An oil company is drilling a series of new wells that are adjacent to an existin
ID: 2613056 • Letter: A
Question
An oil company is drilling a series of new wells that are adjacent to an existing oil field. About 20% of the new wells will be dry holes and will produce zero oil. If the wells do, in fact, strike oil, they have different expected values. Well 1 is expected to produce oil worth $3 million per year for 10 years, and Well 2 is expected to produce $2 million a year for 15 years. The wells will cost $10 million apiece to drill.
The Beta for a producing well is 0.7. The market risk premium is 7.5%, and the risk-free-rate is 3.6%. For simplicity assume there are no taxes and make further assumptions as necessary.
a. What is the correct discount rate for cash flows from the developed wells? The oil company executive proposes to add 20 percentage points to the discount rate to offset the risk of a dry hole. He calls this a “fudge factor.”
b. Calculate the NPV of each well with this adjusted discount rate.
c. What do you say the NPVs of the two wells are?
Explanation / Answer
Answer:a
Nominal Discount rate=Rf+Beta(MArket risk Premium)
=3.6%+0.7(7.5%)
=8.85%
Assume expected inflation is 4%.
Real Discount Rate=
(1+Real Discount Rate)=(1+ nominal discount rate)/(1+inflation rate)
(1+Real Discount Rate)=(1+8.85%)/(1+4%)
Real Discount Rate=(1.0885/1.04)-1
=4.66%
Answer:b Calculation of the NPV:
NPV1=-10 million+$3 million(PVIFA24.66%,10)
=-10 million+$3 million(3.607709)
=$823127.3521
NPV2=-10 million+$2 million(PVIFA24.66%,15)
=-10 million+$3 million(3.90652222)
=$1719566.68
Answer:c
Expected income from Well 1: [(0.2 *0) + (0.8 *3 million)] = $2.4 million
Expected income from Well 2: [(0.2 * 0) + (0.8 * 2 million)] = $1.6 million
Discounting at 4.66 percent gives:
NPV1=-10 million+$2.4 million(PVIFA4.66%,10)
=-10 million+$2.4 million(7.8508)
=$8841920
NPV2=-10 million+$1.6 million(PVIFA4.66%,15)
=-10 million+$1.6 million(10.62237)
=$6995792.