A hydroelectric dam is projected to produce annual benefits that grow in concert with the
regional economic growth rate of 2%. The first benefit amount, $600,000, occurs at the end
of year 5 (after the dam is constructed and the reservoir fills). If the interest rate is 8% and
the benefits are assumed to continue growing through year 50 (50-year planning period),
what is the present value of benefits at period 0? Also, draw the cash flow diagram.
In the world of finance and project evaluation, understanding the present value of future cash flows is crucial for making informed decisions. This essay discusses the calculation of the present value of benefits for a hydroelectric dam project over a 50-year planning period. The benefits are expected to grow in line with the regional economic growth rate of 2%, with an initial benefit of $600,000 occurring at the end of year 5. The discount rate for this analysis is 8%. Additionally, a cash flow diagram will be presented to visually represent the project’s cash flows.
Present Value Calculation: To calculate the present value of the benefits generated by the hydroelectric dam project, we can use the formula for the present value of a growing annuity:
��=�×(1−(1+�)−�)�−�
Where: PV = Present Value C = Initial Benefit in year 5 = $600,000 g = Growth rate = 2% or 0.02 r = Discount rate = 8% or 0.08 n = Number of years = 50 – 5 = 45 (the project’s planning period)
Now, let’s plug in the values into the formula:
��=600,000×(1−(1+0.02)−45)0.08−0.02
Calculating this expression gives us the present value of benefits at period 0.
��=600,000×(1−(1.02)−45)0.06 ��≈600,000×(1−0.5202)0.06 ��≈600,000×0.47980.06 ��≈287,8800.06 PV \approx $4,798,000
The present value of the benefits at period 0 is approximately $4,798,000.
A cash flow diagram is a valuable visual tool for representing the project’s cash flows over time. In this case, the cash flow diagram for the hydroelectric dam project would look like this:
Year 0 Year 5 Year 50
|--------------|----------------------|
| |
| |
$4,798,000 $600,000 (growing)
In the diagram, Year 0 represents the initial investment or cost associated with building the dam. Year 5 marks the first benefit of $600,000, which then grows annually by 2% until Year 50.
Understanding the present value of benefits is essential for evaluating the feasibility and profitability of long-term projects like a hydroelectric dam. In this scenario, the present value of benefits at period 0 is approximately $4,798,000. This calculation provides project stakeholders with valuable information for making investment decisions. The accompanying cash flow diagram visually represents the timing and magnitude of cash flows over the project’s 50-year planning period, aiding in better project planning and decision-making.
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