NPV AND IRR QUESTION I have an exam tomorrow and was wandering if someone could help me, thankyou?

Question

NPV AND IRR QUESTION I have an exam tomorrow and was wandering if someone could help me, thankyou?

Answer 1

2

Answer 2

1

Answer 3

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Answer 4

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Answer 5

Multiple steps here, but here's the general outline:



Step 1: Compute a 5 year schedule of cash flows

Step 2: Compute a Discounted Cash flow

Step 3: Compute NPV

Step 4: Compute IRR

Step 4: Calculate PI



Step 1: Schedule of Cash flows

You will have 6 cash flows

Year 0 = - outflow of the initial investment + (-cash outlay for the project)

Year 1,2,3,4,5 = Revenue from selling meals - cost of meals - depreciation - transport costs



Year 0 = -2,500 + (-30,000) = -32,500

Year 1 = [ 1 x 30,000 ] - [ 0.60 x 30,000] - 1,500 - 2,000 = 8,500

Year 2 = [ 1 x 32,000 ] - [ 0.60 x 32,000] - 1,500 - 2,000 = 7,300

Year 3 = [ 1 x 32,000 ] - [ 0.60 x 32,000] - 1,500 - 2,000 = 7,300

Year 4 = [ 1.20 x 33,000 ] - [ 0.70 x 33,000] - 1,500 - 2,000 = 13,000

Year 5 = [ 1.20 x 33,000 ] - [ 0.70 x 33,000] - 1,500 - 2,000 = 13,000



Step 2: Discounted Cash Flow

This will entail you taking the future cash flows dividing it by (1+r)^n

r = cost of capital

n = number of years



Year 0 = -32,500 (do not discount the initial cash outlay....only future years)

Year 1 = 8,500 / (1+0.14)^1 = 7,456.14

Year 2 = 7,300 / (1+0.14)^2 = 5,617.11

Year 3 = 7,300 / (1+0.14)^3 = 4,927.29

Year 4 = 16,500 / (1+0.14)^4 = 9,769.32

Year 5 = 16,500 / (1+0.14)^5 = 8,569.58



Step 3: Net Present Value

Simply sum up the Cash flows

-32,500 + 7,456.14 + 5,617.11 + 4,927.29 + 9,769.32 + 8,569.58 = 18338.90



Step 4: IRR

You'll need a financial calculator. IRR here means you want to find the required rate of return that will make the NPV = 0

Using the series of cash flows above, IRR = 3.62%



Step 5: Payback Period

Payback period = Cash outlay/Cash inflows (we're simply finding when we'll breakeven on the project)



Year 1 = -32,500 + 8,500 = -24,000 (so at least 1 year)

Year 2 = -24,000 + 7,300 = -16,700 (so at least 2 years)

Year 3 = -16,700 + 7,300 = -9,400 (so at least 3 years)

Year 4 = -9,400 + 13,000 = 3,600 (so between 3 and 4 years)



To find the fraction of the year in the 3rd year take the amount that is still needed to be back and divide it by the total cash inflow for the year:



fraction of year = 9,400/13,000 = 0.723



So, the profitabilitiy index is 3.723 years which meets management's critera of within 4 years. However, even if the PI was > 4 years, you would still accept the project because it is not factoring in cash flows beyond year 5 and because the discount rate is being used as a hurdle and shows that the project is profitable anyhow over a 5 year period



That was fun



Edit:

@Sk...it's included, and to be honest, I am still unsure about whether or not to amortize that cost out across all 5 years. Depends on what the teacher wants, and in the real world, the accounting treatment says to do that

Answer 6

Good luck for your exam.



EDIT: I was going to leave a cynical answer, but I am feeling like a sympathetic git.



Listen up, this is straightforward BS. if by this point you don't understand this, you need to work a lot harder, this is just simple formula manipulation.



You should have answers to this if this is past papers - the only thing I am unsure about is this feasibility study cost; however, harking back to my uni days, I think I can recall that sunk costs (i.e. costs already ploughed into the project) should not be included. I think this figure of £2,500 is included to trick you.



1)



Year 0: cash OUT flow = -30,000

Year 1: net cash flow = (30,000 * (1.00 - 0.60) ) - 4000 = 8,000

Year 2: net cash flow = (32,000 * (1.00 - 0.60) ) - 4000 = 8,800

Year 3: net cash flow = (32,000 * (1.00 - 0.60) ) - 4000 = 8,800

Year 4: net cash flow = (33,000 * (1.20 - 0.70) ) - 4000 = 12,500

Year 5: net cash flow = (33,000 * (1.20 - 0.70) ) - 4000 = 12,500



Discounted cash flows (DCF) = (30,000) + 7,017.54 + 6,771.31 + 5,939.75 + 7,401.00 + 6,492.11



NPV (cash flows only) = 3,621.72

NPV (assuming scrap at year 5) = 3,621.72 + 11,685.79 = 26,121.72 (note, it wasn't clear exactly what this depreciation charge was on, just the cooking equipment or what?)



2) IRR



You need to remember that IRR is such that -30,000 + 8,000/(1+r) + 8,800/(1+r)^2 + 8,800/(1+r)^3 + 12,500/(1+r)^4 + 12,500/(1+r)^5 has to = 0.



You cannot solve for r directly, use trial and error.



If I substitute 10% for r, i will get 7456.21. So I tried 18%, which yielded 366.86 (getting closer). Then 19%, which yielded -369. So r is between 18% and 19%. 18.5% yields -4.908. I think for the purpose of your exam, 18.5% is sufficient as an approximation for r.



3) Payback period



It is simply the length of time it will take for the the project to pay back the initial investment. No discounting needed. So how long will it take for the cashflows to add up to the initial £30,000?



The net cash flows up to year 3 totals £25,600, and up to year 4 totals £38,100. So we know the payback period is between year 3 and 4.



In year three it is £25,600, short by 4,400. In year 4 we will receive 12,500. 4,400/12,500 = 0.352.



So the payback period is 3.352 years.



sk



EDIT



@greenglow560: kindly point me to any resource that says to include sunk costs? for the purpose of your knowledge, refer here: http://www.investopedia.com/exam-guide/cfa-level-1/corporate-finance/cash-flow-npv-net-present-value-applications.asp#axzz247Ki6Odw



heck, just google sunk costs and NPV.