Analytical Tools
•Marginal
•Discounted cash
flow
•Benefit-cost
•Supply-demand
Marginal Analysis
Resources are limited, therefore we want
the most “bang for our bucks” -- benefits
from resources allocated to a project
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
Marginal Analysis
• Economic efficiency
– Profit maximized where marginal cost =
marginal revenue (MC = MR)
Price (P)
ATC
Market equilibrium
exists when,
MC
MR = MC = ATC
P = MR
Quantity (Q)
No “pure profit”
(economic rent) to
attract new firms to
industry
Marginal Analysis
Price (P)
Pure profit = P1*Q1 - P2*Q1, or
ATC
= (P1 – P2) *Q1
MC
P1
P2
Assumes perfect
competition, i.e., P = MR
Quantity (Q)
Q2 Q1
Financial Maturity of Tree
Age Volume
b.f.
Tree value
given $/bf
Change Return on
in value investment
70
240
$120 @ $0.5
n.a.
n.a.
75
310
$186@$0.6
$66
80
360
$234@$0.65
$48
85
400
$260@0.65
$26
66/120 =
55%
48/310 =
15%
26/234 =
11%
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
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
Solve Compounding Multiplier
for i
Vn = V0 (1+i)n
Vn/ V0 = (1+i)n
(V
1/n = ((1+i)n)1/n = (1+i)n/n = 1+i
/
V
)
n
0
(Vn/ V0 )1/n – 1 = i
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
NPV and IRR
Time line of benefit and cost flows
$ Revenue (R2)
$ Revenue (R8)
C0
C1
C2
C3
C4
C5
C6
Cost in each year for 8 years plus “year zero”
All revenues and costs
discounted to year zero
C7
C8
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
NPV Using Summation Notation
n
NPV =
where,

(Rt – Ct)/(1+i)t
t=1
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)
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
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
Net Present Value (NPV) for a
Single Rotation
• NPV will include the initial cost of land and land
value at time n
n
t
NPV  
where,
t 0
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
N
(1 i)
t
Soil Expectation Value (SEV)
r
 ( R  C )1  i 
t
SEV 
r j
t
t 0
(1  i)  1
where,
r = rotation length
j = index on year” 0, 1, 2, . . . r
Rt = revenue in jth year
Ct = expenditure in jth year
r
Contract Rent
• Def. - actual
payments “tenants”
make for their use of
property owned by
someone else.
Rent
Housing services
Owner of house
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
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
P2
Economic Rent =
(P1 - P2) *Q1
Quantity
Q2 Q1
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
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.
Capital Budgeting Process
3. Measure cash (benefit)
flows from alternative
capital investment
opportunities
4. Evaluate proposals
using selected criteria
5. Select alternatives to
fund and implement
6. Review performance
for feed-back
Increase log inventory to reduce
risk of mill downtime during
Spring breakup?
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
Q1
Q
Q2
Graphic Solution Method
• 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
TR
$’s
TC
MC
1 unit Q
FC
P
1 unit Q
Break-even
point
Q
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)