Question

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)

Answer 1

• 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%