The Ewert Exploration Company is considering two mutually exclusive plans for ex

Question

The Ewert Exploration Company is considering two mutually exclusive plans for extracting oil on property for which it has mineral rights. Both plans call for the expenditure of $9.5 million to drill development wells. Under Plan A, all the oil will be extracted in 1 year, producing a cash flow at t = 1 of $10.5 million; under Plan B, cash flows will be $1.4 million per year for 20 years.

Identify each project's IRR. Round your answers to two decimal places.

Indicate the crossover rate. Round your answer to two decimal places.
%

Explanation / Answer

IRR is the rate at which NPV = 0

NPV is calculated by discounting the cashflows

PV = C/(1+r)^n

C - Cashflow

r - Discount rate

n - years to the cashflow

Project A:

NPV = -9.5 + 10.5/(1+r)^1 = 0

r = 10.52%

Project B:

NPV = -9.5 + 1.4/(1+r)^1 + 1.4/(1+r)^2 + 1.4/(1+r)^3 + 1.4/(1+r)^4 + 1.4/(1+r)^5 + 1.4/(1+r)^6 + 1.4/(1+r)^7 + 1.4/(1+r)^8+  1.4/(1+r)^9 + 1.4/(1+r)^10 + 1.4/(1+r)^11 + 1.4/(1+r)^12 + 1.4/(1+r)^13 + 1.4/(1+r)^14 + 1.4/(1+r)^15 + 1.4/(1+r)^16 + 1.4/(1+r)^17 + 1.4/(1+r)^18 + 1.4/(1+r)^19 + 1.4/(1+r)^20 = 0

r = 13.58%

Cross over rate is where NPV A = NPV B

NPV A - NPV B = 0

0 = [-9.5 + 10.5/(1+r)^1] - [-9.5 + 1.4/(1+r)^1 + 1.4/(1+r)^2 + 1.4/(1+r)^3 + 1.4/(1+r)^4 + 1.4/(1+r)^5 + 1.4/(1+r)^6 + 1.4/(1+r)^7 + 1.4/(1+r)^8+  1.4/(1+r)^9 + 1.4/(1+r)^10 + 1.4/(1+r)^11 + 1.4/(1+r)^12 + 1.4/(1+r)^13 + 1.4/(1+r)^14 + 1.4/(1+r)^15 + 1.4/(1+r)^16 + 1.4/(1+r)^17 + 1.4/(1+r)^18 + 1.4/(1+r)^19 + 1.4/(1+r)^20]

r = 14.14%

Crossover rate = 14.14%

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