What is the NPV for a project whose cost of capital is 15 percent and initial...

What is the NPV for a project whose cost of capital is 15 percent and initial after-tax cost is $5,000,000 and is expected to provide after-tax operating cash inflows of $1,800,000 in year 1, $1,900,000 in year 2, $1,700,000 in year 3, and $1,300,000 in year 4?

Group of answer choices

a) $1 700,000

b) 371,764

c) -4,862,947

d) -137,053

Solutions

Expert Solution

Option (d) is correct

Net Present value (NPV) is the present value of future cash inflows minus the initial investment.

First we will calculate the present value of cash inflows for first 4 years as per below:

Here we will use the following formula:

PV = FV / (1 + r%)n

where, FV = Future value, PV = Present value, r = rate of interest = 15%, n= time period

For calculating the present value the given cash flows, we will calculate the present values of all the years and add them up. Now,putting the values in the above equation, we get,

PV = $1800000 / (1 + 15%) + $1900000 / (1 + 15%)2 + $1700000 / (1 + 15%)3 + $1300000 / (1 + 15%)4

PV = $1800000 / (1 + 0.15) + $1900000 / (1 + 0.15)2 + $1700000 / (1 + 0.15)3 + $1300000 / (1 + 0.15)4

PV = $1800000 / (1.15) + $1900000 / (1.15)2 + $1700000 / (1.15)3 + $1300000 / (1.15)4

PV = $2070000 + ($1900000 / 1.3225) + ($1700000 / 1.520875) + ($1300000 / 1.74900625)

PV = $1565217.39 + $1436672.97 + $1117777.60 + $743279.22

PV = $4862947.18

So, required present value is $4862947.18

Initial investment = $5000000

Net present value (NPV) = Present value of cash flows - Initial investment

Net Present value (NPV) = $4862947.18 - $5000000 = - $137053

jeff jeffy answered 1 year ago

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