Answer:
a. The payback period for project A=3.44 years, and the payback period for project B=2.21 years.
b. Net present value for project A=$78,560.951, and the Net present value for project B=$11,694.239
c. IRR for Project A= 16.57% and IRR for Project B=25.72%
d. Probability index (P.I) for Project A=1.187 and the Probability index (P.I) for Project B=1.316
e. The final decision should be based on the NPV since it doesn't have the ranking problem that is usually associated with other capital budgeting techniques. I would choose Project A since it has a higher Net Present Value (NPV) as compared to Project B.
Explanation:
PROJECT A PROJECT B
Year Cash flow Cash flow
0. $419,000 $37,000
1. $47,000 $19,800
2. $59,000 $13,900
3. $76,000 $15,600
4. $534,000 $12,400
a.
The payback period for Project A can be determined as follows;
The cash flows at Year 0 represent the initial investment to the project. The payback period is the number of years it will take until the return on the project is equal to the initial investment. This can be calculated as shown;
419,000-(47,000+59,000+76,000)
=419,000-182,000=$237,000
After 3 years, the total cash flow will be=$182,000 which is still $237,000 less from the initial investment. Determine the number of months in the fourth year that it will take to cover the remainder;
(237,000/534,000)=0.44 years
Total number of years=3+0.44=3.44 years
The payback period for project A=3.44 years
The payback period for Project B can be determined as follows;
37,000-(19,800+13,900)
=37,000-33,700=$3,300
After 2 years, the total cash flow will be=$33,700 which is still $3,300 less from the initial investment. Determine the number of months in the third year that it will take to cover the remainder;
(3,300/15,600)=0.21 years
Total number of years=2+0.21=2.21 years
The payback period for project B=2.21 years
b.
Net present value for project A is;
NPV=-419,000+{47,000/(1+0.11)}+{59,000/((1+0.11)^2)}+{76,000/((1+0.11)^3)}+534,000/((1+0.11)^4)=-419,000+(42,342.342+47,885.724+55,570.545+351,762.340=$42,378,560.61
Net present value for project A=$78,560.951
Net present value for project B is;
NPV=-37,000+{19,800/(1+0.11)}+{13,900/((1+0.11)^2)}+{15,600/((1+0.11)^3)}+12,400/((1+0.11)^4)=-37,000+(17,837.837+11,281.552+11,406.586+8,168.264=$11,694.239
Net present value for project B=$11,694.239
c.
The IRR for each project A is:
$419,000 = $47,000 / (1 + IRR) + $59,000 / (1 + IRR)^2 + $76,000 / (1 + IRR)^3 + $534,000 / (1 + IRR)^4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR = 16.57%
The IRR for each project B is:
$37,000 = $19,800 / (1 + IRR) + $13,900 / (1 + IRR)^2 + $15,600 / (1 + IRR)^3 + $12,400 / (1 + IRR)^4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR = 25.72%
d.
Probability index (P.I) for Project A;
P.I=[{47,000/(1+0.11)}+{59,000/((1+0.11)^2)}+{76,000/((1+0.11)^3)}+534,000/((1+0.11)^4)]/419,000=(42,342.342+47,885.724+55,570.545+351,762.340=1.187
The Probability index (P.I) for Project A=1.187
Probability index (P.I) for Project B;
[{19,800/(1+0.11)}+{13,900/((1+0.11)^2)}+{15,600/((1+0.11)^3)}+12,400/((1+0.11)^4)]/37,000=(17,837.837+11,281.552+11,406.586+8,168.264=1.316
The Probability index (P.I) for Project B=1.316
e.
The final decision should be based on the NPV since it doesn't have the ranking problem that is usually associated with other capital budgeting techniques. I would choose Project A since it has a higher Net Present Value (NPV) as compared to Project B.