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- This topic has 1 reply, 2 voices, and was last updated 1 year ago by Cath.
- June 12, 2021 at 2:13 pm #625042AndySiMember
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I have come across the following question:
A machine costing $150,000 has a useful life of 8 years, after which time its estimated resale value will be $25,000. Annual running costs will be $5000 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 day of the year to which they relate.
Using a discount rate, what would be the annual equivalent cost of using the machine if it were bought and replaced every 8 years in perpetuity?
Answer: $43,900 arrived at as follows:
NPV = -150,000+(25,000 x 0.233) – (5,000 x 2.106) – (8,000 x 2.991 x 0.579)
Why in the answer they multiply 8,000 by 0.579 and not 0.402 which is the discount factor of 20% at year 5?
AndyAugust 23, 2021 at 11:31 pm #632674CathParticipant
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This is an example of a delayed annuity.
So we have yr4,yr5,yr6,yr7,yr8 each with a cost of $8,000
So the value of $8,000 for 5 yr annuity at 20% is
$8000 * 2.991 =$23,928
However, annuity factors assume the first cashflow will be in year 1..but the above annuity doesnt begin until year 4….
So we need to discount it again to find the value of the cost at the end of yr3 ( hence we use the 3 yr discount factor at 20% of 0.579) to discount its value to year 0 ( today)
Hope that explains ok
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