Question

What is the payback period, NPV, IRR of A. Using this information, should we accept Project A. Why or why not.

Given the following information answer the question above. The discount rate is 10 percent.

     PROJECT A      

t           Cash Flow      

0          (150,000)       

1          40,000          

2          40,000             

3          40,000         

4           40,000          

5            40,000              

ROUND TO NEAREST DOLLAR OR TEN %

Answer 1

NPV of a project= PV of cash inflows - PV of cash outflows

= cash flow per year*annuity factor(10%, 5 years) - initial investment

= 40,000*3.791 - 1,50,000= $1,640 (approx)

Since the NPV is positive, hence the project should be accepted.

Payback Period= initial investment/ annual cash inflows

= 1,50,000/ 40,000= 3.75 years

This means that if we invest in this project, it will taken 3 years and 9 months to recover the initial investment in the form of annual cash flows.

Internal Rate of Return (IRR)= It is the discount rate at which the PV of cash inflows is equal to the PV of cash outflows, i.e, NPV=0.

This is computed by trial and error method, i.e, taking a rate and applying the same to check if the NPV is equal to 0. Let the required IRR be r :

-1,50,000+ 40,000/(1+r) + 40,000/(1+r)^2 + 40,000/(1+r)^3 + 40,000/(1+r)^4 + 40,000/(1+r)^5 = 0

Putting r=10%, we get NPV= 1640

Putting r=10.5%, we get NPV= -286

Hence, we can say that the IRR lies in between 10% and 10.5%.

We will apply interpolation technique to find this rate, as follows, by applying the following formula:

IRR = L + (A/ (A-B)) X (H-L)

Where,

L = Lower Discount Rate

H = Higher Discount Rate

A = NPV at Lower Discount Rate

B = NPV at Higher Discount Rate

hence, as per the question, IRR= 10 + (1640/ (1640- (-286))) * (10.5-10) = 10.42% (approx)

As per the above results, since we are assessing one particular project, hence NPV is a good technique to take a decision. Since the NPV is positive, we should accept the project.