Question

XYZ Limited is contemplating a replacement cycle for new machinery. This machinery will cost Sh100 million to purchase. The operating and maintenance costs for the future years are as follows;

Year                                                                       0             1           2                3

Operating and Maintenance Cost Shs.’000’   0    120,000   130,000 140,000

The resale values of the machinery in the second hand market are as follows;

Year                                                                  0             1                 2                3

Resale Value Shs. ‘000’                                 0      80,000           65,000     35,000

Assume;

a. The replacement is by an identical machine

b. There is no inflation, tax or risk c.

The cost of capital is 11%.

Required; Advise XYZ Limited on whether to replace this new machine on a one, two or three year cycle. (Use the equivalent annual cost method)

Answer 1

EAC or equivalent annual cost is capital budgeting method followed by the companies for calculating the cost of owning, operating, and maintaining an asset over its entire life. This method helps the company to find out the cost-effectiveness of the assets that have uneven lifespans.

The formula for calculating is;

EAC = asset price * discount rate / 1 - ( 1 + discount rate)

the optimal replacement cycle for the machine is;

for this, we need step by step solution.

1. calculate NPV of cost for each potential replacement.

2. calculate EAC for each potential replacement year.

3. Take decision based on the calculation.

1. calculation of NPV

at one year replacement cycle

year 2 replacement cycle

NPV at three-year replacement cycle

STEP TWO

calculation of EAC.

For this we need to find out annuity of each year using the following equation;

= 1 - ( 1 / 1 + r) ^ t / r

where, R = cost of capital

t = no: of periods. here 1st, 2nd and 3rd year.

calculated annuity for each year = .9009 at year 1

1.7125 at year 2

2.44 at year 3

EAC for one year cycle

= 100,036,360 / .9009 = 111,040,470

EAC for two-year cycle

= 100,089,140 / 1.7125 = 58,446,213

EAC for three-year cycle

= 100,165,916 / 2.44 = 41,051,604

the THREE YEAR replacement cycle is said to be optimal replacement cycle because the cost is very less in the three year replacement cycle. It stands at 41,051,604.