Question

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Problem 4-28 Valuing a business Permian Partners (PP) produces from aging oil fields in west Texas. Production is 1.82 million barrels per year in 2018, but production is declining at 9% per year for the foreseeable future. Costs of production, transportation, and administration add up to $25.20 per barrel. The average oil price was $65.20 per barrel in 2018. PP has 7.2 million shares outstanding. The cost of capital is 11%. All of PP's net income is distributed as dividends. For simplicity, assume that the company will stay in business forever and that costs per barrel are constant at $25.20. Also, ignore taxes. a. Assume that oil prices are expected to fall to $60.20 per barrel in 2019, $55.20 per barrel in 2020, and $50.20 per barrel in 2021. After 2021, assume a long-term trend of oil-price increases at 7% per year. What is the ending 2018 value of one PP share? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Share value 2016 b-1. What is PP's EPS/P ratio? (Do not round intermediate calculations. Round your answer to 4 decimal places.) EPS/Prat b-2. Is it equal to the 11% cost of capital? Yes O No

Answer 1

Formula	Time period (n)		1	2	3
	Year	2018	2019	2020	2021	Perpetuity
Pn = Pn*(1-9%)	Production (P)	1,820,000	1,656,200	1,507,142	1,371,499	1,248,064
Pb Year 4 = Year 3 Pb*(1+7%)	Price per barrel (Pb)	65.2	60.2	55.2	50.2	53.71
	Cost per barrel (Cb)	25.2	25.2	25.2	25.2	25.2
P*Pb	Revenue ('R)	118,664,000	99,703,240	83,194,238	68,849,261	67,033,533
P*Cb	Total cost ('C)	45,864,000	41,736,240	37,979,978	34,561,780	31,451,220
R-C	Net income (NI)	72,800,000	57,967,000	45,214,260	34,287,481	35,582,313
[(1+7%)*(1-9%)]-1	Growth rate of revenue after 2021 (g1)					-2.63%
R perpetuity/(c-g1) where c = 11%	Horizon value of Revenue in 2022 (HVr)					491,808,753
Since production is decreasing at 9% p.a. and cost per barrel is constant, annual cost per barrel will also decrease @ -9%	Growth rate of cost after 2021 (g2)					-9%
Total cost perpetuity/(c-g2) where c = 11%	Horizon value of Total Cost in 2022 (HVtc)					157,256,101
HVr - HVtc	Horizon value net income (HVni)					334,552,652
NI + HVni	Total cash flows (TCF)		57,967,000	45,214,260	34,287,481	334,552,652
1/(1+11%)^n	Discount factor @ 11%		0.901	0.812	0.731	0.659
TCF*Discount factor	PV of TCF		52,222,523	36,696,908	25,070,710	220,380,195
Sum of all PVs	Total present value (TPV)	334,370,335
	Shares O/S (s)	7,200,000
TPV/s	Price per share (Ps)	46.44
a). Share value (at the end of 2018) = $46.99
b-1). EPS/P ratio:
EPS in 2018 = net income/shares outstanding = 72,800,000/7,200,000 = 10.11
EPS/P = 10.11/46.99 = 0.215 (or 21.5%)
b-2). No, it is not equal to the cost of capital.
Note: The only point of note in this question is the calculation of horizon value. Revenues and costs in perpetuity have to be calculated separately since both have different perpetual growth rates