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A firm evaluates all of its projects by using the NPV decision rule. Year   Cash Flow...

A firm evaluates all of its projects by using the NPV decision rule.
Year   Cash Flow
0   –$30,000
1   18,000
2   17,000
3   10,000
  
a. At a required return of 13 percent, what is the NPV for this project?
6173
6482
5926
6297
6050

b. At a required return of 35 percent, what is the NPV for this project?
-3438.12
-3143.42
-3339.89
-3208.91
-3274.40

Solutions

Expert Solution

(a) Option (a) 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 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 = 13%, 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 = $18000 / (1 + 13%)+ $17000 / (1 + 13%)2 + $10000 / (1 + 13%)3

PV = $18000 / (1 + 0.13)+ $17000 / (1 + 0.13)2 + $10000 / (1 + 0.13)3

PV = $18000 / (1.13)+ $17000 / (1.13)2 + $10000 / (1.13)3

PV = $15929.20+ ($17000 / 1.2769) + ($10000 / 1.442897)

PV = $15929.20 + $13313.49 + $6930.50

PV = $36173.19

So, required present value is $36173

Initial investment = $30000

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

Net Present value (NPV) = $36173.19 - $30000 = $6173

(b) Option (e) 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 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 = 35%, 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 = $18000 / (1 + 35%)+ $17000 / (1 + 35%)2 + $10000 / (1 + 35%)3

PV = $18000 / (1 + 0.35)+ $17000 / (1 + 0.35)2 + $10000 / (1 + 0.35)3

PV = $18000 / (1.35)+ $17000 / (1.35)2 + $10000 / (1.35)3

PV = $13333.33+ ($17000 / 1.8225) + ($10000 / 2.460375)

PV = $13333.33 + $9327.85 + $4064.43

PV = $26725.60

So, required present value is $26725.60

Initial investment = $30000

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

Net Present value (NPV) = $26725.60 - $30000 = - $3274.40

jeff jeffy answered 2 years ago
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