Analytical Tools

1
Analytical Tools

• Marginal analysis
• Discounted cash flow

2
Computer software well use

• Excel Spreadsheets

3
Marginal Analysis

• Resources are limited, therefore we want the
  most bang for our bucks -- benefits from
  resources allocated to a project

4
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
5
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)
6
Marginal Analysis
Price (P)
Pure profit P1Q1 - P2Q1, or
(P1 P2) Q1
MC
ATC
P1
Assumes perfect competition, i.e., P MR
P2
Quantity (Q)
Q1
Q2
7
Advantage of Marginal Analysis

• Dont have to do a complete analysis of costs and
  revenues
• Can estimate MC directly from market price by
  assuming a given profit percentage
• Can estimate MR from market price and knowledge
  of market structure, i.e. perfectly competitive,
  monopolistic, or somewhere in-between.

8
Applications of Marginal Analysis

• Financial maturity of individual tree
• Minimum size tree to harvest
• Break-even analysis

9
Biological Maturity
Output (volume)
Inflection point
Biological maturity
10
Biological vs. Financial Maturity

• Financial maturity is based on benefit from
  letting tree/stand grow for another time period
  compared to cost for doing so.
• Would you expect biological and financial
  maturity to occur at the same point in time?

11
Financial Maturity of Tree
12
Financial Maturity of Tree

• Compare return on investment with return from
  other 5-year investments
• If rate of return on the alternative is 10 then
  dont cut yet
• If rate of return on the alternative is gt 20,
  then cut at age 80
• More practical to compare with prevailing annual
  compound rates of interest?
• How can we compute annual compound rate of
  interest for changes in value over a 5-year
  period?

13
Estimating Annual Compound Rate of Interest

• Use basic compounding multiplier,
• Vn V0 (1i)n, where,
• Vn value n years in future
• V0 value in year 0 (current time)
• n number of years
• i annual compound rate of interest

14
Before solving for I lets review how compounding
and discounting multipliers are used
15
Example of use of compounding multiplier

• Buy 100 worth of stock today
• If it increases in value at a rate of 18 each
  year, what will it be worth in 5 years?
• V5 ?, V0 100, i 0.18, n 5
• V5 100 (1.18)5 100 x 2.29 229

16
Example of use of discounting multiplier

• Solve compounding multiplier for V0 by dividing
  both sides by (1i)n
• Vn V0 (1i)n
• V0 Vn /(1i)n Vn 1/ (1i)n

17
Solve Compounding Multiplier for i

• Vn V0 (1i)n
• Vn/ V0 (1i)n
• (Vn/ V0 )1/n ((1i)n)1/n (1i)n/n 1i
• (Vn/ V0 )1/n 1 i

18
Calculate compound rate of interest for 5 year
value increments

• Age 70 to 75
• i (186/120)1/5 1 (1.55)0.2 1 1.09 1
  0.09
• Age 75 to 80
• i (234/186)1/5 1 (1.26)0.2 1 1.05 1
  0.05
• Age 80 to 85
• i (260/234)1/5 1 (1.11)0.2 1 1.02 1
  0.02

19
When should we cut?
20
When should we cut?

• Depends on what rate of return the owner is
  willing to accept.
• We refer to this rate as the owners guiding rate
  or, alternative rate of return.
• Rate is based on owners alternative uses for the
  capital tied-up in the trees.

21
When should we cut?

• If owners alternative rate of return is
• 10 - cut at age 70
• 7 - cut at age 75
• 5 - cut at age 75
• 1 - let grow to age 85

22
How does an owner select her alternative rate of
return?

• Borrowing rate if she would have to borrow
  money if tree wasnt get, she could use the
  interest rate she would have to pay on the loan,
  i.e. the borrowing rate
• Lending rate if owner could lend the revenue
  from cutting the tree now to someone else, she
  could use the rate she would get by making the
  loan

23
Minimum Size Tree to Cut

• Logger buys cutting rights on 200 acre tract
  of pine pulpwood for lump sum amount of 40,000.
  Landowner placed no limits on what logger can
  cut. Logger wants to cut to maximize net revenue
  (profit). Should he give cutting crew a minimum
  size tree to cut? Answer with marginal approach.

24
Calculate Marginal Cost
25
Compare MC and MB

• If price per cord received by logger is 30, then
  shouldnt cut any tree less than about 7 inches.
• If price per cord increases to 35, then cut down
  to 5 inches.
• If price per cord decreases to 25, then cut down
  to about 9 inches

26
Minimum diameter (q) for lump sum payment for
stumpage
s
TR
TC
Stumpage cost
Fixed cost
q
Declining cutting diameter
27
Pay as cut contract

• Would minimum diameter change if logger paid for
  stumpage as trees were cut (log scale) instead of
  for lump sum amount in advance?
• Yes, stumpage now a variable cost, not a fixed
  cost

28
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

29
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
30
Formula for NPV for a given interest rate ( i )
NPV0 - C0 - C1/(1i)1 - C2/(1i)2 - C3/(1i)3
- . . . . - C8/(1i)8 R2/(1i)2 R8/(1i)8
Simplify by netting Rs and Cs for given year

• C0 - C1/(1i)1 (R2 -C2)/(1i)2 - C3/(1i)3 . .
  . .
• (R8 - C8)/(1i)8

31
NPV Using Summation Notation
n
?
NPV (Rt Ct)/(1i)t
t0
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)
32
Internal Rate of Return Using Summation Notation
n
?
NPV (Rt Ct)/(1i)t
t1
where, NPV 0 Rt revenue (income) in year
t Ct expense (cost) in year t t index
number for years i unknown
33
Finding Internal Rate of Return

• Calculate NPV using spreadsheet
• Make i a variable referenced to one cell
• Change i in that cell until NPV equals
  approximately zero