Question

In: Economics

  An upgrade to a compressor costs $30,000 and results in the following net revenues (income minus...

  An upgrade to a compressor costs $30,000 and results in the following net revenues (income minus expenses).

Year      Net Revenue

1             $13,000

2               12,000

3               10,500

4                9,000

5                8,200

       Determine the internal rate of return.

Solutions

Expert Solution

As per the information provided in the question the upgradation of computer cost is $30000,

so the cash flow in period 0 is -$30000

the net revenue are given below upto year 5

Years Cash flow PVF@20% PV of Cashflow PVF@25% PV of Cashflow
0 -30000 1 -30000 1 -30000
1 13000 0.8333 10832.9 0.8000 10400
2 12000 0.6944 8332.8 0.6400 7680
3 10500 0.5787 6076.35 0.5120 5376
4 9000 0.4823 4340.7 0.4096 3686.4
5 8200 0.4019 3295.58 0.3277 2687.14
NPV at 20%= 2878.33 NPV at 25%= -170.46

Internal Rate of return (IRR) is the interest at which the NPV=0, to estimate it we have followed trial and error method, first we have taken the PV factor = 20%, where the NPV =$2878.33, which is positive and then we have taken the PV factor = 25%, where the NPV = -$170.46, which is negative. So the Rate of return must fall in between 20% to 25%.

Therefore

R1 = 20%              NPV1=$2878.33

R2= 25%               NPV2= -$170.46

Using linear interpolation method of estimation of Internal Rate of Return (IRR)

IRR= R1 + (R2-R1)X[NPV1/(NPV1-NPV2)]

IRR = 20 + (25-20)[(2878.33)/ {2878.33-(-170.46)}]

IRR = 20 + (5)[(2878.33)/(2878.33+170.46)]

IRR = 20 + 5(2878.33/ 3048.79)

IRR = 20 + 5(0.944089)

IRR = 20 + 4.72

IRR = 24.72%

The internal rate of return (IRR) is 24.72%

Rahul Sunny answered 11 months ago
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