ou are evaluating two mutually exclusive projects with the following net cash flows:
Project X Project Y
Year Cash Flow Cash Flow
0 -$1000 -$1100
1 100 1000
2 300 100
3 400 150
4 700 50
The cost of capital is 12 percent.
What is each project’s payback period? If the cutoff period is 3 year, then which project would you choose?
What is each project’s discounted payback period? If the cutoff period is 3 year, then which project would you choose?
What is each project’s NPV? Which project would you choose based on NPV rule?
What is each project’s IRR? Which project would you choose based on IRR rule?
What is each project’s profitability index? Based on profitability index, which project is preferred?
What is each project’s equivalent annual annuity (EAA)? Based on EAA, which project is preferred?
| Payback | ||
| Year | Project X | Incremental Cash flow |
| 0 | -1,000 | |
| 1 | 100 | 100 |
| 2 | 300 | 400 |
| 3 | 400 | 800 |
| 4 | 700 | 1,500 |
| Year | Project y | Incremental Cash flow |
| 0 | -1100 | |
| 1 | 1000 | 1000 |
| 2 | 100 | 1,100 |
| 3 | 150 | 1,250 |
| 4 | 50 | 1,300 |
If we consider payback method project y has earlier payback then the project X so the company should accept projrct y
If the cutoff period is 3 year, then which project would you choose?
then also company should choose project Y
What is each project’s discounted payback period? If the cutoff period is 3 year, then which project would you choose?
| Discounted Payback | ||||
| Year | Project X | Discount Factor @ 12% |
pv | Incremental Cash flow |
| 1 | 100 | 0.89286 | 89.28571429 | 89.28571429 |
| 2 | 300 | 0.79719 | 239.1581633 | 328.44388 |
| 3 | 400 | 0.71178 | 284.7120991 | 613.15598 |
| 4 | 700 | 0.63552 | 444.8626549 | 1,058.01863 |
in the three year we recover 613. dollar so remaning 386 we have to recover in the year 4
= 386.84 *365/ 444.1058
=318 days
Total paybeck = 3 year and 318 days
| Year | Project y | Discount Factor @ 12% |
pv | Incremental Cash flow |
| 1 | 1000 | 0.89286 | 892.8571429 | 892.8571429 |
| 2 | 100 | 0.79719 | 79.71938776 | 972.57653 |
| 3 | 150 | 0.71178 | 106.7670372 | 1,079.34357 |
| 4 | 50 | 0.63552 | 31.77590392 | 1,111.11947 |
in the three year we recover 1079. dollar so remaning 386 we have to recover in the year 4
= 20 *365/ 31.77
=237 days
If we consider payback method project y has earlier payback then the project X so the company should accept projrct y
If the cutoff period is 3 year, then which project would you choose?
then also company should choose project Y
Total paybeck = 3 year and 237 days
What is each project’s NPV? Which project would you choose based on NPV rule?
| Net prasent value | |||
| Year | Project X | Discount Factor @ 12% |
pv |
| 0 | -1000 | 1 | -1000 |
| 1 | 100 | 0.89286 | 89.28571429 |
| 2 | 300 | 0.79719 | 239.1581633 |
| 3 | 400 | 0.71178 | 284.7120991 |
| 4 | 700 | 0.63552 | 444.8626549 |
| 58.01863156 | |||
| Year | Project y | Discount Factor @ 12% |
pv |
| 0 | -1100 | 1 | -1100 |
| 1 | 1000 | 0.89286 | 892.8571429 |
| 2 | 100 | 0.79719 | 79.71938776 |
| 3 | 150 | 0.71178 | 106.7670372 |
| 4 | 50 | 0.63552 | 31.77590392 |
| 11.1194717 | |||
Based on the NPV we should choose projrct X becase it hase higher NPV then the project Y
What is each project’s IRR? Which project would you choose based on IRR rule?
the formulla of IRR is
0 = P0 + P1/(1+IRR) + P2/(1+IRR)2 + P3/(1+IRR)3 + . . . +Pn/(1+IRR)n
Project x
0 = -$1000 + ($100)/(1+IRR)+ ($300)/(1+IRR.)2 + ($400)/(1+IRR)3 + $700/(1+IRR)4
Project Y
0 = -$1100 + ($1000)/(1+IRR)+ ($100)/(1+IRR.)2 + ($150)/(1+IRR)3 + $50/(1+IRR)4
Using trial and error method we have found IRR =
| Project x | 14.11% |
| Project y | 12.84% |
Baseed on IRR , We should chose project Y because it hase higher IRR i.e 12.84%
What is each project’s profitability index? Based on profitability index, which project is preferred?
| NPv | Invest ment | P.I | P. I. | |
| Project x | 1058.02 | 1000 | NPV / Investment | 1.05802 |
| Project y | 1111.11 | 1100 | NPV / Investment | 1.0101 |
Based on PI we should choose project X has higher PI
