Hi Moustafa,
I see that you are confused from the explantation above. Please see an easier way out with the end result being more or less same. There might be a difference which will be due to rounding off.
Year 0 (cash outflow) = $500,000
Year 1 (cash inflow) = (40,000 (dep tax shield) + 30,000 (op. cash flow)) * 0.8333 = $58,331
Year 2 (cash inflow) = (40,000 + 30,000) * 0.6944 = $48,608
Year 3 (cash inflow) = (40,000+ 240,000) * 0.5787 = $162,036
Year 4 (cash inflow) = (40,000+ 240,000) * 0.4823 = $135,044
Year 5 (cash inflow) = (40,000+ 240,000) * 0.4019 = $112,532
Total cash inflow = $516,551
NPV = $516,551 - $500,000 = $16,551 - Project acceptable - Answer is option D.
Please note, the formula above will also get the same answer. It is just that they have added the present value factors.
Year 1 and 2 - cash inflows are same - so --- 70,000*(0.8333+0.6944) = $106,939
Year 3, 4 and 5 - cash inflows are same - so --- 280,000 (0.5787+0.4823+0.4019) = $409,612
$106,939+$409,612= $516,551
Now, your question as to why why he subtract year3 from year 2,1 - It is not the case. Sum of 5 year PV factor - sum of 2 years PV factor is calculated = sum of PV for 3 years. I hope I am making sense now. Let me showcase you again.
Year 1 and 2 = Cash inflows are same = 70,000*(0.8333+0.6944) = $106,939
Year 3, 4 and 5 = Cash inflows are same = 280,000*(Sum of PV factors for 5 years - Sum of PV factors for 2 years) = 280,000*(2.9906-1.5274) = $409,696
$106,939+$409,696= $516,635
NPV= $16,635 (difference due to rounding off)
Now, I hope I am clear.
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Nupur Mahajan
nupur1188@...Hartford CT United States
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Original Message:
Sent: 02-24-2021 01:48 PM
From: Nupur Mahajan
Subject: Part2_Investment Decision
Hi Moustafa,
So it should be a simple calculation that has been complexed. Please refer below.
(rounded to 4 decimals)
Year 0 PV factor = 1
Year 1 PV factor = 0.8333
Year 2 PV factor = 0.6944
Year 3 PV factor = 0.5787
Year 4 PV factor = 0.4823
Year 5 PV factor = 0.4019
Using the numbers above I am calculating the cumulative range as below:
Cumulative factor at year 2 end = 1.5277 (0.8333+0.6944) - they are using this because the cash flows for year 1 and 2 are same
Cumulative factor at year 5 end = 2.9906 (0.8333+0.6944+0.5787+0.4823+0.4019)
Now, PV factor to be used for the cash flows from year 3-5 ($280,000) is 1.4629 (2.9906 - 1.5277). Again they are using this because the cash flows for year 3-5 are same.
Please note, the differences are due to rounding off.
I think this is a confusing method to be used, i would have quickly used the straight method of Cash flow * PV factor to get discounted cash flow for each year's end.
I hope I am making sense.
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Nupur Mahajan
<maskemail>nupur1188@...</maskemail>
Hartford CT United States
Original Message:
Sent: 02-24-2021 01:36 AM
From: Moustafa Mohamed Aly Abdel Nabi
Subject: Part2_Investment Decision
Hi there,
Can any one explain to me that question as attached & answer as well, why he subtract year3 from year 2,1
However all questions required the NPV we calculating every year separately.
Please advice..
Regards,
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Moustafa Mohamed Aly Abdel Nabi
Controller
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