of the present value of the annual net income over the three years would be:

$1,517.93 (Year 1) + $2,873.17 (Year 2) + $4,083.06 (Year 3) = $8,474.16

Thus, the NPV would not be any of the provided answer options.

Answer 2

The correct answer is b. $(4,890).

Step-by-step explanation:

The net present value is calculated by discounting all relevant cashflows. Detail calculation is given below.

NPV = -45,000 + (1,700+15,000)* Annuity factor

NPV = ($ 4,890)

Annuity factor = (1- (1+12%)^-3)/12%= 2.402