Analytical Tools

1. Analytical Tools Marginal Discounted cash flow Benefit-cost Supply-demand

2. Marginal Analysis Resources are limited, therefore we want the most “bang for our bucks” -- benefits from resources allocated to a project

3. Marginal Analysis • Economic efficiency • Maximize “profit”, i.e. total revenue - total costs (TR - TC) Slope of TR curve is MR Profit Slope of TC curve is MC

4. Marginal Analysis • Economic efficiency • Profit maximized where marginal cost = marginal revenue (MC = MR) Price (P) Market equilibrium exists when, MR = MC = ATC MC ATC P = MR No “pure profit” (economic rent) to attract new firms to industry Quantity (Q)

5. Marginal Analysis Price (P) Pure profit = P1*Q1 - P2*Q1, or = (P1 – P2) *Q1 MC ATC P1 Assumes perfect competition, i.e., P = MR P2 Quantity (Q) Q2 Q1

6. Financial Maturity of Tree

7. Financial Maturity of Tree • Compare return on investment with return from other 5-year investments • If alternative is 10% ROI then don’t cut yet • If alternative is > 20%, cut at age 80 • Why not compare with prevailing interest rate? • Need to compute annual compound rate of interest

8. Estimating Annual Compound Rate of Interest Use compounding multiplier, Vn = V0 (1+i)n, where, Vn = value n years in future V0 = value in year 0 (current time) n = number of years ahead i = annual compound rate of interest

9. Solve Compounding Multiplier for i Vn = V0 (1+i)n Vn/ V0 =(1+i)n (Vn/ V0 )1/n = ((1+i)n)1/n = (1+i)n/n = 1+i (Vn/ V0 )1/n – 1 = i

10. Analytical Tools • Discounted cash flow • Net present value • Discount or compound all cash flows to same point in time • Calculate using an assumed interest rate • Internal rate of return • Interest rate (i) that makes NPV zero, i.e. equates PV of all costs and all benefits • “Calculate” the interest rate

11. NPV and IRR Time line of benefit and cost flows $ Revenue (R2) $ Revenue (R8) C0 C1 C2 C3 C4 C5 C6 C7 C8 Cost in each year for 8 years plus “year zero” All revenues and costs discounted to year zero

12. Formula for NPV for a given interest rate ( i ) NPV0 = - C0 - C1/(1+i)1 - C2/(1+i)2 - C3/(1+i)3 - . . . . - C8/(1+i)8 + R2/(1+i)2 + R8/(1+i)8 Simplify by netting R’s and C’s for given year • C0 - C1/(1+i)1 +(R2 -C2)/(1+i)2 - C3/(1+i)3 . . . . • + (R8 - C8)/(1+i)8

13. NPV Using Summation Notation n  NPV = (Rt – Ct)/(1+i)t t=1 where, NPV = unknown n = number of years Rt = revenue (income) in year t Ct = cost (expense) in year t t = index number for years i = discount rate (alternative rate of return)

14. Internal Rate of Return Using Summation Notation n  NPV = (Rt – Ct)/(1+i)t t=1 where, NPV = 0 Rt = revenue (income) in year t Ct = expense (cost) in year t t = index number for years i = unknown

15. Soil Expectation Value (SEV) • Financial criteria used to make even-aged timber management decisions. • Simply the present value of a perpetual series of even-aged rotations • Also known as Faustman formula

16. Net Present Value (NPV) for a Single Rotation • NPV will include the initial cost of land and land value at time n where, Nt = net cash flow in period t (Rt - Ct) Rt = revenue in year t Ct = expenditure year t n = number of years involved i = discount rate

17. Soil Expectation Value (SEV) where, r = rotation length j = index on year” 0, 1, 2, . . . r Rt = revenue in jth year Ct = expenditure in jth year

18. Contract Rent • Def. - actual payments “tenants” make for their use of property owned by someone else. Rent Housing services Owner of house

19. Economic rent • Surplus of income from selling a good or service above minimum supply price it takes to bring a factor into production, i.e. pure profit • $100 in the example

20. Economic rent Surplus of income above the minimum supply price it takes to bring a factor into production, can also be thought of as pure profit Price (P) MC ATC P1 Economic Rent = (P1 - P2) *Q1 P2 Quantity Q2 Q1

21. Land Rent • Economic rent when land is the factor of production analyzed • Surplus of income from selling product of land above minimum supply price for land

22. Capital Budgeting Process 1. Determine total investment capital requirements for the alternative investment opportunities 2. Assess organizations ability to generate investment capital for capital budgeting period Buy tree bailing machine or shearing machine? Use break-even analysis to determine how many trees need to be processed before machine is more cost-effective than hand bailing.

23. Capital Budgeting Process 3. Measure cash (benefit) flows from alternative capital investment opportunities 4. Evaluate proposals using selected criteria • Select alternatives to fund and implement • Review performance for feed-back Increase log inventory to reduce risk of mill downtime during Spring breakup?

24. Break-Even Analysis • Study of interrelationships among a firm’s sales, costs, and operating profit at various levels of output • Break-even point is the Q where TR = TC (Q1 to Q2 on graph) $’s TC TR Profit Q Q1 Q2

25. Graphic Solution Method TR • Draw a line through origin with a slope of P (product price) to represent TR function • Draw a line that intersects vertical axis at level of fixed cost and has a slope of MC • Intersection of TC and TR is break-even point $’s TC MC 1 unit Q FC P Q 1 unit Q Break-even point

26. Algebraic Solution • Equate total revenue and total cost functions and solve for Q TR = P x Q TC = FC + (VC x Q) TR = TC P x QB = FC + VC x QB (P x QB) – (VC x QB) = FC QB (P – VC) = FC QB = FC/(P – VC)