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24 July, 15:32

You are considering two independent projects. The required rate of return is 11.25 percent for project A and 11.85 percent for project B. Project A has an initial cost of $38,900 and cash inflows of $11,400, $16,900, and $26,200 for Years 1 to 3, respectively. Project B has an initial cost of $41,300 and cash inflows of $20,000 a year for three years. Which project (s), if either, should you accept?

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  1. 24 July, 15:57
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    The net present value of project B is higher than Project A, so Project B should be accepted.

    Explanation:

    In this question, we have to use the net present value formula which is shown below:

    Net present value = Present value of all years cash flows - Initial investment

    where,

    Present value of cash inflows is calculated by applying the discount rate which is presented below:

    For this, we have to first compute the present value factor which is computed by a formula

    = 1 : (1 + rate) ∧ number of year

    number of year = 0

    number of year = 1

    Number of year = 2

    number of year = 3

    So,

    Rate = 11.25%

    For year 1 = 0.8989 (1 : 1.1125) ∧ 1

    For year 2 = 0.8080 (1 : 1.1125) ∧ 2

    For year 3 = 0.7263 (1 : 1.1125) ∧ 3

    Now, multiply this present value factor with yearly cash inflows

    So

    For Project A,

    The present value of year 1 = $11,400 * 0.8989 = $10,247.191

    The present value of year 2 = $16,900 * 0.8080 = $13,654.842

    The present value of year 3 = $26,200 * 0.7263 = $19028.354

    and the sum of all year cash inflow is $42,930.387

    So, the Net present value would be equal to

    = $42,930.387 - $38,900 = $4,030.387

    And,

    For Project B

    Rate = 11.85%

    For year 1 = 0.8941 (1 : 1.1185) ∧ 1

    For year 2 = 0.7993 (1 : 1.1185) ∧ 2

    For year 3 = 0.7146 (1 : 1.1185) ∧ 3

    Now, multiply this present value factor with yearly cash inflows

    So

    For Project B,

    The present value of year 1 = $20,000 * 0.8941 = $17,881.091

    The present value of year 2 = $20,000 * 0.7993 = $15,986.670

    The present value of year 3 = $20,000 * 0.7146 = $14,292.955

    and the sum of all year cash inflow is $48,160.716

    So, the Net present value would be equal to

    = $48,160.716 - $41,300 = 6,860.716

    Since the net present value of project B is higher than Project A, so Project B should be accepted.
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