Transcript Economic Concepts Related To Appraisals

Economic Concepts Related to
Appraisals
Time Value of Money
• The basic idea is that a dollar today is worth
more than a dollar tomorrow
• Why?
– Consumption
– Risk (uncertainty)
– Investment
– Inflation
– Other?
Present Value
• Present value (PV) is the value today of a sum
of money to be received in the future
• This can be the value of an amount at one
time period in the future or it can be the value
of a stream of payments into the future
• The PV is determined by discounting, the
future value is ‘discounted’ to the present
• The interest rate used is sometimes referred
to as the discount rate
Present Value, cont.
• Lump sum
• PV = Future value/ (1 + i)n = FV*1/(1+i)n
where:
– i = the interest or discount rate
– n = the time period
• PV of $8,000 in 10 years at a 4% discount rate
– PV = $8000* 1 / (1 + .04)10 = $8000 * .6756 =
$5,405
Present Value, cont.
• PV of an annuity or series of payments over
time is:
– PV = Payment * (1-(1 + i)-n / i )
• Tables have been developed to use for either
the present value factor for a lump sum or a
series of payments. Excel is very useful
• If we assume an infinite number of years and
equal payments the PV formula reduces to:
– PV = Pmt/i
Present Value of a $100 Annuity
$5,500
$5,250
$5,000
$4,750
$4,500
$4,250
$4,000
$3,750
$3,500
$3,250
$3,000
$2,750
$2,500
$2,250
$2,000
$1,750
$1,500
$1,250
$1,000
$750
$500
$250
$0
$5,000
$2,500
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
146
151
156
161
166
171
176
181
186
191
196
201
$1,667
Number of Years
2%
4%
6%
Impact of Changing Income on Present Value
$8,000
$7,000
$6,000
$5,000
$4,000
$3,000
$2,000
$1,000
$0
10
20
30
40
50
$50
75
100
110 120 130 150
Number of Years
$100
$200
160
170
180
$300
190
200
250
Example 1
• What is the present value of an annuity of
$150 for:
– 25 years at 4%
• $150 * 15.62208 = $2,343
– 25 years at 2%
• $150 * 19.52346 = $2,929
– 22 years at 6%
• $150 * 12.04158 = $1,806
Example 2
• What is the present value of $150 at 6% in
perpetuity?
– $150/.06 = $2,500
• What is the payment used if the present value
is $5,064 and the interest rate is 4%
– $5,064 = X/.04 = $5,064 * .04 = X X = $203
Example 3
• You want to know what will have the lowest
cost to control erosion, building a dam or
changing tillage practices and using cover
crops. The discount rate is 4%
– Dam costs $5,000 to build, $5 a year to maintain
and in 25 years there will need to be major repairs
for $1,000. Expected life is 75 years
– Cover crop will be $135 a year.
Present value Example 3
• Dam
• Maintenance
$5,000
• $5 * (1-(1+i)-n)/I = 5*23.68041
$ 118
• Rebuild
• $1,000 * 1 / (1+i)
n
= 1000*.3751
• Cover Crop
• $135 * 23.68041 =
$ 375
$5,493
$3,197
Example 4
• What is the value of an orchard if the initial
cost of the trees is $1,000 and there is a $60
expense in year 2, $30 expenses in years 3, 4,
and 5 and then there is income of $125 for the
next 50 years? Use a 6% discount rate.
• Expenses $1,000
– $60 * .8900 = $53
– $30 * .8396 + 30*.7921 + 30*.7473 =
– 25 + 24 + 22 = $71
• PV of expenses $1000 + $53 + $71 = $1,124
Example 4 Cont
• Income
– PV $125 for 50 years at 6%
–$125 * 15.76186 = $1,970
• PV of orchard
$1,970 - $1,124 - $527 = $319
Future Value
• The future value is the amount of money to be
received at some point in the future or it is the
amount a present value will grow to when
invested at a given interest rate.
• The present value is discounted but the future
value is compounded.
• Compounding and discounting are the
opposite of each other
Future Value, cont.
• FV = PV * (1 + i)n where the variables are the
same as before
• FV of an annuity;
– FV = PMT * ((1 + i)n – 1) / i
• Rule of 72; if you divide 72 by the interest
rate you get the approximate time it takes an
investment to double
FV
$
FV
$
?
?
PV
PMT
PMT
PMT
PMT
$
$
Time
$
$
Time
Future Value
$
$
$
FV
$
PV
?
PV
PMT
PMT
?
$
$
Time
Time
PRESENT VALUE
PMT PMT
$
$
Example 1
• Land is worth $1,500 today. You expect that it
will increase in value by 3% a year. What will
be the value of the land in 15 years?
• $1,500 * 1.5580 = $2,337
Example 2
• Assume we had a farm that sold for $500, 000
seven years ago. What would we have to sell
it for today to earn 6% on the investment?
• FV of $500,000 today earning 6% for 7 years
– $500,000 * 1.5036 = $751,800
Example 3
• You think you’ll need $30,000 for your child to
go to college in 8 years. You deposit $4000 a
year into an 5% savings account. How much
will you have when they start school?
• $4,000 * 9.5491 = $38,196
• How much should you have saved to just have
$30,000?
– $30,000 / 9.5491 = $3,142
Investment Analysis
• Investment analysis or capital budgeting is
used to determine profitability and/or
compare alternatives
• Investment analysis requires knowing:
 Initial costs
 Actual total expenditure not just down payment or list
price
Investment Analysis, cont.
Need to know continued
 Net cash flow for each time period over the life
of the investment
 Only cash revenues and expenses; DO NOT include
depreciation or any financing charges
 Terminal value (salvage value);
 For land estimate of the market value when investment
is terminated or if assumed to be held indefinitely the
terminal value can be ignored
Investment Analysis, cont.
4. Discount rate
Opportunity cost of capital, cost of
borrowing, weighted average,
Risk premium especially when comparing
alternatives with different risks
Other adjustments to remember when
considering a discount rate include; tax
differences and inflation
Increasing discount rate lowers value of
investment
Net Present Value
• Preferred method of evaluation
– Also called discounted cash flow method
• NPV is the sum of the present values for each
year’s net cash flow minus the initial cost of
the investment
• NPV = P1/(1+i) + P2/(1+i)2 + … + Pn/(1+i)n – C
• Calculations in Excel or from Present Value
factor tables
Net Present Value, cont
•
•
•
•
NPV > 0 accept
NPV < 0 reject
NPV = 0 indifferent
NPV > 0 means rate of return higher than the
discount rate; C could be higher and investor
could still receive the discount rate
• Discount rate is critical
Internal Rate of Return
• Internal rate of return (IRR) is another
technique used to compare investments
• IRR is the discount rate that makes the NPV
just equal 0
• 0 = (.)-C C = (.) so that the IRR is the i to
make C = 0
• IRR > cost of capital is profitable, some people
only invest if IRR is greater than a certain level
• Hard to calculate; doesn’t account for size;
assumes same rate possible every period
Financial Feasibility
• IRR and NPV don’t consider the financing
except through the discount rate
• It is important to think about financing when
considering an investment
• Financing can affect the cash flows, especially
in the early years; some cases with negative
cash flows may not even be possible
• Something can be profitable but not feasible
because of the cash flow associated with
financing
Example 1
• Which would you prefer, an investment A that
returns $3,000 a year for 5 years or
investment B that returns
– Year 1
– Year 2
– Year 3
– Year 4
– Year 5
$1,000
$2,000
$3,000
$4,000
$6,000
• Both Cost $10,000 and use a 6% discount rate
Example 1 cont
• Investment A
– $3,000 *
.9434 =
$2,830
– $3,000 *
.8900 =
$2,670
– $3,000 *
.8396 =
$2,519
– $3,000 *
.7921 =
$2,376
– $3,000 *
.7473 =
$2,242
–Total
$12,637
–Less cost
$10,000
NET PRESENT VALUE $ 2,637
• Investment B
– $1,000 *
.9434 =
$943
– $2,000 *
.8900 = $1,780
– $3,000 *
.8396 = $2,519
– $4,000 *
.7921 = $3,168
– $6,000*
.7473 = $4,484
–Total
$12,894
–Less costs
$10,000
– NPV
$ 2,894
• Investment A
• Investment B
NPV $2,637
NPV $2,894
• Both earn more than 6%
• Could afford to pay more for either
investment
• What if there had been a terminal or salvage
value
Other thoughts
• Discount rate;
– Inflation adjustments
• Adjust if some costs and/or revenues will move
differently over time; Otherwise NPV will be the same
• Inflation premium should be ADDED to the real
discount rate to obtain the adjusted rate
– Risk adjustments
• Adjust for risk if there is a difference in the perceived
risks of the investment
• Risk premium so you add to the real discount rate
because you need a higher rate of return
Other Economic Considerations with Land
• There is an intrinsic value to land; people just
want to own it especially a particular parcel of
land
• There is a social value to land; land is the basis for
many societies and for the wealth of a society;
How we treat the land says who we are
• Why people own land is not always as an
investment; legacy; security, retirement
• Don’t own land to make money but own land to
own it