Question:AST Company is attempting to select among the two mutuallyexc

QUESTION

Question:AST Company is attempting to select among the two mutuallyexclusive projects both ofwhich cost Rs. 100,000. The firm has a cost of capital equal to13%. After-tax cashinflows associated with each project are shown in the followingtable :Year Pr
Answer: i) Calculate the Payback Period for eachproject. Initial Investment = 100,000 Payback Period for Project A: In year one, 40,000 will be covered, and (100,000-40,000) =60,000 should be covered. In year two, further 25,000 will be covered, and (60,000-25,000)= 35,000 should be covered. In year three, 35,000 will be covered, which we have to coverfrom the project. So, our payback period is 3 years for ProjectA. Payback Period for Project B: In year one, 45,000 will be covered, and (100,000-45,000) =55,000 should be covered. In year two, further 25,000 will be covered, and (55,000-25,000)= 30,000 should be covered. In year three, 20,000 will be covered, and (30,000-20,000) =10,000 should be covered yet. In year four, 20,000 will be covered, but we have to cover10,000 only, So these 10,000 will take the time in years = 10,000/20,000 =0.5 years OR 10,000 will take the time in months = 10,000/20,000 * 12 = 6months OR 10,000 will take the time in days = 10,000/20,000 * 365 =182.5 days So, payback period for Project B is 3.5 years, or 3years and 6 months or 3 years and 182.5 days . ii) Calculate the Net Present Value (NPV) ofeach project. NPV for Project A: NPV = -Initial Investment ? Cash Flows / (1 r) t NPV = -100,000 [40,000 / (1 0.13) 1 ] [25,000 /(1 0.13) 2 ] [35,000 / (1 0.13) 3 ] [25,000/ (1 0.13) 4 ] [20,000 / (1 0.13) 5 ] NPV = -100,000 [40,000 / (1.13) 1 ] [25,000 /(1.13) 2 ] [35,000 / (1.13) 3 ] [25,000 /(1.13) 4 ] [20,000 / (1.13) 5 ] NPV = -100,000 [40,000 / 1.13]

[25,000 / 1.2769] [35,000 /1.442897] [25,000 / 1.63047361] [20,000 / 1.8424351793] NPV = -100,000 [35398.23] [19578.67] [24256.76] [15332.97] [10855.2] NPV = 5421.83 NPV for Project B: NPV = -Initial Investment ? Cash Flows / (1 r) t NPV = -100,000 [45,000 / (1 0.13) 1 ] [25,000 /(1 0.13) 2 ] [20,000 / (1 0.13) 3 ] [20,000/ (1 0.13) 4 ] [20,000 / (1 0.13) 5 ] NPV = -100,000 [45,000 / (1.13) 1 ] [25,000 /(1.13) 2 ] [20,000 / (1.13) 3 ] [20,000 /(1.13) 4 ] [20,000 / (1.13) 5 ] NPV = -100,000 [45,000 / 1.13] [25,000 / 1.2769] [20,000 /1.442897] [20,000 / 1.63047361] [20,000 / 1.8424351793] NPV = -100,000 [39823] [19578.67] [13861] [12266.37] [10855.2] NPV = -3615.76 iii) Calculate the Internal Rate of Return(IRR) for each project. Internal rate of return (IRR) is a rate where, NPV becomes zerolets compute IRR for both projects, We know the formula for Interpolation given as: Rate1 ((NPV1 / (NPV1 NPV2)) * (Rate2 Rate1)) But to apply this formula, we need another rate, where NPVshould be in opposite sign, so, IRR for Project A: Lets take a rate of 16 percent, our NPV becomes: NPV = -Initial Investment ? Cash Flows / (1 r) t NPV = -100,000 [40,000 / (1 0.16) 1 ] [25,000 /(1 0.16) 2 ] [35,000 / (1 0.16) 3 ] [25,000/ (1 0.16) 4 ] [20,000 / (1 0.16) 5 ] NPV = -100,000 [40,000 / (1.16) 1 ] [25,000 /(1.16) 2 ] [35,000 / (1.16) 3 ] [25,000 /(1.16) 4 ] [20,000 / (1.16) 5 ] NPV = -100,000 [40,000 / 1.16] [25,000 / 1.3456] [35,000 /1.560896] [25,000 / 1.81063936] [20,000 / 2.1003416576] NPV = -100,000 [34482.76] [18579.07] [22423.02] [13807.28] [9522.26] NPV = -1185.61 Applying Interpolation formula to get IRR: Data:- At 13%, NPV = 5421.83 At 16%, NPV = -1185.61 IRR = Rate1 ((NPV1 / (NPV1 NPV2)) * (Rate2 Rate1)) IRR = 13% ((5421.83 / (5421.83 (1185.61))) * (16% -13%)) IRR = 13% ((5421.83 / 6607.44) * (3)) IRR = 13% ((0.8206) * (3)) IRR = 13% (2.4618) IRR = 15.46% approximately IRR for Project B: Lets take a rate of 11 percent, our NPV becomes: NPV = -Initial Investment ? Cash Flows / (1 r) t NPV = -100,000 [45,000 / (1 0.11) 1 ] [25,000 /(1 0.11) 2 ] [20,000 / (1 0.11) 3 ] [20,000/ (1 0.11) 4 ] [20,000 / (1 0.11) 5 ] NPV = -100,000 [45,000 / (1.11) 1 ] [25,000 /(1.11) 2 ] [20,000 / (1.11) 3 ] [20,000 /(1.11) 4 ] [20,000 / (1.11) 5 ] NPV = -100,000 [45,000 / 1.11] [25,000 / 1.2321] [20,000 /1.367631] [20,000 / 1.51807041] [20,000 / 1.6850581551] NPV = -100,000 [40540.54] [20290.56] [14623.83] [13174.62] [11869.03] NPV = 498.58 Applying Interpolation formula to get IRR: Data:- At 13%, NPV = -3615.76 At 11%, NPV = 498.58 IRR = Rate1 ((NPV1 / (NPV1 NPV2)) * (Rate2 Rate1)) IRR = 11% ((498.58 / (498.58 (3615.76))) * (13% 11%)) IRR = 11% ((498.58 / 4114.34) * (2)) IRR = 11% ((0.1212) * (2)) IRR = 11% (0.2424) IRR = 11.24% approximately iv) Summarize and compare the above findings for both projectsand indicate which project you would recommend and why? Answer: Paybackperiod NPV IRR Project A 3years 5421.83 15.46% Project B 3.5years -3615.76 11.24% Project A should be recommended, because Project A is profitable isall aspects as compare to Project B, as first of all it has lowpayback period, i.e., low amount of time for the recovery ofinitial investment, secondly it has higher or positive net presentvalue, while Project B has not, thirdly, it internal rate of return(15.46%) is higher than its cost of borrowing (13%) from investors,while Project Bs cost of borrowing from investors (13%) ishigher than its internal rate of return (11.24%), it means ProjectB is not profitable at all, so Project A should be selected.

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