This paper consists of answers to questions about present value, net present value, profitability index, IRR and MIRR.
¶ … Value
PV = $15,000 / (1+.07)^1 = $14,018.69.
At 4%, this is $15,000 / (1.04) = $14,423.08
The PV of Account A is 6500 / 1.06 = $6,132.07. The PV of Account B. is 12,600 / (1.06)^2 = $11,213.96
Income
PV
NPV
The present value of the entire income stream is $168,459,500.
Income
PV
NPV
Income
PV
NPV
What this example shows is that the net present value of a future cash flow increases with a lower discount rate. The reason for this is that a lower discount rate means the less purchasing power of the future cash flow is diminished. So in this situation the gold mine is worth more at a 3% rate than a 5% rate, and both are worth more than at a 7% rate.
A. The project's NPV at a discount rate of 0% is $670,000
The project's NPV at a discount rate of 2% is $614,353
The project's NPV at a discount rate of 6% is $514,815
The project's NPV at a discount rate of 11% is $408,997
The project's modified internal rate of return is 28% at the 11% reinvest rate. If the reinvest rate is 6%, the MIRR is 33%, and if the project's reinvest rate is 2%, then the MIRR is 37%.
The graph shows that the rate of return for this to deliver an even net present value is very high -- around 45%. At any point below 45% on the horizontal axis, this project will have a positive net present value. Once the x-axis has been crossed, the project will have a negative NPV.
B. The internal rate of return on this project is 4%.
If the discount rate is 1%, the NPV is $65,358
If the discount rate is 4%, the NPV is $7,593
If the discount rate is 10%, the NPV is -$91,777
If the discount rate is 18%, the NPV is -$197,892
The curve in this case intersects the x-axis at 4%. This is consistent with the IRR that was calculated and with the fact that at a 4% discount rate the NPV was near zero. For discount rates above 4%, the project had a negative net present value.
C. The profitability index is calculated as the PV of future cash flows / initial investment (Investopedia, 2011). Thus:
0.94 = x / 4.2
X = 3.948
If the present value of proceeds is $3.948 million, subtract this from the initial value to get the NPV:
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