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Good Day,
Please could you assist me, I am currently using the Kaplan exam practice kit after going through the Open Tuition notes and Lectures. I have come across the following question and I am unsure of the calculations to get the answer. The question reads:
A machine costing $150,000 has a useful life of eight years, after which its estimated resale value will be $30,000. Annual running costs will be $6,000 for the first three years of use and $8,000 for each of the next five years. All running costs are payable on the last days of the year to which they relate. Using a discount rate of 20% per annum, what is the equivalent annual cost (to the nearest $100) of using the machine, if it were bought and replaced every 8 years in perpetuity?
A) $21,100
B) $34,000
C) $30,400
D) $46,600Your assistance would be greatly appreciated.
Hi,
Thank you for posting your question. I am glad you have found Open Tuition CIMA notes helpful.In terms of an Equivalent Annual Cost – this is simply the Net Present Value of the project divided by the annuity factor for the relevant discount rate (20% here) and the length of the replacement cycle ( 8yrs)
So we find the NPV of the project cashflows discounting at 20% in normal way. This comes to approx net outflow of ($169,494)
The 8 year annuity factor at 20% is 3.837So 169494/ 3.837 = $ 44,174
This tells us the that the 8 yr replacement plan is the equivalent of paying $44174 on an annual basis. The method shares all the different costs in present value terms across the replacement cycle length.
This gives you an average cost per year in present value terms.
Hope that helps?
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