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)

Profit

Slope of TR curve is MR

Slope of TC curve is MC

Marginal Analysis

• Economic efficiency– Profit maximized where marginal cost =

marginal revenue (MC = MR)

MCATC

Price (P)

P = MR

Quantity (Q)

Market equilibrium exists when,

MR = MC = ATC

No “pure profit” (economic rent) to attract new firms to industry

Marginal Analysis

P1

MCATC

Quantity (Q)

Price (P)

P2

Q1Q2

Pure profit = P1*Q1 - P2*Q1, or

= (P1 – P2) *Q1

Assumes perfect competition, i.e., P = MR

Financial Maturity of Tree

Age Volume b.f.

Tree value given $/bf

Change in value

Return on investment

70 240 $120 @ $0.5 n.a. n.a.

75 310 $186@$0.6 $66 66/120 = 55%

80 360 $234@$0.65 $48 48/310 = 15%

85 400 $260@0.65 $26 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

(Vn/ V0 )1/n = ((1+i)n)1/n = (1+i)n/n = 1+i

(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 IRRTime line of benefit and cost flows

Cost in each year for 8 years plus “year zero”

C0 C1 C2 C3 C4 C5 C6 C7 C8

$ Revenue (R2) $ Revenue (R8)

All revenues and costs discounted to year zero

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

NPV = (Rt – Ct)/(1+i)tt=1

n

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)

Internal Rate of Return Using Summation Notation

NPV = (Rt – Ct)/(1+i)tt=1

n

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

where,Nt = net cash flow in period t (Rt - Ct)Rt = revenue in year tCt = expenditure year tn = number of years involvedi = discount rate

n

t 0t

t

i)(1

NNPV

1)1(

1)(SEV 0

r

r

t

jrtt

i

iCR

Soil Expectation Value (SEV)

where,r = rotation lengthj = index on year” 0, 1, 2, . . . rRt = revenue in jth yearCt = expenditure in jth year

Contract Rent

• Def. - actual payments “tenants” make for their use of property owned by someone else.

Owner of house

Housing services

Rent

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

P1

MCATC

Price (P)

P2

Q2

Economic Rent =

(P1 - P2) *Q1

Q1

Quantity

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)

TR

TC

Q

$’s

Profit

Q1 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

TC

FC

Break-even point

MC

P

1 unit Q

1 unit Q Q

$’s

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)