Question: AST Company isattempting to select among the two mutually exclusive pr
ID: 2662159 • Letter: Q
Question
Question:
AST Company isattempting to select among the two mutually exclusive projects bothof
which cost Rs.100,000. The firm has a cost of capital equal to 13%. After-taxcash
Year
Project A (Rs.)
Project B (Rs.)
1
40,000
45,000
2
25,000
25,000
3
35,000
20,000
4
25,000
20,000
5
20,000
20,000
(i) Calculate the Payback Period for each project. (2+3)
(ii) Calculate the Net Present Value (NPV)of each project. (5+5)
(iii) Calculate the Internal Rate of Return(IRR) for eachproject. (6+6)
(IRRmust be calculated by using “Trial & Error Method withInterpolation
Formula”. IRR calculated directly byusing Excel or Financial Calculators, will
not beawarded full marks.)
(iv) Summarize and compare the above findings forboth projects and indicate which
project you would recommend andwhy? (3)
Year
Project A (Rs.)
Project B (Rs.)
1
40,000
45,000
2
25,000
25,000
3
35,000
20,000
4
25,000
20,000
5
20,000
20,000
Explanation / 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 zerolet’s 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:
Let’s 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:
Let’s 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%
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