A project that provides annual cash flows of $18,200 for nine years costs $88,00

Question

A project that provides annual cash flows of $18,200 for nine years costs $88,000 today.

  

What is the NPV for the project if the required return is 8 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.)

  

  

At a required return of 8 percent, should the firm accept this project?

  

What is the NPV for the project if the required return is 20 percent? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

At a required return of 20 percent, should the firm accept this project?

  

At what discount rate would you be indifferent between accepting the project and rejecting it? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

A project that provides annual cash flows of $18,200 for nine years costs $88,000 today.

Explanation / Answer

Part A)

NPV is the difference between the present value of cash inflows and cash outflows. It can be calculated with the use of following formula:

NPV = Cash Flow Year 0 + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3 + Cash Flow Year 4/(1+Discount Rate)^4 + Cash Flow Year 5/(1+Discount Rate)^5 + Cash Flow Year 6/(1+Discount Rate)^6 + Cash Flow Year 7/(1+Discount Rate)^7 + Cash Flow Year 8/(1+Discount Rate)^8 + Cash Flow Year 9/(1+Discount Rate)^9

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Using the values provided in the question, we get,

NPV = - 88,000 + 18,200/(1+8%)^1 + 18,200/(1+8%)^2 + 18,200/(1+8%)^3 + 18,200/(1+8%)^4 + 18,200/(1+8%)^5 + 18,200/(1+8%)^6 + 18,200/(1+8%)^7 + 18,200/(1+8%)^8 + 18,200/(1+8%)^9 = $25,693.36

_____________

Part B)

Yes, the project should be Accepted at 8% discount rate as it results in a positive NPV.

_____________

Part C)

Using the values provided in the question, we get,

NPV = - 88,000 + 18,200/(1+20%)^1 + 18,200/(1+20%)^2 + 18,200/(1+20%)^3 + 18,200/(1+20%)^4 + 18,200/(1+20%)^5 + 18,200/(1+20%)^6 + 18,200/(1+20%)^7 + 18,200/(1+20%)^8 + 18,200/(1+20%)^9 = -$14,636.41

_____________

Part D)

No, the project Should Not be Accepted at the discount rate of 20% as it results in a negative NPV.

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Part E)

To determine the discount rate, we need to calculate the internal rate of return. At this rate, we would be indifferent between accepting or rejecting a project because NPV is 0 with IRR. The IRR can be calculated with the of IRR function EXCEL/Financial Calculator. The basic formula for calculating IRR is:

NPV = 0 = Cash Flow Year 0 + Cash Flow Year 1/(1+IRR)^1 + Cash Flow Year 2/(1+IRR)^2 + Cash Flow Year 3/(1+IRR)^3 + Cash Flow Year 4/(1+IRR)^4 + Cash Flow Year 5/(1+IRR)^5 + Cash Flow Year 6/(1+IRR)^6 + Cash Flow Year 7/(1+IRR)^7 + Cash Flow Year 8/(1+IRR)^8 + Cash Flow Year 9/(1+IRR)^9

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IRR has been calculated with the use of EXCEL in the below table:

The discount rate at which there would be no difference between accepting and rejecting the project is 14.63%.

Year Cash Flow 0 -88,000 1 18,200 2 18,200 3 18,200 4 18,200 5 18,200 6 18,200 7 18,200 8 18,200 9 18,200 IRR =IRR(-88000,18200,18200,18200,18200,18200,18200,18200,18200,18200) = 14.63%

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