Question
What is the internal rate of return on an investment that costs $80K initially, saves $15K/yr,...
What is the internal rate of return on an investment that costs $80K initially, saves $15K/yr, and has a salvage value of $10K at the end of 8 years? Please state your answer o the nearest tenth of a percent unless you are confident stating it to a greater level of recision. Hint: you may start at any interest rate, but 10% is recommended. (30 pts)
Answers
- IRR is the rate at which NPV = 0
- We can calculate it by hit and trial or by using excel's goal seek function or a financial calculator
- If we use 10% discount rate, our NPV is positive, calculated as follows:
Year CF Discount Factor Discounted CF 0 $ -80.00 1/(1+0.1)^0= 1 1*-80= $ -80.00 1 $ 15.00 1/(1+0.1)^1= 0.909090909 0.909090909090909*15= $ 13.64 1 $ 15.00 1/(1+0.1)^1= 0.909090909 0.909090909090909*15= $ 13.64 3 $ 15.00 1/(1+0.1)^3= 0.751314801 0.751314800901578*15= $ 11.27 4 $ 15.00 1/(1+0.1)^4= 0.683013455 0.683013455365071*15= $ 10.25 5 $ 15.00 1/(1+0.1)^5= 0.620921323 0.620921323059155*15= $ 9.31 6 $ 15.00 1/(1+0.1)^6= 0.56447393 0.564473930053777*15= $ 8.47 7 $ 15.00 1/(1+0.1)^7= 0.513158118 0.513158118230706*15= $ 7.70 8 $ 15.00 1/(1+0.1)^8= 0.46650738 0.466507380209733*15= $ 7.00 8 $ 10.00 1/(1+0.1)^8= 0.46650738 0.466507380209733*10= $ 4.67 NPV = Sum of all Discounted CF $ 5.93 - This means that the IRR should be greater than 10% because as we go on decreasing the discount rate, the NPV goes on decreasing.
- Randomly trying a higher discount rate, At 12% NPV is almost negligible, we can say it is 0
Year CF Discount Factor Discounted CF 0 $ -80.00 1/(1+0.12)^0= 1 1*-80= $ -80.00 1 $ 15.00 1/(1+0.12)^1= 0.892857143 0.892857142857143*15= $ 13.39 1 $ 15.00 1/(1+0.12)^1= 0.892857143 0.892857142857143*15= $ 13.39 3 $ 15.00 1/(1+0.12)^3= 0.711780248 0.711780247813411*15= $ 10.68 4 $ 15.00 1/(1+0.12)^4= 0.635518078 0.635518078404831*15= $ 9.53 5 $ 15.00 1/(1+0.12)^5= 0.567426856 0.567426855718599*15= $ 8.51 6 $ 15.00 1/(1+0.12)^6= 0.506631121 0.506631121177321*15= $ 7.60 7 $ 15.00 1/(1+0.12)^7= 0.452349215 0.452349215336893*15= $ 6.79 8 $ 15.00 1/(1+0.12)^8= 0.403883228 0.403883227979369*15= $ 6.06 8 $ 10.00 1/(1+0.12)^8= 0.403883228 0.403883227979369*10= $ 4.04 NPV = Sum of all Discounted CF $ -0.01 - So we can say IRR is 12%, however if we want greater precision and want to eliminate the tedious process of hit and trial, we use excel and arrive at an IRR of 11.9958% so if we round off to 2 decimal places, it would still be 12%
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