Forums › Ask ACCA Tutor Forums › Ask the Tutor ACCA FM Exams › Investment Appraisal: using (1+r^x) VERSUS using the annuity factor for NPV calc

- This topic has 1 reply, 2 voices, and was last updated 1 month ago by John Moffat.

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- December 1, 2022 at 11:33 am #673016
Good morning!

Please can you kindly advise how to identify when to use the annuity factor v.s when to use the formula (1+r^x)?

In the following example, the solution multiplies the cost by the annuity factor to find the present value, but goes on to divide the scrap value by (1+r^3), to get the present value please can you help me understand why 2 different methods are used here, and how to know when to use which method?

Example:

A machine will initially cost $540,000, have a life of 3 years, scrap value of $120,000 and annual running costs of $47,000. Cost of capital is 10% – assume all cash flows except the initial cost occur at the end of the relevant year. What is the equivalent annual cost of the machine?

Solution:

Negative NPV ($’000) = ($540 + $47 x 2.487) – ($120 ÷ 1.10^3) = $566.731

Equivalent annual cost = $566.731 ÷ 2.487 = $227.875

Therefore answer = $228,000 to the nearest $’000.Thank you very much in advance!

December 1, 2022 at 5:07 pm #673059You use the annuity discount factor to get the present value of an equal annual cash flow. You use the present value factor to discount one individual flow.

I do suggest that you watch my free Paper MA lectures on investment appraisal, because this is revision from Paper MA.

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