Question

Compute the Profitability Index statistic for 345 Rayzor Sharp Project and note whether the firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 10 percent. CF0 = -1000 CF1 = 500 CF2 = 480 CF3 = 400 CF4 = 300 CF5 = 150 0.19, reject 0.45, reject 1.19, accept 1.45, accept

Answer 1

Option (d) is correct

The formula for calculating the profitability index is:

Profitability index = Present value of cash flows / Initial investment

First we will calculate the present value of cash flows:

Here we will use the following formula:

PV = FV / (1 + r%)n

where, FV = Future value, PV = Present value, r = rate of interest = 10%, 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 = $500 / (1 + 10%) + $480 / (1 + 10%)2  + $400 / (1 + 10%)3 + $300 / (1 + 10%)4 + $150 / (1 + 10%)5

PV = $500 / (1 + 0.10) + $480 / (1 + 0.10)2  + $400 / (1 + 0.10)3 + $300 / (1 + 0.10)4 + $150 / (1 + 0.10)5

PV = $500 / (1.10) + $480 / (1.10)2  + $400 / (1.10)3 + $300 / (1.10)4 + $150 / (1.10)5

PV = $454.54 + ($480 / 1.21)  + ($400 / 1.331) + ($300 / 1.4641) + ($150 / 1.61051)

PV = $454.54 + $396.69421 + $300.52592 + $204.9040 + $93.138198

PV = $1449.80

So, required present value is $1449.80

Initial investment = $1000

Now, we will calculate the profitability index as below:

Profitability index = Present value of cash flows / Initial investment

Profitability index = $1449.80 / $1000 = 1.45

Since the value of profitability index is greater than 1, so we should accept the project.