Question

PLEASE SHOW ALL WORK

1.  (35 points) You are considering the following two mutually exclusiveprojects. Both projects will be depreciated using straight-line depreciation to a zero book value over the life of the project. Neither project has any salvage value.

Year	Project(A)	Project (B)
0	-$30,000	-$30,000
1	13,000	5,000
2	11,000	5,000
3	9,000	5,000
4	7,000	5,000
5	0	5,000
6 7 8 9 10	0 0 0 0 0	5,000 5,000 5,000 5,000 5,000

         

           The required rate of return is 10%.

           

(1). (4 points) What is the NPV for each of the projects? Which project should be accepted if NPV method is applied? Explain why.

(2). (4 points) What is the IRR for each of the projects? Which project should be accepted if IRR method is applied? Explain why.

(3). (4 points) What is the payback period for each of the projects? Which project should be accepted if payback period method is applied? Assume that the target payback period is 4 years. Explain why.

(4). (4 points) What is the discounted payback period for each of the projects? Which project should be accepted if discounted payback period method is applied? Assume that the target discounted  payback period is 4 years. Explain why.

Explain why.

(5). (4 points) What is the profitability index for each of the projects? Which project should be accepted if profitability index method is applied? Explain why.

(6). (4 points) What is the average accounting return (AAR) for each of the projects, assuming that cash flows occurring after year 0 are net income? Which project should be accepted if AAR method is applied? Also, assume that the target AAR is 20%.

(7). (4 points) Define and find the crossover rate.

(8). (7 points) Sketch the NPV profile. Plot all the relevant coordinates (i.e., the points on the xand yaxis; and the cross-over rate) on the graph.

Answer 1

Solution Project A Calculation of NPV NPV = Present value of cash inflow - Present value of cash outflow 1 Present Value of Cash outflow Intial Investment $ 30,000.00 Year 1 Year 2 Year 3 Year 4 0 1 2 3 Particluars Cash Inflows From Project NET CASH INFLOW FROM PROJECT Present value Factor @ 10% Present Value of Cash Inflow Total Present Value of Cash Inflow NPV of Project $ 13,000.00 $ 11,000.00 $ 9,000.00 $ 7,000.00 0.909 0.826 0.751 0.683 $ 11,818.18 $ 9,090.91 $ 6,761.83 $ 4,781.09 $ 32,452.02 2,452.02 4 $ Project B NPV = Present value of cash inflow - Present value of cash outflow Present Value of cash Outflow = Intial Investment $ 30,000.00 5 6 7 8 9 0 1 2 3 4 5 Present Value of Cash Inflow Discount Rate = 10% P.v Annuity Factor For 10 Years Annual Cash Inflow P.V of Cash Inflow at T=0 NPV of Project $ $ 6.1446 5,000.00 30,723.00 723 = 6 7 Since the NPV of Project A is More so Project A is viable

Solution Project A Internal Rate of Project (IRR) IRR is the rate where the NPV of the project is ZERO or we can say that where Present Value of Cash Inflow - Present value of Cash Outflow So IRR 14.16% Proof OF IRB Present Value of Cash outflow Intial Investment $ 30,000.00 Year1 Year 2 Year 3 Yeart Particlvars Cash Inflows From Project NET CASH INFLOW FROM PROJECT Present value Factor @ 14.16% Present Value of Cash Inflow Total Present Value of Cash Inflow NPV of Project $ 13,000.00 $ 11,000.00 $9,000.00 $7,000.00 0.876 0.767 0.672 0.589 $ 11,387.53 $ 8,440.43 $ 6,049.24 $ 4,121.38 $ 29,999 -1.43 (which is Approximately Zero as difference due to Decimals) $ Project B Internal Rate of Project (IRR) IRR is the rate where the NPV of the project is ZERO or we can say that where Present Value of Cash Intlow = Present value of Cash Outflow So IRR 10.56% Proof OF IRR Present Value of Cash outflow Intial Investment $ 30,000.00 Present Yalue of Cash Infloy Discount Rate = 10.56% P.v Annuity Factor For 10 Year Annual Cash Inflow P.V of Cash Inflow at T=0 NPV of Project 5.9999 $ 5,000.00 $ 29,999.50 29999.5 (which is Approximately Zero as difference due to Decimals)

Solution Project A Calculation of Payback Period Years Total Flow Cumulative Flow 0 -30,000.00 -30,000.00 1 $ 13,000.00 -17,000.00 2 $ 11,000.00 -6,000.00 3 $ 9,000.00 3,000.00 4 $ 7,000.00 10,000.00 Now For payback Period we have to follow the following Steps Step 1 Pick the year in which the outflow have become positive, so in these case it is 2 Step 2 Divide the total cumalative cash flow in the year in which the cash flow became positive by the total flow of the consecutive year 0.67 so that's 6000 9000 Step 1 +Step 2 is the payback period Step 3 The Payback period 2.67 years Project B

4 $ 7,000.00 10,000.00 Now For payback Period we have to follow the following Steps Step 1 Pick the year in which the outflow have become positive, So in these case it is 2 Step 2 Divide the total cumalative cash flow in the year in which the cash flow became positive by the total flow of the consecutive year 0.67 so that's 6000 9000 Step 1 +Step 2 is the payback period Step 3 The Payback period 2.67 years Project B Calculation of Payback Period when even cash flow reciecved Payback Period 6 Years Intial Investment Net Annual cash Inflow 30000 5000 Since the target in Payback period is 4 Years, so the project A is viable as they have payback period od 2.67 years

Solution Project A Calculation of Discounted Payback Period Years Total Discounted Flow Cumulative Flow 0 -30,000.00 -30,000.00 1 $ 11,818.18 -18,181.82 2 $ 9,090.91 -9,090.91 3 $ 6,761.83 -2,329.08 4 $ 4,781.09 2,452.02 Now For payback Period we have to follow the following Steps Step 1 Pick the year in which the outflow have become positive, so in these case it is 3 Step 2 Divide the total cumalative cash flow in the year in which the cash flow became positive by the total flow of the consecutive year so that's 2329 0.49 4781 Step 3 Step 1 +Step 2 is the payback period The Payback period 3.49 years Project B

Step 3 Step 1+ Step 2 is the payback period The Payback period 3.49 years Project B 1 Years Cash Inflow 0 1 2 3 4 5 6 7 8 9 10 PX Factor Total Discounted Flow Cumulative Flow -30000 -30,000.00 -30,000.00 5000 0.909 $ 4,545.45 -25,454.55 5000 0.826 4.132.23 -21,322.31 5000 0.751 $ 3,756.57 -17,565.74 5000 0.683 $ 3,415.07 - 14.150.67 5000 0.621 3,104.61 -11,046.07 5000 0.564 2,822.37 -8,223.70 5000 0.513 $ 2,565.79 -5,657.91 5000 0.467 $ 2,332.54 -3,325.37 5000 0.424 2,120.49 -1,204.88 5000 0.386 $ 1,927.72 722.84 Now For payback Period we have to follow the following Steps Step 1 Pick the year in which the outflow have become positive, So in these case it is 9 Step 2 Divide the total cumalative cash flow in the year in which the cash flow became positive by the total flow of the consecutive year = 0.62 so that's 1204 1927 Step 1+ Step 2 is the payback period Step 3 The Payback period 9.62 years Since the target in Payback period is 4 Years, so the project A is viable as they have payback period od 3.49 years