Equivalent annual annuity Corcoran Consulting is deciding which of two computer
ID: 2643801 • Letter: E
Question
Equivalent annual annuity
Corcoran Consulting is deciding which of two computer systems to purchase. It can purchase state-of-the-art equipment (System A) for $20,000, which will generate cash flows of $5,000 at the end of each of the next 6 years. Alternatively, the company can spend $10,000 for equipment that can be used for 3 years and will generate cash flows of $5,000 at the end of each year (System B).
What is its EAA? Round your answer to the nearest cent.
Unequal Lives
Haley's Graphic Designs Inc. is considering two mutually exclusive projects. Both projects require an initial investment of $8,000 and are typical average-risk projects for the firm. Project A has an expected life of 2 years with after-tax cash inflows of $4,000 and $12,000 at the end of Years 1 and 2, respectively. Project B has an expected life of 4 years with after-tax cash inflows of $6,000 at the end of each of the next 4 years. The firm's WACC is 10%.
If the projects cannot be repeated, which project should be selected if Haley uses NPV as its criterion for project selection?
Assume that the projects can be repeated and that there are no anticipated changes in the cash flows. Use the replacement chain analysis to determine the NPV of the project selected.
Make the same assumptions as in Part b. Using the equivalent annual annuity (EAA) method, what is the EAA of the project selected? Round your answer to the nearest cent.
Explanation / Answer
Part a)
Equal Lives:
Step 1: Calculate NPV for Both Projects:
NPV is the difference between the present value of costs and present value of benefits. The formula for calculating NPV for a cash flow stream is:
NPV = -Present Value of Cash Outflows + Present Value of Cash Inflows. Another formula to solve NPV (particularly in this question) is:
NPV = -Initial Investment + Cash Inflow Year 1/(1+Discount Rate)^1 + Cash Inflow Year 2/(1+Discount Rate)^2 and so on, where discount rate is WACC.
______________________________
Using the information provided in the question we calculate NPV for both projects. Here discount rate is assumed to be 10% (since it is not provided in the question)
NPV (System A) = -20,000 + 5,000/(1+10%)^1 + 5,000/(1+10%)^2 + 5,000/(1+10%)^3 + 5,000/(1+10%)^4 + 5,000/(1+10%)^5 + 5,000/(1+10%)^6 = $1,776.30
NPV (System B) = -10,000 + 5,000/(1+10%)^1 + 5,000/(1+10%)^2 + 5,000/(1+10%)^3 = $2,434.26
____________________________
Step 2: Calculate Equivalent Annual Annuity:
The EAA can be easily determined with the use of EXCEL/Financial Calculator. The formula/function for calculating EAA is PMT(Rate,Nper,-PV,FV) where Rate is WACC, Nper is Period, PV is NPV and FV is Future Value (if any)
For System A, Rate = 10%, Nper = 6, PV = 1,776.30, FV = 0
EAA = PMT(10%,6,-1776.30,0) = $407.85
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For System B, Rate = 10%, Nper = 3, PV = 2,434.26, FV = 0
EAA = PMT(10%,3,-2434.26,0) = $978.85
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Part b):
Unequal Lives:
1)
NPV is the difference between the present value of costs and present value of benefits. The formula for calculating NPV for a cash flow stream is:
NPV = -Present Value of Cash Outflows + Present Value of Cash Inflows. Another formula to solve NPV (particularly in this question) is:
NPV = -Initial Investment + Cash Inflow Year 1/(1+Discount Rate)^1 + Cash Inflow Year 2/(1+Discount Rate)^2 and so on, where discount rate is WACC.
______________________________
Using the information provided in the question we calculate NPV for both projects,
Project A (NPV) = -8,000 + 4,000/(1+10%)^1 + 12,000/(1+10%)^2 = $5,553.72
_______
Project B (NPV) = -8,000 + 6,000/(1+10%)^1 + 6,000/(1+10%)^2 + 6,000/(1+10%)^3 + 6,000/(1+10%)^4 = $11,019.19
Based on the above calculations, Project B should be selected as it has a higher NPV.
________________
2)
In this case, we will have to calculate the NPV of project A, as project B already extends out to 4 years, we will take its NPV as $11,019.19
Cash flow for Project A for calculating its NPV using replacement chain analysis would be:
Cash Flow Year 1 = $4,000
Cash Flow Year 2 = $12,000 - $8,000 = $4,000
Cash Flow Year 3 = $4,000
Cash Flow Year 4 = $12,000
Using the above cash flows, we calculate the project A's extended NPV,
Extended NPV of Project A = -8,000 + 4,000/(1+10%)^1 + 4,000/(1+10%)^2 + 4,000/(1+10%)^3 + 12,000/(1+10%)^4 = $10,143.57
Since Project B's NPV is again higher than that of A, we would select project B.
________________
3)
The EAA can be easily determined with the use of EXCEL/Financial Calculator. The formula/function for calculating EAA is PMT(Rate,Nper,-PV,FV) where Rate is WACC, Nper is Period, PV is NPV and FV is Future Value (if any)
Here Project B is selected, so we will use the information for Project B. Rate is 10%, Nper is 4 Years, PV is $11,019.19 and FV is 0. Using this information in the above formula/function we get,
EAA = PMT(10%,4,-11019.19,0) = $3,746.23
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