You are offered an asset that costs $14,000 and has cash flows as follows below
ID: 2793670 • Letter: Y
Question
You are offered an asset that costs $14,000 and has cash flows as follows below at the end of each quarter for the next 8 years. Then it will be sold for $2,500. Your cost of capital is 6.5 percent. An alternative (mutually exclusive) project is available which offers an accounting rate of return of 8%, a classical payback period of 5 years and a discounted payback period of 5 years. Year 1: $800 each quarter Year 2: $850 each quarter Year 3: $850 each quarter Year 4: $950 each quarter Year 5: $800 each quarter Year 6: $600 each quarter Year 7: $500 each quarter Year 8: $400 each quarter a) What is the IRR of the asset? (2 points) b) What is the NPV of the asset? (1 point 2 points) c) What are the PI and NPI of the asset? (BONUS QUESTION: 1 point) d) What are the classical and discounted payback periods? (BONUS QUESTION: 1 point) e) What are the four accounting rate of returns (utilizing cash flows)? (BONUS QUESTION: 1 point) f) Should you purchase it? Base your answer on your solutions to parts a through e a and b (IRR and NPV) and explain why. (3 points 5 points) (Use your calculator to make sure that the answers are correct. Read chapter 19 before you start doing the problem.)
Explanation / Answer
Asset Cost =$14,000
Cost of Capital =6.50% or 1.625% per quarter
NPV of asset = -14000 + 800x{(1-(1+0.01625)-4)/0.01625}x(1+0.01625)-0 + 850x{(1-(1+0.01625)-4)/0.01625}x(1+0.01625)-4 + 850x{(1-(1+0.01625)-4)/0.01625}x(1+0.01625)-8 + 950x{(1-(1+0.01625)-4)/0.01625}x(1+0.01625)-12 + 800x{(1-(1+0.01625)-4)/0.01625}x(1+0.01625)-16 + 600x{(1-(1+0.01625)-4)/0.01625}x(1+0.01625)-20 + 500x{(1-(1+0.01625)-4)/0.01625}x(1+0.01625)-24 + 400x{(1-(1+0.01625)-4)/0.01625}x(1+0.01625)-28 + 2500x(1+0.01625)-32
= -14000 + 3074.11 + 3062.29 + 2871.07 + 3008.47 + 2375.25 + 1670.20 + 1304.93 + 978.75 + 1492.53
= 5837.60
To calculate IRR, we need to equate NPV to zero and identify the rate using Trial and Error method i.e.
0 = -14000 + 800x{(1-(1+IRR)-4)/IRR}x(1+IRR)-0 + 850x{(1-(1+IRR)-4)/IRR}x(1+IRR)-4 + 850x{(1-(1+IRR)-4)/IRR}x(1+IRR)-8 + 950x{(1-(1+IRR)-4)/IRR}x(1+IRR)-12 + 800x{(1-(1+IRR)-4)/IRR}x(1+IRR)-16 + 600x{(1-(1+IRR)-4)/IRR}x(1+IRR)-20 + 500x{(1-(1+IRR)-4)/IRR}x(1+IRR)-24 + 400x{(1-(1+IRR)-4)/IRR}x(1+IRR)-28 + 2500x(1+IRR)-32
Using Trial and Error Method in Excel,
IRR = 4.228%
Annual IRR =4 x 4.228 = 16.91%
Profitability Index = PV of Cash Flows/Initial Cost = 19837.60/14000 = 1.42
Clasical Payback = 4 + (14000-13800)/3200 = 4+0.0625 = 4.0625 years
Discounted Payaback = 4 + (14000-12016)/2375 = 4+ 1984/2375 = 4.835 years
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