Please solve the following questions and give me an excellent answer.

Directions: Answer the following questions on a separate document. Explain how you reached the answer or show your work if a mathematical calculation is needed, or both. Submit your assignment using the assignment link in the course shell. This homework assignment is worth 100 points. Use the following information for Questions 1 through 3: Assume you are presented with the following mutually exclusive investments whose expected net cash flows are as follows: EXPECTED NET CASH FLOWS: Year Project A Project B 0 $400 $650 1 528 210 2 219 210 3 150 210 4 1,100 210 5 820 210 6 990 210 7 325 210 1. (a) What is each project's IRR? (b) If each project's cost of capital were 10%, which project, if either, should be selected? If the cost of capital were 17%, what would be the proper choice? 2. a) What is each project's MIRR at the cost of capital of 10%? At 17%? (Hint: Consider Period 7 as the end of Project B's life.) 3. What is the crossover rate, and what is its significance? Use the following information for Question 4: The staff of Porter Manufacturing has estimated the following net after-tax cash flows and probabilities for a new manufacturing process: Line 0 gives the cost of the process, Lines 1 through 5 give operating cash flows, and Line 5* contains the estimated salvage values. Porter's cost of capital for an average-risk project is 10%. Net After-Tax Cash Flows Year P = 0.2 P = 0.6 P = 0.2 0 $100,000 $100,000 $100,000 1 20,000 30,000 40,000 2 20,000 30,000 40,000 3 20,000 30,000 40,000 4 20,000 30,000 40,000 5 20,000 30,000 40,000 5* 0 20,000 30,000 4. Assume that the project has average risk. Find the project's expected NPV. (Hint: Use expected values for the net cash flow in each year.) Question -1 a) IRR (Using hit and trial method) Project-A:IRR is the rate of return at which Present value of Cash inflows equates Present value of cash outflows resulting in 0 NPV Let IRR be 20% Particulars Year Cash Flow Cash Flow Cash Flow Cash Flow 0 1 2 3 Cash Flow Cash Flow Cash Flow Cash Flow 4 5 6 7 Present Value factor of 20% 1 0.833333333 0.694444444 0.578703704 0.482253086 0.401877572 0.334897977 0.279081647 Net Present Value As at 20% the NPV is positive, so IRR will be above 20% Amount ($400.00) ($528.00) ($219.00) ($150.00) $1,100.0 0 $820.00 $990.00 ($325.00) Present Value ($400.00) ($440.00) ($152.08) ($86.81) $530.48 $329.54 $331.55 ($90.70) $21.98 So Let IRR Be 21% Present Value factor of 21% Cash Flow 0 1 Cash Flow 1 0.826446281 Cash Flow 2 0.683013455 Cash Flow 3 0.56447393 Cash Flow 4 0.46650738 Cash Flow 5 0.385543289 Cash Flow 6 0.318630818 Cash Flow 7 0.263331254 Net Present Value As at 21% the NPV is negative, so IRR will be below 21% Particulars Year Now we need to interpolate the IRR IRR = 20% + 1% x 21.98/(21.98+11.45) = 20.66% (approx.) Present Value ($400.00) ($400.00) ($528.00) ($436.36) ($219.00) ($149.58) ($150.00) ($84.67) $1,100.00 $513.16 $820.00 $316.15 $990.00 $315.44 ($325.00) ($85.58) ($11.45) Amount Project-B:IRR is the rate of return at which Present value of Cash inflows equates Present value of cash outflows resulting in 0 NPV Let IRR be 25% Present Value Amount factor of 25% ($650.00 Cash Flow 0 1 ) Cash Flow 1 0.8 $210.00 Cash Flow 2 0.64 $210.00 Cash Flow 3 0.512 $210.00 Cash Flow 4 0.4096 $210.00 Cash Flow 5 0.32768 $210.00 Cash Flow 6 0.262144 $210.00 Cash Flow 7 0.2097152 $210.00 Net Present Value As at 25% the NPV is positive, so IRR will be above 25% Particulars Year Present Value ($650.00) $168.00 $134.40 $107.52 $86.02 $68.81 $55.05 $44.04 $13.84 So Let IRR Be 26% Present Value Amount factor of 26% ($650.00 Cash Flow 0 1 ) Cash Flow 1 0.793650794 $210.00 Cash Flow 2 0.629881582 $210.00 Cash Flow 3 0.499906018 $210.00 Cash Flow 4 0.396750808 $210.00 Cash Flow 5 0.314881593 $210.00 Cash Flow 6 0.249906027 $210.00 Cash Flow 7 0.198338116 $210.00 Net Present Value As at 26% the NPV is negative, so IRR will be below 26% Particulars Year Now we need to interpolate the IRR IRR = 25% + 1% x 13.84/(21.98+11.45) = 25.85% (approx.) Present Value ($650.00) $166.67 $132.28 $104.98 $83.32 $66.13 $52.48 $41.65 ($2.50) b) If each project's cost of capital were 10%, which project, if either, should be selected? If the cost of capital were 17%, what would be the proper choice? At 10% :Project B Present Present Value Amount Value ($650.00 Cash Flow 0 1 ($400.00) ($400.00) ) ($650.00) Cash Flow 1 0.909090909 ($528.00) ($480.00) $210.00 $190.91 Cash Flow 2 0.826446281 ($219.00) ($180.99) $210.00 $173.55 Cash Flow 3 0.751314801 ($150.00) ($112.70) $210.00 $157.78 Cash Flow 4 0.683013455 $1,100.00 $751.31 $210.00 $143.43 Cash Flow 5 0.620921323 $820.00 $509.16 $210.00 $130.39 Cash Flow 6 0.56447393 $990.00 $558.83 $210.00 $118.54 Cash Flow 7 0.513158118 ($325.00) ($166.78) $210.00 $107.76 NPV $478.83 NPV $372.37 As the net present value of Project A is higher than Project B thus Project A will be chosen. Particulars Year Present Value factor of 10% Amount Project A At 17% :Project B Present Present Value Amount Value ($650.00 Cash Flow 0 1 ($400.00) ($400.00) ) ($650.00) Cash Flow 1 0.854700855 ($528.00) ($451.28) $210.00 $179.49 Cash Flow 2 0.730513551 ($219.00) ($159.98) $210.00 $153.41 Cash Flow 3 0.624370556 ($150.00) ($93.66) $210.00 $131.12 Cash Flow 4 0.533650048 $1,100.00 $587.02 $210.00 $112.07 Cash Flow 5 0.456111152 $820.00 $374.01 $210.00 $95.78 Cash Flow 6 0.389838592 $990.00 $385.94 $210.00 $81.87 Cash Flow 7 0.333195378 ($325.00) ($108.29) $210.00 $69.97 NPV $133.76 NPV $173.70 As the net present value of Project A is lower than Project B thus Project B will be chosen. Particulars Year Present Value factor of 17% Amount Project A Question -2 a) What is each project's MIRR at the cost of capital of 10%? At 17%? (Hint: Consider Period 7 as the end of Project B's life.) MIRR is rate of return considering the reinvestment of intermediate cash flows at a predetermined rate of return. At 10% :First compute the Present Value of Cash Outflows at Year 0 Project A Project B Present Value Present Present factor of 10% Cash Outflows Cash Outflows Value Value Cash Flow 0 1 $400.00 $400.00 $650.00 $650.00 Cash Flow 1 0.909090909 $528.00 $480.00 $0.00 $0.00 Cash Flow 2 0.826446281 $219.00 $180.99 $0.00 $0.00 Cash Flow 3 0.751314801 $150.00 $112.70 $0.00 $0.00 Cash Flow 7 0.513158118 $325.00 $166.78 $0.00 $0.00 Initial Initial $1,340.47 $650.00 Investment Investment Then compute Future Value of Cash Inflows at the end of project year considering reinvestment at discount rate. Particular s Year Particular s Reinvestmen t Years Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow 6 5 4 3 2 1 0 Project A Future Value factor of 10% Cash Inflows Future Value 1.771561 $0.00 $0.00 1.61051 $0.00 $0.00 1.4641 $0.00 $0.00 1.331 $1,100.00 $1,464.10 1.21 $820.00 $992.20 1.1 $990.00 $1,089.00 1 $0.00 $0.00 Terminal Value $3,545.30 Project B Cash Inflows Future Value $210.00 $372.03 $210.00 $338.21 $210.00 $307.46 $210.00 $279.51 $210.00 $254.10 $210.00 $231.00 $210.00 $210.00 Terminal Value $1,992.31 Now, MIRR is the rate at which present value of terminal value equates the Initial Investment. Project A Initial Investment = Terminal value of cash flow x Present value factor of MIRR of year 7 Present value factor of MIRR of year 7 = Initial Investment /Terminal value of cash flow Present value factor of MIRR of year 7 = $1340.47/$3545.30 = 0.37809645 Referring to present value factor table we get 14.91% Project B Initial Investment = Terminal value of cash flow x Present value factor of MIRR of year 7 Present value factor of MIRR of year 7 = Initial Investment /Terminal value of cash flow Present value factor of MIRR of year 7 = $650/$1992.31 = 0.326255118 Referring to present value factor table we get 17.36% At 17% :First compute the Present Value of Cash Outflows at Year 0 Project A Present Value Year Present factor of 10% Cash Outflows Value Cash Flow 0 1 $400.00 $400.00 Cash Flow 1 0.854700855 $528.00 $451.28 Cash Flow 2 0.730513551 $219.00 $159.98 Cash Flow 3 0.624370556 $150.00 $93.66 Cash Flow 7 0.333195378 $325.00 $108.29 Initial $1,213.21 Investment Then compute Future Value of Cash Inflows at the end of project year discount rate. Particular s Particular s Reinvestmen t Years Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow 6 5 4 3 2 1 0 Project A Future Value factor of 10% Cash Inflows Future Value 2.565164202 $0.00 $0.00 2.192448036 $0.00 $0.00 1.87388721 $0.00 $0.00 1.601613 $1,100.00 $1,761.77 1.3689 $820.00 $1,122.50 1.17 $990.00 $1,158.30 1 $0.00 $0.00 Terminal Value $4,042.57 Project B Present Cash Outflows Value $650.00 $650.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 Initial $650.00 Investment considering reinvestment at Project B Cash Inflows Future Value $210.00 $538.68 $210.00 $460.41 $210.00 $393.52 $210.00 $336.34 $210.00 $287.47 $210.00 $245.70 $210.00 $210.00 Terminal Value $2,472.12 Now, MIRR is the rate at which present value of terminal value equates the Initial Investment. Project A Initial Investment = Terminal value of cash flow x Present value factor of MIRR of year 7 Present value factor of MIRR of year 7 = Initial Investment /Terminal value of cash flow Present value factor of MIRR of year 7 = $1213.21/$4042.57 = 0.300108077 Referring to present value factor table we get 18.76% Project B Initial Investment = Terminal value of cash flow x Present value factor of MIRR of year 7 Present value factor of MIRR of year 7 = Initial Investment /Terminal value of cash flow Present value factor of MIRR of year 7 = $650/$2472.12 = 0.262931942 Referring to present value factor table we get 21.02% Question -3 What is the crossover rate, and what is its significance? First we need to compute differential Cash flows which are as follows:Particular s Year Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow 0 1 2 3 4 5 6 7 Project A Cash Outflows ($400.00) ($528.00) ($219.00) ($150.00) $1,100.00 $820.00 $990.00 ($325.00) Project B Cash Outflows ($650.00) $210.00 $210.00 $210.00 $210.00 $210.00 $210.00 $210.00 Difference in cash flows (A-B) $250.00 ($738.00) ($429.00) ($360.00) $890.00 $610.00 $780.00 ($535.00) Now the crossover rate is the rate at which the present value of difference in cash flows will be 0 So Let crossover rate be 15% Particular s Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Year 0 1 2 3 4 5 6 7 Present Value Amount factor of 15% 1 $250.00 0.869565217 ($738.00) 0.756143667 ($429.00) 0.657516232 ($360.00) 0.571753246 $890.00 0.497176735 $610.00 0.432327596 $780.00 0.37593704 ($535.00) Net Present Value As the NPV is negative thus crossover rate will be below 15% Now, let crossover rate be 14% Present Value $250.00 ($641.74) ($324.39) ($236.71) $508.86 $303.28 $337.22 ($201.13) ($4.60) Particulars Year Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow 0 1 2 3 4 5 6 7 Present Value Amount factor of 14% 1 $250.00 0.877192982 ($738.00) 0.769467528 ($429.00) 0.674971516 ($360.00) 0.592080277 $890.00 0.519368664 $610.00 0.455586548 $780.00 0.399637323 ($535.00) Net Present Value Present Value $250.00 ($647.37) ($330.10) ($242.99) $526.95 $316.81 $355.36 ($213.81) $14.86 Now we need to interpolate the IRR Crossover rate = 14% + 1% x 14.86/(14.86 + 4.60) = 14.76% (approx.) This implies that in discounting at rate below 14.76% Project A will be better but discounting at rate above this rate Project B will be better to the level of its IRR. Significance Crossover rate is the rate at which an investor is indifferent between two projects, in other words it is the point at which NPV of two projects is equal. It determines the range of returns and accordingly which project to be chosen. Question -4 Assume that the project has average risk. Find the project's expected NPV. (Hint: Use expected values for the net cash flow in each year.) Projects expected NPV is computed as follows:- Particulars Initial Investment Cash Flows Cash Flows Cash Flows Cash Flows Cash Flows Terminal Value Year Present Value factor of 10% 0 1 2 3 4 5 5 1.00000 0.90909 0.82645 0.75131 0.68301 0.62092 0.62092 Probability 0.20 ($100,000.0 0) $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $0.00 Thus Projects Expected NPV is $24,900.19 (Approx.) Cash flows Probability 0.60 ($100,000.0 0) $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $20,000.00 Expected Cash Flows Probability 0.20 ($100,000.0 ($100,000.0 0) 0) $40,000.00 $30,000.00 $40,000.00 $30,000.00 $40,000.00 $30,000.00 $40,000.00 $30,000.00 $40,000.00 $30,000.00 $30,000.00 $18,000.00 Net Present Value Expected Present Value ($100,000.00 ) $27,272.73 $24,793.39 $22,539.44 $20,490.40 $18,627.64 $11,176.58 $24,900.19 Question -1 a) IRR (Using hit and trial method) Project-A:IRR is the rate of return at which Present value of Cash inflows equates Present value of cash outflows resulting in 0 NPV Let IRR be 20% Particulars Year Cash Flow Cash Flow Cash Flow Cash Flow 0 1 2 3 Cash Flow Cash Flow Cash Flow Cash Flow 4 5 6 7 Present Value factor of 20% 1 0.833333333 0.694444444 0.578703704 0.482253086 0.401877572 0.334897977 0.279081647 Net Present Value As at 20% the NPV is positive, so IRR will be above 20% Amount ($400.00) ($528.00) ($219.00) ($150.00) $1,100.0 0 $820.00 $990.00 ($325.00) Present Value ($400.00) ($440.00) ($152.08) ($86.81) $530.48 $329.54 $331.55 ($90.70) $21.98 So Let IRR Be 21% Present Value factor of 21% Cash Flow 0 1 Cash Flow 1 0.826446281 Cash Flow 2 0.683013455 Cash Flow 3 0.56447393 Cash Flow 4 0.46650738 Cash Flow 5 0.385543289 Cash Flow 6 0.318630818 Cash Flow 7 0.263331254 Net Present Value As at 21% the NPV is negative, so IRR will be below 21% Particulars Year Now we need to interpolate the IRR IRR = 20% + 1% x 21.98/(21.98+11.45) = 20.66% (approx.) Present Value ($400.00) ($400.00) ($528.00) ($436.36) ($219.00) ($149.58) ($150.00) ($84.67) $1,100.00 $513.16 $820.00 $316.15 $990.00 $315.44 ($325.00) ($85.58) ($11.45) Amount Project-B:IRR is the rate of return at which Present value of Cash inflows equates Present value of cash outflows resulting in 0 NPV Let IRR be 25% Present Value Amount factor of 25% ($650.00 Cash Flow 0 1 ) Cash Flow 1 0.8 $210.00 Cash Flow 2 0.64 $210.00 Cash Flow 3 0.512 $210.00 Cash Flow 4 0.4096 $210.00 Cash Flow 5 0.32768 $210.00 Cash Flow 6 0.262144 $210.00 Cash Flow 7 0.2097152 $210.00 Net Present Value As at 25% the NPV is positive, so IRR will be above 25% Particulars Year Present Value ($650.00) $168.00 $134.40 $107.52 $86.02 $68.81 $55.05 $44.04 $13.84 So Let IRR Be 26% Present Value Amount factor of 26% ($650.00 Cash Flow 0 1 ) Cash Flow 1 0.793650794 $210.00 Cash Flow 2 0.629881582 $210.00 Cash Flow 3 0.499906018 $210.00 Cash Flow 4 0.396750808 $210.00 Cash Flow 5 0.314881593 $210.00 Cash Flow 6 0.249906027 $210.00 Cash Flow 7 0.198338116 $210.00 Net Present Value As at 26% the NPV is negative, so IRR will be below 26% Particulars Year Now we need to interpolate the IRR IRR = 25% + 1% x 13.84/(21.98+11.45) = 25.85% (approx.) Present Value ($650.00) $166.67 $132.28 $104.98 $83.32 $66.13 $52.48 $41.65 ($2.50) b) If each project's cost of capital were 10%, which project, if either, should be selected? If the cost of capital were 17%, what would be the proper choice? At 10% :Project B Present Present Value Amount Value ($650.00 Cash Flow 0 1 ($400.00) ($400.00) ) ($650.00) Cash Flow 1 0.909090909 ($528.00) ($480.00) $210.00 $190.91 Cash Flow 2 0.826446281 ($219.00) ($180.99) $210.00 $173.55 Cash Flow 3 0.751314801 ($150.00) ($112.70) $210.00 $157.78 Cash Flow 4 0.683013455 $1,100.00 $751.31 $210.00 $143.43 Cash Flow 5 0.620921323 $820.00 $509.16 $210.00 $130.39 Cash Flow 6 0.56447393 $990.00 $558.83 $210.00 $118.54 Cash Flow 7 0.513158118 ($325.00) ($166.78) $210.00 $107.76 NPV $478.83 NPV $372.37 As the net present value of Project A is higher than Project B thus Project A will be chosen. Particulars Year Present Value factor of 10% Amount Project A At 17% :Project B Present Present Value Amount Value ($650.00 Cash Flow 0 1 ($400.00) ($400.00) ) ($650.00) Cash Flow 1 0.854700855 ($528.00) ($451.28) $210.00 $179.49 Cash Flow 2 0.730513551 ($219.00) ($159.98) $210.00 $153.41 Cash Flow 3 0.624370556 ($150.00) ($93.66) $210.00 $131.12 Cash Flow 4 0.533650048 $1,100.00 $587.02 $210.00 $112.07 Cash Flow 5 0.456111152 $820.00 $374.01 $210.00 $95.78 Cash Flow 6 0.389838592 $990.00 $385.94 $210.00 $81.87 Cash Flow 7 0.333195378 ($325.00) ($108.29) $210.00 $69.97 NPV $133.76 NPV $173.70 As the net present value of Project A is lower than Project B thus Project B will be chosen. Particulars Year Present Value factor of 17% Amount Project A Question -2 a) What is each project's MIRR at the cost of capital of 10%? At 17%? (Hint: Consider Period 7 as the end of Project B's life.) MIRR is rate of return considering the reinvestment of intermediate cash flows at a predetermined rate of return. At 10% :First compute the Present Value of Cash Outflows at Year 0 Project A Project B Present Value Present Present factor of 10% Cash Outflows Cash Outflows Value Value Cash Flow 0 1 $400.00 $400.00 $650.00 $650.00 Cash Flow 1 0.909090909 $528.00 $480.00 $0.00 $0.00 Cash Flow 2 0.826446281 $219.00 $180.99 $0.00 $0.00 Cash Flow 3 0.751314801 $150.00 $112.70 $0.00 $0.00 Cash Flow 7 0.513158118 $325.00 $166.78 $0.00 $0.00 Initial Initial $1,340.47 $650.00 Investment Investment Then compute Future Value of Cash Inflows at the end of project year considering reinvestment at discount rate. Particular s Year Particular s Reinvestmen t Years Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow 6 5 4 3 2 1 0 Project A Future Value factor of 10% Cash Inflows Future Value 1.771561 $0.00 $0.00 1.61051 $0.00 $0.00 1.4641 $0.00 $0.00 1.331 $1,100.00 $1,464.10 1.21 $820.00 $992.20 1.1 $990.00 $1,089.00 1 $0.00 $0.00 Terminal Value $3,545.30 Project B Cash Inflows Future Value $210.00 $372.03 $210.00 $338.21 $210.00 $307.46 $210.00 $279.51 $210.00 $254.10 $210.00 $231.00 $210.00 $210.00 Terminal Value $1,992.31 Now, MIRR is the rate at which present value of terminal value equates the Initial Investment. Project A Initial Investment = Terminal value of cash flow x Present value factor of MIRR of year 7 Present value factor of MIRR of year 7 = Initial Investment /Terminal value of cash flow Present value factor of MIRR of year 7 = $1340.47/$3545.30 = 0.37809645 Referring to present value factor table we get 14.91% Project B Initial Investment = Terminal value of cash flow x Present value factor of MIRR of year 7 Present value factor of MIRR of year 7 = Initial Investment /Terminal value of cash flow Present value factor of MIRR of year 7 = $650/$1992.31 = 0.326255118 Referring to present value factor table we get 17.36% At 17% :First compute the Present Value of Cash Outflows at Year 0 Project A Present Value Year Present factor of 10% Cash Outflows Value Cash Flow 0 1 $400.00 $400.00 Cash Flow 1 0.854700855 $528.00 $451.28 Cash Flow 2 0.730513551 $219.00 $159.98 Cash Flow 3 0.624370556 $150.00 $93.66 Cash Flow 7 0.333195378 $325.00 $108.29 Initial $1,213.21 Investment Then compute Future Value of Cash Inflows at the end of project year discount rate. Particular s Particular s Reinvestmen t Years Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow 6 5 4 3 2 1 0 Project A Future Value factor of 10% Cash Inflows Future Value 2.565164202 $0.00 $0.00 2.192448036 $0.00 $0.00 1.87388721 $0.00 $0.00 1.601613 $1,100.00 $1,761.77 1.3689 $820.00 $1,122.50 1.17 $990.00 $1,158.30 1 $0.00 $0.00 Terminal Value $4,042.57 Project B Present Cash Outflows Value $650.00 $650.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 Initial $650.00 Investment considering reinvestment at Project B Cash Inflows Future Value $210.00 $538.68 $210.00 $460.41 $210.00 $393.52 $210.00 $336.34 $210.00 $287.47 $210.00 $245.70 $210.00 $210.00 Terminal Value $2,472.12 Now, MIRR is the rate at which present value of terminal value equates the Initial Investment. Project A Initial Investment = Terminal value of cash flow x Present value factor of MIRR of year 7 Present value factor of MIRR of year 7 = Initial Investment /Terminal value of cash flow Present value factor of MIRR of year 7 = $1213.21/$4042.57 = 0.300108077 Referring to present value factor table we get 18.76% Project B Initial Investment = Terminal value of cash flow x Present value factor of MIRR of year 7 Present value factor of MIRR of year 7 = Initial Investment /Terminal value of cash flow Present value factor of MIRR of year 7 = $650/$2472.12 = 0.262931942 Referring to present value factor table we get 21.02% Question -3 What is the crossover rate, and what is its significance? First we need to compute differential Cash flows which are as follows:Particular s Year Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow 0 1 2 3 4 5 6 7 Project A Cash Outflows ($400.00) ($528.00) ($219.00) ($150.00) $1,100.00 $820.00 $990.00 ($325.00) Project B Cash Outflows ($650.00) $210.00 $210.00 $210.00 $210.00 $210.00 $210.00 $210.00 Difference in cash flows (A-B) $250.00 ($738.00) ($429.00) ($360.00) $890.00 $610.00 $780.00 ($535.00) Now the crossover rate is the rate at which the present value of difference in cash flows will be 0 So Let crossover rate be 15% Particular s Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Year 0 1 2 3 4 5 6 7 Present Value Amount factor of 15% 1 $250.00 0.869565217 ($738.00) 0.756143667 ($429.00) 0.657516232 ($360.00) 0.571753246 $890.00 0.497176735 $610.00 0.432327596 $780.00 0.37593704 ($535.00) Net Present Value As the NPV is negative thus crossover rate will be below 15% Now, let crossover rate be 14% Present Value $250.00 ($641.74) ($324.39) ($236.71) $508.86 $303.28 $337.22 ($201.13) ($4.60) Particulars Year Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow 0 1 2 3 4 5 6 7 Present Value Amount factor of 14% 1 $250.00 0.877192982 ($738.00) 0.769467528 ($429.00) 0.674971516 ($360.00) 0.592080277 $890.00 0.519368664 $610.00 0.455586548 $780.00 0.399637323 ($535.00) Net Present Value Present Value $250.00 ($647.37) ($330.10) ($242.99) $526.95 $316.81 $355.36 ($213.81) $14.86 Now we need to interpolate the IRR Crossover rate = 14% + 1% x 14.86/(14.86 + 4.60) = 14.76% (approx.) This implies that in discounting at rate below 14.76% Project A will be better but discounting at rate above this rate Project B will be better to the level of its IRR. Significance Crossover rate is the rate at which an investor is indifferent between two projects, in other words it is the point at which NPV of two projects is equal. It determines the range of returns and accordingly which project to be chosen. Question -4 Assume that the project has average risk. Find the project's expected NPV. (Hint: Use expected values for the net cash flow in each year.) Projects expected NPV is computed as follows:- Particulars Initial Investment Cash Flows Cash Flows Cash Flows Cash Flows Cash Flows Terminal Value Year Present Value factor of 10% 0 1 2 3 4 5 5 1.00000 0.90909 0.82645 0.75131 0.68301 0.62092 0.62092 Probability 0.20 ($100,000.0 0) $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $0.00 Thus Projects Expected NPV is $24,900.19 (Approx.) Cash flows Probability 0.60 ($100,000.0 0) $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $20,000.00 Expected Cash Flows Probability 0.20 ($100,000.0 ($100,000.0 0) 0) $40,000.00 $30,000.00 $40,000.00 $30,000.00 $40,000.00 $30,000.00 $40,000.00 $30,000.00 $40,000.00 $30,000.00 $30,000.00 $18,000.00 Net Present Value Expected Present Value ($100,000.00 ) $27,272.73 $24,793.39 $22,539.44 $20,490.40 $18,627.64 $11,176.58 $24,900.19