Question
In: Finance
Payback period, net present value, profitability index, and internal rate of return calculations) You are considering...
Payback period, net present value, profitability index, and internal rate of return calculations) You are considering a project with an initial cash outlay of
$73 comma 00073,000
and expected cash flows of
$21 comma 17021,170
at the end of each year for six years. The discount rate for this project is
9.99.9
percent.
a. What are the project's payback and discounted payback periods?
b. What is the project's NPV?
c. What is the project's PI?
d. What is the project's IRR?
a. The payback period of the project is
nothing
years.
Solutions
Expert Solution
a.
| Year | Cash flow stream | Cumulative cash flow | Discounting factor | Discounted cash flows project |
| 0 | -73000 | -73000 | 1 | -73000 |
| 1 | 21170 | -51830 | 1.099 | 19262.96633 |
| 2 | 21170 | -30660 | 1.207801 | 17527.72187 |
| 3 | 21170 | -9490 | 1.327373299 | 15948.79151 |
| 4 | 21170 | 11680 | 1.458783256 | 14512.09418 |
| 5 | 21170 | 32850 | 1.603202798 | 13204.81727 |
| 6 | 21170 | 54020 | 1.761919875 | 12015.30234 |
| Payback period is the time by which undiscounted cashflow cover the intial investment outlay |
| this is happening between year 3 and 4 |
| therefore by interpolation payback period = 3 + (0-(-9490))/(11680-(-9490)) |
| 3.45 Years |
| Discounted payback period is the time by which discounted cashflow cover the intial investment outlay |
| this is happening between year 4 and 5 |
| therefore by interpolation payback period = 4 + (0-(-5748.43))/(7456.39-(-5748.43)) |
| 4.44 Years |
| Where |
| Discounting factor =(1 + discount rate)^(corresponding year) |
| Discounted Cashflow=Cash flow stream/discounting factor |
b.
| Discount rate | 9.900% | ||||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Cash flow stream | -73000 | 21170 | 21170 | 21170 | 21170 | 21170 | 21170 |
| Discounting factor | 1.000 | 1.099 | 1.208 | 1.327 | 1.459 | 1.603 | 1.762 |
| Discounted cash flows project | -73000.000 | 19262.966 | 17527.722 | 15948.792 | 14512.094 | 13204.817 | 12015.302 |
| NPV = Sum of discounted cash flows | |||||||
| NPV Project = | 19471.69 | ||||||
| Where | |||||||
| Discounting factor = | (1 + discount rate)^(Corresponding period in years) | ||||||
| Discounted Cashflow= | Cash flow stream/discounting factor | ||||||
| c. | |||||||
| PI= (NPV+initial inv.)/initial inv. | |||||||
| =(19471.69+73000)/73000 | |||||||
| 1.27 | |||||||
| d. | |||||||
| Project | |||||||
| IRR is the rate at which NPV =0 | |||||||
| IRR | 18.56% | ||||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Cash flow stream | -73000.000 | 21170.000 | 21170.000 | 21170.000 | 21170.000 | 21170.000 | 21170.000 |
| Discounting factor | 1.000 | 1.186 | 1.406 | 1.666 | 1.976 | 2.342 | 2.777 |
| Discounted cash flows project | -73000.000 | 17856.463 | 15061.562 | 12704.120 | 10715.666 | 9038.445 | 7623.744 |
| NPV = Sum of discounted cash flows | |||||||
| NPV Project = | 0.000 | ||||||
| Where | |||||||
| Discounting factor = | (1 + discount rate)^(Corresponding period in years) | ||||||
| Discounted Cashflow= | Cash flow stream/discounting factor | ||||||
| IRR= | 18.56% | ||||||
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