Question

an investment has an installed cost of $574,380. the cash flows over the four-year life of the investment are projected to be $216,700, $259,300, $214,600, and $167,410, respectively. a. if the discount rate is zero, what is the npv? (do not round intermediate calculations.) b. if the discount rate is infinite, what is the npv? (a negative answer should be indicated by a minus sign. do not round intermediate calculations.) c. at what discount rate is the npv just equal to zero? (do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

To calculate NPV at zero discount rate, sum the cash flows and subtract the installed cost, resulting in $283,630. At an infinite discount rate, NPV is just the negative of the installed cost, -$574,380. To find the discount rate making NPV zero, solve the present value equation equating cash flows to installed cost.

Step-by-step explanation:

The question is regarding the calculation of Net Present Value (NPV) for an investment with an installed cost of $574,380 and cash flows over four years. The calculations must be done under three different scenarios: a discount rate of zero, a discount rate of infinity, and the discount rate that makes the NPV equal to zero.

NPV with a Discount Rate of Zero:

With a discount rate of zero, all future cash flows are worth their face value today. Hence, the NPV is simply the sum of the cash flows minus the installed cost:

NPV = ($216,700 + $259,300 + $214,600 + $167,410) - $574,380 = $283,630

NPV with an Infinite Discount Rate:

At an infinite discount rate, all future cash flows are worth nothing today. Therefore, the NPV is equal to the negative of the installed cost:

NPV = -$574,380

Discount Rate for NPV of Zero:

To find the discount rate that sets the NPV to zero, one would have to solve for the discount rate that equates the present value of cash flows to the installed cost, typically done using numerical methods or financial calculator tools since it involves solving the equation:

0 = ($216,700 / (1+r)^1) + ($259,300 / (1+r)^2) + ($214,600 / (1+r)^3) + ($167,410 / (1+r)^4) - $574,380

Where 'r' is the discount rate.

Answer 2

NPV is calculated by subtracting the initial investment from the present value of cash inflows. At a 0% discount rate, the NPV is $283,630, at an infinite discount rate, NPV is -$574,380. To find the discount rate where NPV equals zero, a trial-and-error calculation for the internal rate of return (IRR) is needed.

Step-by-step explanation:

The student is asking about the calculation of Net Present Value (NPV), which is a key concept in finance and investment analysis. NPV is used to assess the profitability of an investment by comparing the present value of its cash inflows to the initial outlay. Here's how to calculate NPV in the given scenarios:

1. If the discount rate is zero, the NPV is simply the sum of the cash flows minus the installed cost, since no discounting is applied. Therefore:
   NPV = ($216,700 + $259,300 + $214,600 + $167,410) - $574,380 = $858,010 - $574,380 = $283,630.
2. If the discount rate is infinite, the present value of future cash flows would be $0, as no amount of money in the future is worth anything today at an infinite discount rate. Hence, NPV = -$574,380.
3. To determine the discount rate at which the NPV is zero, we have to solve for the rate that makes the sum of the discounted cash flows equal to the installed cost. This requires more complex calculations or the use of financial software, as it is a trial-and-error method known as the internal rate of return (IRR).