| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Cash outflow | ($90,000) | ($55,000) | |||||||
| Cash inflow | $42,000 | $30,425 | $30,425 | $30,425 | $30,425 | $30,425 | $30,425 | $30,425 | $45,425 |
| Net cash flow | ($48,000) | ($24,575) | $30,425 | $30,425 | $30,425 | $30,425 | $30,425 | $30,425 | $45,425 |
| Cumulative cash flow | ($48,000) | ($72,575) | ($42,150) | ($11,725) | $18,700 | $49,125 | $79,550 | $109,975 | $155,400 |
| Discount rate | 8% |
| NPV | $84,019.60 |
| IRR | 30% |
| Payback period | 3.385 years |
| Present value of future cash flows | $132,019.60 |
| Initial investment | $90,000 |
| Profitability index (Present value of future cash flows/initial investment) | 1.4669 |
Delegate your assignment to our experts and they will do the rest.
NPV = + +
When r =8%
NPV = $84,019.60
IRR is the discount rate r when
NPV = + + = 0
IRR =30%
Payback period = Year cumulative cash flow is last negative + (remaining amount to zero/cash flow in the next period)
Payback period = 3 years + $11,725/$30,425 = 3.385 years
New Backhoes
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Cash outflow | ($200,000) | ||||||||
| Cash inflow | $43,900 | $43,900 | $43,900 | $43,900 | $43,900 | $43,900 | $43,900 | $133,900 | |
| Net cash flow | ($200,000) | $43,900 | $43,900 | $43,900 | $43,900 | $43,900 | $43,900 | $43,900 | $133,900 |
| Cumulative cash flow | ($200,000) | ($156,100) | ($112,200) | ($68,300) | ($24,400) | $19,500 | $63,400 | $107,300 | $241,200 |
| Discount rate | 8% |
| NPV | $100,901.65 |
| IRR | 18% |
| Payback period | 4.556 years |
| Present value of future cash flows | $300,901.65 |
| Initial investment | $200,000 |
| Profitability index (Present value of future cash flows/Initial investment) | 1.5045 |
NPV = + +
When r =8%
NPV = $100,901.65
IRR is the discount rate r when
NPV = + + = 0
IRR = 18%
Payback period = Year cumulative cash flow is last negative + (remaining amount to zero/cash flow in the next period)
Payback period = 4 years + $24,400/43,900 = 4.556 years
NPV
The NPV for investing in the old backhoes is $84,019.60 lower than the NPV of investing in the new backhoes, $100,901.65. A higher NPV of the investment in the new back holes implies that the return value is higher than an investment in the old backhoes meaning that Waterways should invest in new backhoes.
IRR
The IRR for the investment in old backhoes is 30% and higher than the investment in new backhoes 18%. A higher IRR means that the investment in old backhoes is more profitable than an investment in new backhoes. Using the IRR, investment in old backhoes would be a better option.
Payback Period
The payback period for old backhoes is 3.385 years as compared to 4.556 years for an investment in new backhoes. A shorter payback period is preferable as it means that an investment would break even more quickly. Using the payback period, investment in old backhoes would be preferable.
Profitability Index
The profitability index estimates the ratio of the payoff of an investment to the initial investment.
Profitability index = Present value of future cash flows/Initial investment
Profitability index for investment in new backhoes = $300,901.65 /$200,000 = 1.5045
Profitability index for investment in old backhoes = $132,019.60 /$90,000 = 1.4669
The profitability index for investment in new backhoes, 1.5045, is higher than that of an investment in old backhoes, meaning that investment in the new backhoes generated more value for every invested dollar. Investment in new backhoes is therefore preferable. In addition to a higher NPV and profitability index, replacing the old backhoes comes with intangible benefits that enhance consumer satisfaction. The new backhoes are faster, more accurate trench digging, the benefit of comfort operating features, and a 1-year maintenance agreement.
