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Asked: 2022-04-13T09:25:11+00:00 In:

Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 –$356,…

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Consider the following two mutually exclusive projects:

Year Cash Flow (A) Cash Flow (B)
0 $ 356,000 $ 40,000
1 31,000 23,000
2 42,000 15,200
3 50,000 14,100
4 445,000 11,200

The required return on these investments is 13 percent.

Required:

(a) What is the payback period for each project? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) 

(b) What is the NPV for each project? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g.,32.16).) 

(c) What is the IRR for each project? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

(d) What is the profitability index for each project? (Do not round intermediate calculations. Round your answers to 3 decimal places (e.g., 32.161).) 

(e) Based on your answers in (a) through (d), which project will you finally choose?

♦ Relevant knowledge

The payback period is the duration a project must get back its initial investment after getting to the breakeven point of the investment. The project that has a shorter payback time should be selected as an investment.

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  1. Best Answer

    (a)

    Project A
    Year Cash flow stream Cumulative cash flow
    0 -356000 -356000
    1 31000 -325000
    2 42000 -283000
    3 50000 -233000
    4 445000 212000
    The payback period is the amount of time that the initial investment was covered by the cashflow.
    This is what happens between years 3 and 4.
    therefore by interpolation payback period = 3 + (0-(-233000))/(212000-(-233000))
    3.52 years
    Project B
    Year Cash flow stream Cumulative cash flow
    0 -40000 -40000
    1 23000 -17000
    2 15200 -1800
    3 14100 12300
    4 11200 23500
    The payback period is the amount of time that the initial investment was covered by the cashflow.
    This is what happens between years 2 and 3.
    therefore by interpolation payback period = 2 + (0-(-1800))/(12300-(-1800))
    2.13 years

    (b)

    Project A
    Get a Discount 13.000%
    Year 0 1 2 3 4
    Cash flow stream -356000 31000 42000 50000 445000
    Factor of discounting 1.000 1.130 1.277 1.443 1.630
    Project on discounted cash flows -356000.000 27433.628 32892.161 34652.508 272926.834
    NPV = Sum discounted cash flows
    NPV Project A = 11905.13
    Where
    Discounting factor = (1 + Discount Rate)(Corresponding Period in Years)
    Discounted Cashflow = Cash flow stream/discounting factor
    Project B
    Get a Discount 13.000%
    Year 0 1 2 3 4
    Cash flow stream -40000 23000 15200 14100 11200
    Factor of discounting 1.000 1.130 1.277 1.443 1.630
    Project on discounted cash flows -40000.000 20353.982 11903.830 9772.007 6869.170
    NPV = Sum discounted cash flows
    NPV Project B = 8898.99
    Where
    Discounting factor = (1 + Discount Rate)(Corresponding Period in Years)
    Discounted Cashflow = Cash flow stream/discounting factor

    (c)

    Project A
    IRR refers to the rate at which the NPV =0
    IRR 14.07%
    Year 0 1 2 3 4
    Cash flow stream -356000.000 31000.000 42000.000 50000.000 445000.000
    Factor of discounting 1.000 1.141 1.301 1.484 1.693
    Project on discounted cash flows -356000.000 27176.943 32279.523 33688.892 262854.641
    NPV = Sum discounted cash flows
    NPV Project A = 0.000
    Where
    Discounting factor = (1 + Discount Rate)(Corresponding Period in Years)
    Discounted Cashflow = Cash flow stream/discounting factor
    Project B
    IRR refers to the rate at which NPV =0
    IRR 24.90%
    Year 0 1 2 3 4
    Cash flow stream -40000.000 23000.000 15200.000 14100.000 11200.000
    Factor of discounting 1.000 1.249 1.560 1.948 2.433
    Project on discounted cash flows -40000.000 18415.417 9744.308 7237.361 4602.914
    NPV = Sum discounted cash flows
    NPV Project B = 0.001
    Where
    Discounting factor = (1 + Discount Rate)(Corresponding Period in Years)
    Discounted Cashflow = Cash flow stream/discounting factor

    (d)

    Project A

    PI= (NPV+initial inv. )/initial inv.
    =(11905.13+356000)/356000
    1.03

    Project B

    PI= (NPV+initial inv. )/initial inv.
    =(8898.99+40000)/40000
    1.22

    (e) Accept project B because it has a higher IRR or profitability index.

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