Blog: Fin622 solution

Being the finance manager of XYZ Company, you are to select one project of two available options i.e. Project A and Project B. The relevant cash flows for both the projects are summarized in given table.
Project A
Project B
Initial investment
Rs. 57,000
Rs. 54,000
Year(n)
Cash inflows (CFn)
Cash inflows (CFn)
1
Rs. 20,000
Rs. 22,000
2
20,000
20,000
3
20,000
18,000
4
20,000
16,000
Assume the discount rate to be 14 percent.
Required:
• Calculate the payback period of each project.
• Calculate the Net present value (NPV) of each project.
• On the basis of results of pay back period and NPV, which project would you recommend to your company and why?
Important Note: Give formulae and show calculations properly as they also carry marks

Solution:-

1) The payback period of each project

THE PAYBACK PERIOD (PP); For the Project A that has equal receipts

= Initial Investment / Cash Flow (I0/Ct)
= 57000/20000
= 2.85year

THE PAYBACK PERIOD (PP); For the Project B

Payback period lie between 2nd year and 3rd year

Sum of the money recovered by the end of second year
= (22000+20000)
= 42000

Sum of money recovered by the end of 3rd year
= (54000 – 42000)
= 12000
= [2+ 12000/18000) years
= 2.667 years

2) The Net present value (NPV) of each project.

NPV for project A;
Formula:
(CFn * PVFA at 14% for 4 years) – Initial Investment

PVFA at 14% for 4 years:

= [1/ (1+i) ^ n + 1/ (1+i) ^ n + 1/ (1+i) ^ n + 1/ (1+i) ^ n]
= [1/ (1+0.14) ^1 + 1/ (1+0.14) ^2 + 1/ (1+0.14) ^3 + 1/ (1+0.14) ^4]
= [0.8772 + 0.7695 + 0.6749 + 0.5920]
= [2.9136]

By putting values in Formula:
= (20000 * 2.9136) – 57000
= 1272

NPV for project B;
Formula:
Sum of the NPV (CFn) – Initial investment

Sum of the NPV (CFn)
= [CF1/ (1+i) ^ n + CF2/ (1+i) ^ n + CF3/ (1+i) ^ n + CF4/ (1+i) ^ n]
= [22000/ (1+0.14) ^1 + 20000/ (1+0.14) ^2 + 18000/ (1+0.14) ^3 + 16000/ (1+0.14) ^4]
= 19298.246 + 15389.352 + 12149.487 + 9473.284
= 56310.368

By putting values
= 56310.368 – 54000
= 2310.368


3) Decision

Project A 1272.00 NPV

Project B 2310.368 NPV

According to the NPV of both projects, I will recommend project B due to greater NPV of project B from A.

Project A 2.85 year PP

Project B 2.667 year PP

According to the PP of both projects, I will also recommend Project B, because in Project B the payback period (PP) is little than Project A.