Critically evaluate whether a change in the cost of capital might produce a conflict between the net present value and modified internal rate of return rankings between the two projects?

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For project cash now are some for each year 250 pondo Presentate interest factor of an ordinary ily by 2.500 to 1.620.50 s as present of cashows present value of Project 10,429.50 - 10.000 20.50 pounds Modified internal rate of return as the rate at which of those Present value of cash outflows in each project 10.000 Terminal value of cash flows is the future value of all this the are manure value of cash flow from Year 10 Future Cashflow value of prot from Cashow Me Prompt pounds pour pound 1.4O643253800 77967205 100003782 3800 2006112300 Future Was Terminal For Project A. Puture Values factored from the Follows for your cash flows the number of periods of period 3 years from year to your 4), FVFX for years, and your chow your way from tom period. FOR 3 cash flow is way from terminal period So Porrar cash flow is terminal value Adding a future value of cash flow terminal values 1225450 pounds 2. For Proiect since the cash flows are nowe Rural of an ordinary nuty 24 years and multiply by 3500 to get terminal Modified one of retumis here at which For 20.000 PV 13,364.50 pounds 10.000 17.256.50/e13254.500.00 1725451.725R16-10 10.000 PV of 16,726.50 pounds 10,000 16,726.50/16,726.500.000 1672786727WR11372-1872.77 Discounted Payback period is the period of time will take to recover the cash utflows based on discoured cash flows each year discounted period Cath towed cash flows For Prict initial cash flow is 10.000 pounds Yardcore cashindows 800 pounds. So,remaining to be covered Year 10000 20450479560 Year 2 diented cash inows 23. mingine recovered after year 2195.50-23011804.50. Indiscounted casino200 My covering the remaining investment 180450. So, the discounted period Present of Cashflows of cash flow chow rompt women to be W pounds pound -10000 -10000 1000 2006 No JO 012 21 2136 2315 cash flows from outflow to Cashflows from project pro in pounds 12% -10000 red 10000 - 10000 1255 27805 3500 0. 4065 300 2 From the methods above, we see the resterande pa back period. Therefore, Project A should be chosen Ans.A. i) Net Present Value = Present value of cash inflows - present value of cash outflows NPV for Project A and Project B is calculated as per following table: 0 3 Present value of Present Cash flows cash flows value of cash from from Cash flows flows from project Ain PVIF @ Proj.A(in from project PVIFA @ Proj.B(in Year pounds) 12% pounds) B(in pounds) 12% pounds) |-10000 1 |-10000 |-10000 -10000 6500 10.893 5804.5 3500 3.037 10629.5 2 3000 0.797 2391 3500 3000 10.712 2136 3500 4 1000 0.636 636 3500 Net Present value 967.5 629.5 Working notes: 1. Both projects have initial investment of 10,000 pounds. So, negative cash inflow(cash outflow) of 10,000 pounds at Year O. 2. Cash inflows from Project A for each year are multiplied by Present Value Interest Factor of $1 @ 12% (since cost of capital is 12%) for each year. For example, PVIF @12% for 1 year = 0.893, for 2 year = 0.797 etc. (From the PV tables). Multiplying cash inflows with present value factors gives us present value of each cash inflow (Column 4). Adding up all cash inflows from Year 1 to Year 4 and subtracting cash outflow 10,000 pounds at Year Ofrom it, gives us Net Present Value of Project A = 967.50 pounds 3. For project B, cash inflows are same for each year,i.e, 3500 pounds, so we use Present Value interest factor of an ordinary annuity @ 12% for 4 years = 3.037, and multiply it by 3,500 to get 10,629.50 pounds as present value of cash inflows. Net present value of Project B = 10,629.50 - 10,000 = 629.50 pounds. Ans.ii) Modified internal rate of return is the rate at which present value of cash outflows is equal to the present value of terminal value of cash inflows Present value of cash outflows in each project = 10,000 pounds Present value of the terminal value of cash inflows for each project is calculated as below: Terminal value of cash inflows is the future value of all cash inflows at the terminal year (end year). Here, it means future value of all cash inflows from Year 1 to Year 4 at Year 4. Future 1 2 Present value of the terminal value of cash inflows for each project is calculated as below: Terminal value of cash inflows is the future value of all cash inflows at the terminal year (end year). Here, it means future value of all cash inflows from Year 1 to Year 4 at Year 4. Future Cash flows value of Future value from cash flows of cash project from Cash flows flows from A(in FVIF @ Proj.A(in from project FVIFA @ Proj.B(in Year pounds) 12% pounds) B(in pounds) 12% pounds) 6500 1.405 9132.5 3500 4.779 16726.5 3000 1.254 3762 3500 3 3000 1.12 3360 3500 4 11000 1 1000 3500 Future Value/Terminal value 17254.5 16,726.50 Working notes: 1. For Project A, Future Value interest factor @ 12% is picked from the FV tables as follows, for Year 1 cash flows the number of periods to terminal period = 3 years (i.e., from year 1 to year 4), so FVIF @12% for 3 years, next Year 2 cash flows are 2 years away from terminal period, so FVIF @12% FOR 2 years, next Year 3 cash flow is 1 year away from terminal period, So FVIF @12% for 1 year and Year 4 cash flow is already at terminal value. Adding up all future value of cash flows, we get terminal value as 17,254.50 pounds. 2. For Project B, since the cash inflows are uniform, we take Future value interest factor of an ordinary annuity @12% for 4 years and multiply by 3500 to get terminal value as 16,726.50 pounds Now, Modified Internal Rate of return is the rate at which: For Project A 10,000 = PV of 17,254.50 pounds 10,000 = 17,254.50 /((1+r)^4) (1+r)^4 = 17,254.50/10,000 (1+r)^4 = 1.72545 1+r = (1.72545)^(1/4) R = 1.146 - 1 = 0.146 or 14.6% For Project B 10,000 = PV of 16,726.50 pounds 10,000 = 16,726.50/((1+r)^4) (1+r)^4 = 16,726.50/10,000 (1+r)^4 = 1.6727 1+r = (1.6727)^(1/4) R = 1.1372 -1 = 0.1372 or 13.72% Ans.ii) Discounted Payback period is the period of time it will take to recover the cash outflows based on discounted cash inflows each year. So, discounted payback period = Initial Cash outflows/ Discounted cash inflows For Project A, initial cash outflow is 10,000 pounds. Year 1 discounted cash inflows are 5804.50 pounds. So, remaining investment to be recovered after Year 1 = 10000- 5804.50=4195.50. Next Year 2 discounted cash inflows = 2391, so remaining investment to be recovered after Year 2 = 4195.50 - 2391 = 1804.50. In Year 3, discounted cash inflows = 2136, which is fully covering the remaining investment of 1804.50. So, the discounted payback period = 3 years Present value Value of initial 0 1 Now, Modified Internal Rate of return is the rate at which: For Project A 10,000 = PV of 17,254.50 pounds 10,000 = 17,254.50/((1+r)^4) (1+r)^4 = 17,254.50/10,000 (1+r)^4 = 1.72545 1+r = (1.72545)^(1/4) R = 1.146 - 1 = 0.146 or 14.6% For Project B 10,000 = PV of 16,726.50 pounds 10,000 = 16,726.50/((1+r)^4) (1+r)^4 = 16,726.50/10,000 (1+r)^4 = 1.6727 1+r = (1.6727)^(1/4) R = 1.1372 - 1 = 0.1372 or 13.72% Ans.iii) Discounted Payback period is the period of time it will take to recover the cash outflows based on discounted cash inflows each year. So, discounted payback period = Initial Cash outflows/ Discounted cash inflows For Project A, initial cash outflow is 10,000 pounds. Year 1 discounted cash inflows are 5804.50 pounds. So, remaining investment to be recovered after Year 1 = 10000- 5804.50=4195.50. Next Year 2 discounted cash inflows = 2391, so remaining investment to be recovered after Year 2 = 4195.50 -2391 = 1804.50. In Year 3, discounted cash inflows = 2136, which is fully covering the remaining investment of 1804.50. So, the discounted payback period = 3 years Present value Value of initial Cash flows of cash flows cash outflow from project PVIF @ from Proj.A (in to be Year A(in pounds) 12% pounds) recovered |-10000 -10000 -10000 6500 0.893 5804.5 -4195.5 2 3000 0.797 2391 -1804.5 3000 0.712 2136 331.5 1000 0.636 636 Similarly, for Project B, discounted payback period is 4 years (working in table below) Value of Present value of initial cash Cash flows cash flows from outflow to from project PVIF @ Proj.B(in be Year Bin pounds) 12% pounds) recovered -10000 |-10000 -10000 3500 10.893 3125.5 |-6874.5 3500 0.797 2789.5 -4085 3500 10.712 2492 -1593 3500 0.636 2226 633 Ans.B From all the methods above, we see that Project A has higher NPV, better MIRR and lower discounted payback period. Therefore, Project A should be chosen. 1 3 0 1 1 2 3 4 Please help with part C only