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?

Question

Business

Bryant Wilkins

20 December, 08:52

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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Answers (1)

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Myles · Answer 1

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.