NPv

1. For the 14,000 a year for 4 years, you multiply 14,000 by the 4 year annuity factor at 8% from the tables provided. For the 20,000 a year from year 5 in perpetuity, you calculate the discount factor by either using the perpetuity factor of 1/r (i.e. here 1/0.08) and subtract the 4 year annuity factor - so you are left with the total from 5 to infinity. (Alternatively, multiply by 1/r for the perpetuity and then multiply by the present value factor for 4 years at 8% because the perpetuity starts 4 years late. The answers will be slightly different because of roundings in the tables, but to the nearest 1,000 it makes no difference). 2. 1 Jan 2018 is effectively the same day as 31 Dec 2017 - we are never worried about just 1 day of interest. So the PV of the first 13,000 is 13,000. There is then 13,000 in perpetuity and the discount factor is 1/r which here is 1/0.1 (I am assuming that the interest is 10% - you have not said). So the PV of the perpetuity is 130,000. So the NPV is 130,000 + 13,000 - 100,000 = 43,000 Does your book not have answers together with workings? And have you watched all of the free lectures on this?

The book does not show the working that is why i asked.

it says from April 2016 to 2017 so we ignore 2016 and 2017 and consider to discount factor for 5 years?but why five years if there is April 2016 to 2017 and till 2020 it will be four yeas.this part became unclear for me.I watched your lecture video also did not comprehend((((((((

Your original question made no mention of April 2016! If the initial investment is on 1 April 2016, then the first flow on 31 March 2017 is one year later. The question says that there are 4 flows of 14,000 and therefore the flows are years 1 to 4 and to discount you multiply by the 4 year annuity discount factor. I have no idea why you want to ignore 2016 and 2017 and consider a discount factor for 5 years.

Year-----Cash flow-------discount factor of 8% 0-----------(120000) 1-----------14000---------------0.926 2-----------14000--------------0.857 3----------14000--------------0.794 4----------14000------------0.735 5----------14000-------------0.681 --------------------------------3.993-0.926=3.067*14000=42938 then (1/0.08)-3.993*20000=170140 120000-42938-170140=93000 why we take into consideration 5 years not four years?in the exercise it says four years?

I assume that these are your workings (since your book does not have workings), in which case I don't know what you are doing!! First, it is a complete waste of time writing down 5 discount factors and then adding them up!! You are given tables for the annuity factors and you can look up the 3.993 directly from the tables. Secondly, you have still not said when the initial investment was made. If it was on 1 April 2016, then the flows of $14,000 a year are for years 1 to 4. If the question says that the initial investment was on 1 April 2015, the the flows are for years 2 to 5, in which case the answer as you have written it is correct.

1st) An investment of 120000$ on 1 April 2016 is forecast to yield a net cash flow of $14000 each year for four years commencing on 31 March 2017,followed by $20000 each year in perpetuity.The appropriate cost of capital is 8% per year What is the positive net present value of the investment? a)$80000 b)$81000 c)$93000 d)$110000 Should be 2016 I am sorry that i have not written it:(

My Dear Tutor i know in the exam it will be given but why 3.993 is the result of 5 years not 4 years.

5 years is of no relevance. As I wrote in my first answer, the flows are: 0 (120,000) 1 - 4 14,000 p.a. 5 - infinity 20,000 p.a. The PV of 14,000 per year is 14,000 x 3.312 (the 4 year annuity factor) = 46,368 The PV of the perpetuity is 20,000 x (1/0.08 - 3.312) = 183,760 The NPV = 43,368 + 183,760 - 120,000 = 107,128 If your book has the answer as 93,000, then this would only be correct if the initial investment was on 1 April 2015. It seems as though there is an error in your book. (If it is in the BPP Revision Kit, or in an ACCA specimen exam, then say which question and then I can check,)