LECTURE 6 Quiz #6 If you are going to finance the purchase of a car, would you want the interest on your loan be compounded daily, monthly, quarterly, annually or continuously?

FV For The Compound Interest Case with unequal sums FV = (PV) 1 (1+i e ) t-1 + (PV) 2 (1+i e ) t-2 +…(PV) n (1+i e ) t-n A landowner receives annual royalty payments of $2,000, $2,200, $1,900, $2,500, $1,500 over the next five years. What is FV of these payments at an interest rate of 8%. FV = $2,000(1+.08) 4 +$2,200(1+.08) 3 +$1,900(1+.08) 2 + $2,500(1+.08) 1 +$1,500(1+.08) 0 FV = $11,908.50

Annuity Annuity – a series of equal periodic payments at regular intervals over a period of time while the interest is compounding. Examples: auto loans, mortgage payments, insurance premiums, installment loans, etc. PV = AV[((1+i e ) t – 1)) / i e (1+i e ) t ] where AV = amount of each equal future payment

Annuity Example #1 An oil company has to pay $10,000 per year, starting one year from today, on a five year loan at 8% interest. Calculate the PV of these five yearly payments. PV = $10,000 [ ((1+0.08) 5 – 1) /.08(1+0.08) 5 ] = $10,000 (3.9927) PV= $39,927

Annuity Example #2 Calculate the Future Value of the annuity given in the previous example. FV = AV[((1+i e ) t – 1)) / i e (1+i e ) t ] (1+i e ) t or; FV = AV((1+i e ) t – 1)) / i e FV = $10,000 [ ((1+.08) 5 –1) / 0.08] FV = $58,666 = $39,927(1+i e ) t

Annuity Example #3 You borrow $20,000 from the bank at 8% and agree to pay off the loan through a series of five equal year-end payments beginning one year from today. What will your yearly payments be? AV = PV [ (i e (1+i e ) t ) /( (1+i e ) t – 1))] AV = $20,000 [ (0.08(1+0.08) 5 ) / ((1+0.08) 5 – 1)] AV = $20,000 ( ) = $5,010 per year

Loan Amortization Loan Amortization = Paying off a debt Example: an oil company borrows $100,000 at 8% for 3 years. Payments will be quarterly with the first 3 months from today. Calculate the quarterly payment amount. AV = $100,000 [ (i n /4(1+ i n /4) t x 4 ) / ((1+ i n /4) t x 4 – 1)] = $100,000 ( ) = $9,456 per quarter

Homework #2 Using annual yearend discounting, calculate the Present Value [PV] for the following future cashflow stream for 5%, 10%, 15% and 50% discount interest rates. Show the resulting Cumulative discounted value for each rate. YearFVPV(5)PV(10)PV(15)PV(50) 1 $2,500,000 2 $2,250,000 3 $2,025,000 4 $1,822,500 5 $1,640,250 6 $1,476,225 7 $1,328,603 8 $1,195,742 9 $1,076, $968,551 Cumulative $16,283,039

FORECASTING Tings we must know or estimate when evaluating a producing property are: - Present producing rate- Future producing rate - Ultimate recovery- Product prices - Operating costs- Capital costs - Ownership Interests- Taxes The development of forecasts of future oil and gas production form wells is an engineering responsibility. It is an essential part of any economic evaluation. IT IS FROUGHT WITH UNCERTAINTY AND RISK, WHILE HUGE SUMS OF MONEY ARE INVESTED BASED ON FORECAST RESULTS