Question

1.Consider the projest that costs $100,000 and yields a return of $30,000 for five years. At the end of the fifth year, there is the cost of $20,000 to dispose of the waste from the project. Should the project be undertaken if the discount rat eis 0? 10 percent? 15 percent? The interest rate at which the net present discounted value of the project is zero is referred to as the internal rate of return of the project

Answer 1

$$Solution$$

Net Present Value = Present Value of Cash inflows - Present Value of Cash outflow.

If Discount Rate is 0 %: Then,

$Net\ Present\ Value\ of\ Project = ( 30,000 + 30,000 + 30,000 + 30,000 + (30,000 - 20,000) ) - 100,000\\ = 130,000 - 100,000\\ =30,000$

Since, Net Present Value of Project is positive at 0 %, thus the project should be undertaken.

If Discount rate is 10 %;

Present Value of Cash inflows$Present\ value\ of\ cash\ inflows=30,000\ \times\ cumulative\ present\ value\ value\ factors\ at\ 10\% \ for\ 4\ years+(30,000-20,000)\times\ Present\ value\ factor\ for\ 5th\ year\ at\ 10\%. =30,000\times\ Cumulative\ present \ \\ =(30,000\times\ 3.1699)+(10,000\times\ 0.621)\\ =101,307$

$=101,307-100,000\\ =1,307(Net\ present\ value\ of\ the\ project)$

Since, Net Present Value of Project is positive at 10 %, thus the project should be undertaken.

If Discount rate is 15 %.

$Present\ value\ of\ cash\ inflows=30,000\ \times\ cumulative\ present\ value\ value\ factors\ at\ 15\% \ for\ 4\ years+(30,000-20,000)\times\ Present\ value\ factor\ for\ 5th\ year\ at\ 15\%\\ =(30,000\times2.8550)+(10,000\times0.4972)\\ =90,622$

Net Present Value of Project

$= 90622 - 100000 = (-) 9378$

Since, Net Present Value of Project is negative at $15\%$ , thus the project should not be undertaken.

Conclusion: The project should be undertaken at $0\%$ and $10\%$ discount rate. The project should not be undertaken at $15\%$ discount rate.