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I am struggling to understand the answer to this question and wondered if you could help?
Q
An electric motor for a passenger ferry costs £20,000 and can be replaced either annually or after 2 years. If the motor is replaced after 2 years, the scrap value falls from £16,000 to £13,000 and running costs rise from £5,000 in year 1 to £5,500 in year 2.
Assuming the owner of the ferry uses a cost of capital of 10% and the 2 year cumulative discount factor is 1.736, calculate the equivalent annual cost (EAC) of the 2 year option in absolute terms.
The answer they give is ;
NPV= -£20,000 -(5,000/1.1) – (£5,500 / [1.1 x1.1] ) + (£13,000/ [ 1.1 x1.1] ) = -18347
EAC in absolute terms ie no +ve or -ve signs = 18347/1.736 = £10,569I do not understand why they have divided the figures by 1.1 and then at the end used the discount factor of 10% for 2 years.
I did an normal NPV calculationYear 0 (20,000) DF 1 (20,0000)
Year 1 (5,000) DF 0.909 (4545)
Year 2 (5,500) DF 0.826 (4543)
Year 2 13,000 DF 0.826 10738
________
Total (18350)
Which is similar to their answer before they discounted it againDividing by 1.1 is the same as applying the one year 10% discount factor: 1/1.1 = 0.90909, which is 0.909 when rounded to three decimal places.
Dividing by 1.1 twoce is the same as applying the two year 10% discount factor: 1/1.1 x 1/1.1= 0.8264, which is 0.826 when rounded to three decimal places.
Then divide the NPV by the 2 year cumulative factor to find the EAC.
Thank you. So really the point i got up to was correct then I just needed to divide by 2 year cumulative to get the EAC. I was not sure how to get EAC but understand now
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