|
|
Best
if printed in landscape.
Capitalizing to determine
value of a long-term asset
An important
decision for a business manager is determining the price to pay for a
long-term asset such as a building or a tract of land. Similarly, a manager must be prepared to determine at what price to sell a long-term asset. In both situations, the fundamental question is "how does one determine the value of a long-term asset?"
General
Rule
The value of
an asset is the revenue it will generate for its owner. This revenue
includes the income received from the sale of the products produced by
the asset, plus the resale value when the asset is disposed of in the
future. However, the cost of operating the asset to produce the
products must be subtracted from the revenue.
- Example.
The current value of farmland reflects 1) the revenue that will be generated
in the future by selling the commodities produced on the land, 2) minus
the cost of producing those commodities, and 3) plus the land's future
selling price.
- For the purpose of this overview discussion, a long term asset means any asset or investment (whether tangible or intangible) that will generate revenue more than one year into the future.
Need
to Discount Future Earnings to Present Value
Because the revenue
from the asset will be received over time, future earnings must be discounted
to present value. Also, each future earnings or payment must
be estimated or calculated, if they are expected to vary over time, before
discounting them to present value.
- Example.
A investment is expected to return $100 one year from now, another
$112 two years from now, and soon thereafter be sold for $500. Assuming a discount rate of 5%, the present
value of the first payment is $95.24 (100/(1+.05)^1), the present value
of the second payment is $101.59 (112/(1+.05)^2), the present value of payment for selling the asset is $453.51 (500/(1+.05)^2), and the total present
value of this short-term investment is $650.34 (95.24 + 101.59 + 453.51). Accordingly, an investor who imposes a 5% discount rate on future income, would be willing to pay no more than $650.34 for this asset.
- A computer spreadsheet can help illustrate these calculations.
|
A |
B |
C |
D |
1 |
Present
value of several future payments |
2 |
Discount
rate (d) |
0.05 |
3 |
Time Periods Until Payment
|
|
|
|
4 |
1 |
Expected annual income |
$100 |
$95.24 |
5 |
2 |
Expected annual income |
$112 |
$101.59 |
6 |
2 |
Resale value |
$500 |
$453.51 |
7 |
Total
Present Value of Payments |
$650.34 |
- Cells
D2, A4, A5, A6, C4, C5 and C6 are used to input the values.
- Cell
D4 is the formula =C4/(1+D$2)^A4; cell D5 is the formula =C5/(1+D$2)^A5;
cell D6 is the formula =C6/(1+D$2)^A6; these cells provide the present value of each payment.
- Cell
D7 is the formula =sum(D4:D6); it provides the final answer.
- This spreadsheet
can readily be modified to accommodate different situations; for example,
additional rows can be inserted below row 7 if the investment will provide
more than two future payments (before being sold). Also, the time period can be expressed
to reflect portions of years; for example, 1.75 years would be the appropriate
time period if the payment will be received 21 months from now (21 months
/12 months).
- Be sure the
time period for the discount rate and the time periods until payment
are the same; for example, if the discount rate is expressed as an annual
rate, the time periods until payment will be the number of years, but
if the discount rate is expressed as a monthly rate, the time periods
until payment must be expressed as the number of months.
Role
of Assumptions
This analytical
process requires the analyst (often the business manager) to make numerous
assumptions or projections about future events, especially if the future
payments will result from a business that purchases inputs from which
a commodity is produced and marketed (such as farmland). In that
case, assumptions may include
- quantity of future
sales,
- price of future
sales (implies an assumption about the impact of inflation and demand
on the selling price),
- time of future
sales,
- type and quantity
of future inputs (implies an assumption about production technology),
- cost of future
inputs (implies an assumption about the impact of inflation on input
costs),
- time when future
inputs will be used, and
- a discount rate
(probably a nominal or market interest rate, that is, a real rate adjusted
for anticipated general rate of inflation).
Inflation
is mentioned three times in this list -- selling price, input costs and
discount rate. However, the inflation rate (or price changes) may
be different for each of these items; thus a manager may need to consider
each of these factors individually.
- If the manger wanted to assume that inflation will equally affect the three factors, present prices for production and inputs and a real interest rate could be used to complete the analysis. More on the distinction between real and nominal interest rate in another section.
Short-hand
Method to Calculate Long-term Asset Value
If the manager anticipates owning the asset for a long-time, such as a tract of land for 40 years, the resale value may not have much of an impact on the present value because the revenue is not expected to be received for such a long time. However, the annual revenue throughout that time will have a major impact on the value of the asset. Accordingly, a
short-hand method to calculate the value of a long-term asset is
V = R/d
where: V is value of the long-term asset, R
is annual earnings of long-term asset, and d
is a real discount rate.
Note that the resale value of this long term asset is not explicitly considered in the short-hand formula.
- Using a real
discount rate implies (assumes) that the annual earnings will change
by the general rate of inflation in the economy; this may or may not
be an accurate assumption.
- Example.
Annual earnings from the asset is expected to be $37 but will change
with inflation, and the real discount rate is 3.5%. The value
of this long-term asset would be $1,057.
|
A |
B |
1 |
Valuing
a Long Term Asset with Constant Income |
2 |
Annual Earnings
(R) |
$37 |
3 |
Discount rate
(d) |
0.035 |
4 |
Value
of long term asset (V) |
$1,057 |
- Cells
B1 and B2 are used to input values; cell B3 is the formula +B1/B2 and
provides the answer.
This
formula (V=R/d), however, assumes no changes in quantity of sales or production
technology. It also assumes that inflation will have an equal impact
on sale price, input costs, and interest rates. But, the world is
not that simple. The remainder of this page describes an expanded
methodology that relaxes some of the simplifying assumptions, but it does
not reduce the number of assumptions (some would suggest that it significantly
increases the number of assumptions). The expanded methodology also
increases the number of computations; fortunately computer programs (such
as a spreadsheet) can help with these calculations. The following
section suggests such a spreadsheet.
Expanded
Method to Calculate Long-term Asset Value
As stated above,
the value of a long-term asset is the present value of its
future earnings. In the case of an asset that will
be used in a business, revenue and operating expenses for each production
period need to be considered. Key considerations for farmland, for
example, include type and quantity of commodities that will be produced,
price or value of the commodities, type and quantity of inputs used, and
input costs.
- This
is the same information used in preparing an enterprise
analysis; thus the business owner who has prepared enterprise budgets
can rely on existing information when valuing land (rather than having
to gather all new information). The owner needs to be certain,
however, that the enterprise analyses are up-to-date.
- The purpose of
this analysis is to determine the value of the land resource.
Therefore in preparing the enterprise analysis, the owner should subtract
all costs except return to land; this would include subtracting an opportunity
cost for non-land inputs, such as the owner's unpaid labor, management,
and return to risk.
- Farmland
often is used to raise several crops; for example, rotating crops is
a common practice to reduce disease. An owner will need to prepare
several enterprise analyses if the land will be used to raise several
crops. This can be handled several ways, depending on how the
land will be operated (one crop each year or several crops each year)
and whether the analysis is calculating a per acre value or a value
for the entire tract.
- Portion
of land used to produce A, portion used to produce B and portion
used to produce C in any given year.
- Entire tract,
multiple crops each year, such as, crop A in year 1, crop B in year
2, crop C in year 3,a nd crop A in year 4, etc.
- Entire tract,
single crop but rotating annually; such as, crop A on 50% of the
land each year, crops B and C each on 25% of the land each year.
- The manager will need
to prepare an analysis for each year if conditions are expected to change,
such as which commodities will be produced, prices, costs, or technology
(which impacts the inputs that will be used). Such a large number
of predictions about the future tend to become guesses the further into
the future the analysis is extended At some point in the analysis,
the manager may stop trying to project all the details, but instead,
rely on simplifying assumptions. Simplifying the approach does
not reduce the number of assumptions; it just reduces how many of them
are explicitly considered.
- A computer helps
assess how changing assumptions can impact the projected asset value.
The
spreadsheet calculates the present value of the future earnings.
The spreadsheet does not eliminate or even reduce the number of assumptions
that need to be made; instead the spreadsheet facilitates making those
assumptions explicit.
- V
= sum of present value of E (future earnings); value equals total present
value of future earnings
- E
= earnings for each future period (TR-TC); earnings equals sum of total
revenue (including resale price) minus total explicit cost for each
period asset is owned
- TR
= total revenue equals quantity of output sold times the selling price
- TC
= total cost equals sum of quantity of each input times the cost of
each input
- Quantity of output
= projected sale of product for each period of ownership
- Price =projected
price for output sold each period of ownership
- Input quantity
= projected quantity of each input used in operating the asset and producing
the product
- C = projected cost
of each input used in operating the asset and producing the product
- The spreadsheet
uses enterprise budget/analysis as the basis of the calculations; that
is, E = TR - TC.
- inflation rate
for input cost, product price, and general inflation rate (this one
impacts the discount rate).
Value
does not Equal Cash Flow (Feasibility)
This procedure
does NOT assess the feasibility of purchasing farm land, for example.
Restated, the analysis described on this page does not assess whether
the land will generate enough cash inflow to pay all cash costs.
Additional analysis is necessary to answer that question.
Bottom
Line
A farm manager
may never go through all the complexities and details described on this
page. But what is important is for the manager to recognize that
all these assumptions are embedded in any discussion about the value of
land.
Last Updated
June 21, 2007
|