Answer:
The amount that could be justified now for the purchase of this piece of equipment is $73,747.41.
Explanation:
Note: This question is not complete as all the data in it are omitted. A complete question is therefore provided before answering the question as follows:
It is estimated that a certain piece of equipment can save $22,000 per year in labor and materials cost. The equipment has an expected life of five years and no market value. If the company must earn a 15% annual return on such investments, how much could be justified now for the purchase of this piece of equipment?
The explanation to the answer is now given as follows:
To calculate this, the formula for calculating the present value of an ordinary annuity is used as follows:
PV = P * [{1 - [1 / (1 + r)]^n} / r] …………………………………. (1)
Where;
PV = Present value of the amount to justify the equipment purchase = ?
P = yearly savings in labor and materials costs = $22,000
r = annual return rate = 15% = 0.15
n = Equipment has an expected life = 5
Substitute the values into equation (1) to have:
PV = $22,000 * [{1 - [1 / (1 + 0.15)]^5} / 0.15]
PV = $22,000 * [{1 - [1 / 1.15]^5} / 0.15]
PV = $22,000 * [{1 - 0.869565217391304^5} / 0.15]
PV = $22,000 * [{1 - 0.497176735298289} / 0.15]
PV = $22,000 * [0.502823264701711 / 0.15]
PV = $22,000 * 3.35215509801141
PV = $73,747.41
Therefore, the amount that could be justified now for the purchase of this piece of equipment is $73,747.41.
