Study Guide Chapter1 12-13

1
Study GuideChapter1 12-13

• Agricultural Economics 330
• Instructor David J. Leatham

2
Question 1
The following graph shows the financing gaps and
surpluses per acre of land. Based on this
graph, what is the approximate financing gap in
the 5th year?
Answer Financing Gap in the 5th year is about
10 per acre
3
Question 2

• When choosing a discount rate, what is the lower
  bound (the lowest acceptable discount rate)?
• The discount rate must be at least as high as the
  cost of capital. Thus the cost of capital forms
  a lower bound. If the discount rate was set any
  lower, investments would be taken that would not
  recover the cost of capital.

4
Question 3

• The lowest marginal tax rate for most farm and
  ranch firms is at least 30.3. Explain why.
• There are two primary taxes Federal Income Tax
  and Self-employment tax. The lowest marginal tax
  rate for federal income taxes is 15 and the
  lowest marginal tax for self-employment taxes is
  15.3. Combined, the marginal tax rate is 30.3

5
Question 4

• Give an example of a mutually exclusive
  investment.
• A farmer has decided on putting in an irrigation
  system. The farmer can use hand set, wheel line,
  flood, or center pivot irrigation. The choice of
  the irrigation system is mutually exclusive
  because the farmer can only choose one system out
  of the four alternatives.

6
Question 5

• Calculate the present value of the after-tax net
  returns to land in the 7th year if the real
  pre-tax net returns to land today are 100, real
  net returns to land are assumed to increase by 4
  each year, the inflation rate is 5, the marginal
  tax rate is 30, and the pretax risk adjusted
  discount rate is 10. Show all your work.

7
Question 5 Answer
Fn F0 (1g)n
greal growth rate 4
n7 F7 100 (1.04)7 131.59
Continued
8
Question 5 Answer Continued
After-tax, risk adjusted discount rate .1(1-.3)
0.07 ot 7
PV(after-tax net return in 7th year 129.62
(1.07)-7 80.72
9
Investment Description
Aggieland Farms is located in the Texas
Blacklands between near Canton, Texas. The
owner, Mr. Agirich has an opportunity to purchase
a 100 acre tract of land nearby that can be
managed as hay meadow. The price of the meadow
land is 800 per acre. Coastal Bermuda and
Crimson Clover grass has already been established
on the land. The grass can be cut three times a
year, May, June and August. Each March the
meadow will be aerated, sprayed for weeds, and
fertilized with 100 pounds of fertilizer. After
the first and second cutting, the meadow will be
aerated and fertilized again. After the last
cutting, the meadow will just be fertilized. The
meadow is expected to produce four tons of hay
(27 square bales/ton) per acre per year. A
neighbor has agreed to buy each bale produced for
three dollars a bale. Aggieland Farms has
equipment for spraying, cutting and stacking the
hay. The farm needs another baler. Operating
receipts are projected to be 324 per acre and
the operating expenses are expected to be 236
per acre. Mr. Agirich plans to sell the land in
three years for 840. Mr. Agririch requires at
least a 8 pre-tax, risk-free return on capital
and a 4 risk premium on land investments.
Without the land purchase, Aggieland Farms net
income is projected to be 55,000 and would pay
4,400 in income and self-employment taxes.
However, Aggieland Farms would have to pay 0.30
in taxes per 1 of additional taxable income.
10
Investment Description
Mr. Agirich has calculated the after-tax cash
flows as follows
11
Question 6

• Calculate the average tax rate for Aggieland
  Farms if the meadow land is not purchased.
• Answer
• Average tax rate (4,400/55,000)
• 8

12
Question 7

• What is the marginal tax rate for Aggieland
  Farms.
• Answer
• 30

13
Question 8

• Calculate the Net Present Value for the meadow
  land investment.

14
Discount RateAfter-tax risk-adjusted rate

• r rbt PREM (1-m)
• r after-tax, risk-adjusted discount rate
• rbt before-tax, risk-free discount rate
• PREM risk premium -- adjustment for risk
• m marginal tax rate
• r .08 .04 (1-.30)
• r 0.12 (1-.30)
• r .084 or 8.4

15
Calculate NPV
NPV -C0 NR(1-m)USPVr,N mD USPVr,N TVat
(1r)-N
NPV -800 61.6USPV8.4,3 0 828
(10.084)-3
NPV -800 157.61 0 650.04 7.65
NPV 7.65 per acre NPV 765 for the 100 acres
16
Question 9

• Calculate the maximum bid price per acre of
  meadow land.

17
Maximum Bid Price
NPV 0 -C PV (after-tax net
returns) TV-(TV-C)m (1r)-N
NPV 0 -C 157.61 840-(840-C).30
(1.084)-3
C 810
Maximum Bid Price of land is 810 per acre
18
Question 10

• Suppose Aggieland Farms wants to borrow 700 per
  acre and the local AGROCASH Bank will lend him
  the money to purchase the 100 acres. The
  AGROCASH Bank will make a 15-year equal principal
  loan (15 uniform principal payments) at 10.5
  with interest calculated using the remaining
  balance method.
• A. Suppose Mr. Agirich decides to borrow the
  money from AGROCASH. Calculate the net cash
  flows after debt for this meadow land investment.
  

19
Annual Principal Payment 700/15 46.67
20
Financial Feasibility
21
Question 10

• Suppose Aggieland Farms wants to borrow 700 per
  acre and the local AGROCASH Bank will lend him
  the money to purchase the 100 acres. The
  AGROCASH Bank will make a 15-year equal principal
  loan (15 uniform principal payments) at 10.5
  with interest calculated using the remaining
  balance method.
• B. How much is the financing gap (or surplus) in
  the second year?
• Answer 33.09

22
Question 10

• Suppose Aggieland Farms wants to borrow 700 per
  acre and the local AGROCASH Bank will lend him
  the money to purchase the 100 acres. The
  AGROCASH Bank will make a 15-year equal principal
  loan (15 uniform principal payments) at 10.5
  with interest calculated using the remaining
  balance method.
• C. Suppose Mr. Agirich plans to keep the land
  for over 15 years. Suppose also that the
  AGROCASH Bank will provide the loan described
  above but the payments must be paid quarterly.
  Calculate the annual percentage rate (APR) and
  the effective interest rate.

23
APR and Effective Rate

• If there are no noninterest costs, and the
  remaining balance method of computing interest is
  used, the contractual rate equal to the APR.
• APR 10.5
• Effective Interest Rate
• ie 1(0.105/4)4 -1
• 10.92

24
Question 11

• Suppose that Mr. Agirich made a mistake when
  calculating the after-tax net returns. Suppose
  that the real operating receipts of 324 per acre
  and the real operating expenses of 236 per acre
  are projected to increase by 2 each year.
  Moreover, inflation is expected to be 3.
  Calculate the present value of the after-tax net
  returns over the three year life of the land
  investment.

25
Calculate CashFlows

• First, calculate real net returns
• Second, calculate nominal net returns

26
Calculate Real Net Returns

• Fn F0 (1g)n
• greal growth rate
• n1
• F1 88 (1.02)1 89.76
• n2
• F2 88 (1.02)2 91.56
• n3
• F3 88 (1.02)3 93.39

27
Calculate Nominal Net Returns
28
PV(After-tax Net Returns) 64.72(1.084)-1
67.0(1.084)-2 71.43(1.084)-3
PV 59.70 61.81 56.07 176.95
29
Question 12

• Aggieland Farms needs another baler for 3 years.
  Mr. Agirich can buy a John Deere standard square
  baler for 20,000 and has calculated the net
  present value to be -6,282. Mr. Agirich can
  also lease the baler. The financial lease is a 3
  year lease with annual lease payments of 3,300
  paid at the beginning of each year. The lease
  payment is tax deductible but is claimed at the
  end of the year instead of at the beginning of
  the year when the lease payment is made. The
  leased baler is the same as the baler that would
  be purchased and must be operated and maintained
  the same. Assume that the discount rate is the
  same as the discount rate used in evaluating the
  land investment. Also assume that Mr. Agirich
  expects inflation to be 3.

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Question 12.A

• Calculate the real after-tax, risk-adjusted
  discount rate.
• Answer

r 5.24
31
Question 12.B

• Calculate the real annuity equivalent for the
  purchased baler

-6,282 A e USPV5.24,3
A e -2,317
32
Question 12.C

• Calculate the real annuity equivalent for the
  leased baler.

33
Lease Payments

• Before Tax Payments
• 3,300
• Tax Savings
• 3,300 .3 990
• Lease Payments after-tax
• 3,300-990 2,310 or
• 3,300(1-.3) 2,310

34
Calculate Net Present Value
NPV -3,300 -2310 USPV8.4,2 990 (10.084)-3
NPV -3,300 - 4,096.9 777.23 -6,619.7
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Annuity Equivalent for Leasing New Tractor
0
1
2
3
r 5.24
A
A
A
-6,619.7
V0 A USPVr,N Present Value of an Uniform
Annuity
-6,619.7 Ae USPV5.24, 3
Ae -2,441.7
5.24
-6,619.7
Ae
3
0
i
PV
PMT
FV
N
36
Question 12.D

• Should Mr. Agirich buy or lease the baler?
• Answer
• Buy
• Ae(buy) -2,317
• Ae(lease -2,441

37
Question 12.E

• The local Production Credit Association (PCA) has
  agreed to lend Mr. Agirich 15,000 if he buys the
  baler. The PCA will make a 5-year loan fully
  amortized at 10 with annual payments. A 150
  loan fee and stock purchase is required. The
  borrower stock requirement is the lesser of
  1,000 or 2 of loan principal. Money will be
  borrowed to cover the loan fee and stock
  requirement.
• Calculate the actuarial, annual percentage (APR)
  and effective interest rates.

38
P L F 15,000 150 15,459.18
(1-s) (1-.02)
S .02(15,459.18) 309.18
L 15,459,18 - 309.18 - 150 15,000
39
PCA
Loan Payment (A) 15,459.18AUSPV10,3 A-6,216.3
7
40
Calculate Actuarial Rate (Yield)
Use Calculator
3
0
1
2
r ?
-6,216.37
- 6,216.37
- 6,216.37
15,000
309.18
15,000 6,216.36 USPVr,3 - 309.18 (1r)-3
41
Calculate APR Effective Rate

• Calculate APR
• APR 0.1086 1 0.1086 or 10.86
• Calculate Effective Rate
• ie 10.1086 -1
• 0.1086 or 10.86

42
Question 13

• Suppose Mr. Agirich is interested in buying a
  tract of farm land and wants to know how much he
  can pay for it and still be a good investment.
  Assume that Mr. Agirich requires at least a 10
  pre-tax, risk-free return on capital, assigns a
  3 risk premium on land investments, has a 30
  marginal tax rate and expects inflation to be 5.
  Calculate the maximum bid price per acre of land
  if Mr. Agirich plans on selling the land for
  3,000 (nominal dollars) in 10 years, and the
  present value of the after-tax net returns is
  798.65. Show all your work.

43
Question 10 Answer
After-tax risk adjusted discount rate .1
.03(1-.3) 0.091 or 9.1
NPV 0 -C PV (after-tax net
returns) TV-(TV-C)m (1r)-N
NPV 0 -C 798.65 3,000-(3,000-C).30
(1.091)-10
C 1,918.5
Maximum Bid Price of land is 1,918.5 per acre
44
Question 14

• Calculate the real annuity equivalent on an
  investment given that the net present value is
  20,000, the life of the investment is 15 years,
  the pre-tax, risk adjusted required rate of
  return is 12, the marginal tax rate is 40, the
  expected inflation rate is 5, and the loan is
  fully amortized at 8 over 10 years. Show all
  your work.

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Question 14 Answer
Discount rate 0.12(1-.4) .072 or 7.2
Real Discount Rate (r)
20,000 Ae USPV2.095, 15
Real Annuity Equivalent Ae 1,576.6
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Question 15
A manager has decided to buy a farm widget. Two
alternative financing methods are available
(A) use a financial lease or (B) purchase the
widget using owner financing and borrowed
capital. The financial lease is a 3 year lease
with annual lease payments of 6,000 paid at the
beginning of each year (a lease payment is tax
deductible assume it can be claimed at the
beginning of each year). The manager can buy
the widget for 20,000 and sell it again in 4
years for 4,000. The IRS will allow the widget
to be depreciated over 10 years. The marginal
tax rate is 30. The manager requires at least
a 14 pre-tax return on capital. Assume the
inflation rate is 0, and the annual operating
returns and costs are the same for leasing and
buying. Should the manager buy or lease?
47
Lease Widget
48
NR(1-m) -6,000(1-.30) -4,200
D0
mD0
TVat 0
49
r 0.14(1-.3) 0.098 or 9.8
NPV -4,200 -4,200 USPV9.8,2
NPV - 4,200 - 7,309 -11,508
50
Annuity Equivalent for Leasing Widget
0
3
1
2
r 9.8
A
A
A
-11,508
V0 A USPVr,N Present Value of an Uniform
Annuity
-11,508 Ae USPV9.8, 3
i
N
PV
FV
PMT
9.8
0
3
-11,508
Ae
Ae -4,612
51
Buy Widget
52
NR(1-m) 0
D20,000/10 2,000
mD2,000(.3) 600
TVat 4,000 - 4,000 -(20,000 - 8,000).3
6,400
53
NPV -20,000 600 USPV9.8,4 6,400(1.098)-4
NPV -20,000 1,910 4,403 -13,687
54
Annuity Equivalent for the Used Tractor
0
4
1
2
...
r 9.8
A
A
A
-13,687
V0 A USPVr,N Present Value of an Uniform
Annuity
-13,687 Ae USPV9.8, 4
i
N
PV
FV
PMT
9.8
0
4
-13,687
Ae
Ae -4,299
55
Widget NPV Annuity Equivalent Buy -13,687
-4,299 Lease -11,508 -4,611
Choose to buy the Widget
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Investment Description
Aggieland Farms is located in the between
Plantersville and Magnolia, Texas. The owner,
Mr. Agirich has an opportunity to purchase an
additional 114 acres, with 38 acres planted in
fruit trees, 10 acres cleared for camping and
parking, and 66 acres that can be cleared for
ranching or orchards. His son Bubba has just
graduated from AM and would like to purchase the
land and start a pick-your-own fruit operation.
He plans to call the business PICK-EM FRESH.
The orchard (broadly defined) includes
strawberries, blackberries, nectarines, plums,
Asian pears and figs. Bubba believes that he
should be able to sell most of the fruit produced
because there are many people who prefer picking
their own fruit rather than buying it at a
store. Mr. Agirich can buy the 114 acres for
300,000. Workers are needed for planting,
pruning, thinning and spraying. The only
machinery needed is a tractor and sprayer.
Operating receipts from the sell of fruit are
projected to be 70,000 per year and the
operating expenses from the production and
marketing of fruit are expected to be 30,000 per
year. Mr. Agirich plans to sell the land in
three years for 360,000. Mr. Agririch can buy
the tractor and sprayer for 45,000 and sell it
for 40,000 in three years. The tractor and
sprayer can be depreciated for tax purposes over
seven years. Mr. Agrich expects the operating
cost of running the tractor and sprayer to be
2,000 per year. Mr. Agririch requires at least
a 8 pre-tax, risk-free return on capital and a
7 risk premium on this type of investments.
Without the land purchase, Aggieland Farms net
income is projected to be 75,000 and would pay
5,000 in income and self-employment taxes.
However, Aggieland Farms will have to pay 0.30
in taxes per 1 of additional taxable income.
57
Investment Description
Mr. Agirich has calculated the nominal after-tax
cash flows as follows
58
Question 16

• Calculate the average tax rate for Aggieland
  Farms if the PICK-EM FRESH investment is not
  purchased.
• Answer
• Average tax rate (5,000/75,000)
• 6.67

59
Question 17

• What is the marginal tax rate for Aggieland
  Farms.
• Answer
• 30

60
Question 18

• Calculate the Net Present Value for the PICK-EM
  FRESH investment.

61
Discount RateAfter-tax risk-adjusted rate

• r rbt PREM (1-m)
• r after-tax, risk-adjusted discount rate
• rbt before-tax, risk-free discount rate
• PREM risk premium -- adjustment for risk
• m marginal tax rate
• r .08 .07 (1-.30)
• r 0.15 (1-.30)
• r .10.5 or 10.5

62
Calculate NPV
NPV -C0 NR(1-m)USPVr,N mD USPVr,N TVat
(1r)-N -C0 NR(1-m)USPVr,N mD
USPVr,N TVat (1r)-N
NPV -300k 28kUSPV10.5,3 0 342k
(10.105)-3 -45k - 1.4kUSPV10.5,3
1,929USPV10.5,3 35,714 (10.105)-3
NPV -300k69,023.46253,477.42
-45k -3,451.174754.1726,470.07
5,273.94
63
Question 19

• Calculate the maximum bid price for the 114-acres
  of land.

64
Maximum Bid Price
NPV 0 -CL PV (after-tax net returns to
land) TVL-(TVL-CL)m (1r)-N -CM PV
(after-tax net returns to Machinery) PV (Tax
Savings Depreciation) TVM-(TVM-CM)m (1r)-N
NPV 0 -CL 69,023 360k-(360k-CL).30
(1.105)-3 -45k-3,4514,75426,470
Maximum Bid Price of land is 306,762
65
Question 20.A

• Suppose Aggieland Farms wants to borrow 280,000
  and the local AGROCASH Bank will lend him the
  money to invest in the PICK-EM FRESH business
  opportunity. The AGROCASH Bank will make a
  15-year fully amortized loan at 12 (annual
  payments) with interest calculated using the
  remaining balance method. Inflation is expected
  to be 3.
• A. Suppose Mr. Agirich decides to borrow the
  money from AGROCASH. Calculate the net cash
  flows after debt for this PICK-EM FRESH
  investment.

66
280kAUSPV12,15 A41,110.79
67
Financial Feasibility
68
Question 20.B

• Suppose Aggieland Farms wants to borrow 280,000
  and the local AGROCASH Bank will lend him the
  money to invest in the PICK-EM FRESH business
  opportunity. The AGROCASH Bank will make a
  15-year fully amortized loan at 12 (annual
  payments) with interest calculated using the
  remaining balance method. Inflation is expected
  to be 3.
• B. How much is the financing gap in the second
  year?
• Answer 2,772.18

69
Question 20.C

• Suppose Aggieland Farms wants to borrow 280,000
  and the local AGROCASH Bank will lend him the
  money to invest in the PICK-EM FRESH business
  opportunity. The AGROCASH Bank will make a
  15-year fully amortized loan at 12 (annual
  payments) with interest calculated using the
  remaining balance method. Inflation is expected
  to be 3.
• C. Suppose Mr. Agirich plans to keep the PICK-EM
  FRESH business indefinitely. Suppose also that
  the AGROCASH Bank will provide the loan described
  above. Also suppose PEACHTREE Bank will lend
  Mr. Agirich 270,000 at 11.25 but the payments
  must be paid monthly.

70
Problem 20.C.1

• 5.C.1 Determine which bank offers the least cost
  loan.
• If there are no noninterest costs, and the
  remaining balance method of computing interest is
  used, the contractual rate equal to the APR.

71
Problem 20.C.1 continued

• PEACHTREE Bank
• APR 11.25
• Effective Interest Rate
• ie 1(0.1125/12)12 -1 11.85
• 11.85
• AGROCASH Bank
• APR 12
• Effective Interest Rate
• ie 1(0.12) -1 12
• PEACHTREE Bank has the Least Cost

72
Problem 20.C.2

• 5.C.2 Also discuss other factors that Mr.
  Agirich should consider when deciding which loan
  he should take.
• Liquidity
• Downpayment is lower with AGROCASH Bank.
• Monthly payments are required with PEACHTREE
  Bank. More difficult to make payments in months
  of cash deficits which are inherent in orchard
  loans.
• Does Mr. Agirich have a long-term banking
  relationship with one of the banks he wants to
  maintain.

73
Question 21

• Suppose that Mr. Agirich made a mistake when
  calculating the after-tax net returns to the
  land. Suppose that the real operating receipts
  of 70,000 and the real operating expenses of
  30,000 are projected to increase by 5 each
  year. Moreover, inflation is expected to be 3.

74
Question 21.A

• 6.A. Calculate the present value of the after-tax
  net returns to land over the three-year life of
  the investment.
• First, calculate real net returns
• Second, calculate nominal net returns

75
Calculate Real Net Returns

• Fn F0 (1g)n
• greal growth rate
• n1
• F1 40k (1.05)1 42k
• n2
• F2 40 (1.05)2 44.1k
• n3
• F3 40 (1.05)3 46.31k

76
Calculate Nominal Net Returns
77
PV(After-tax Net Returns) 30.28(1.105)-1
32.75(1. 105)-2 35.42(1. 105)-3
PV 27.40326.82226.252 80.477k or 80,477
78
Question 21.B

• B. By how much was the NPV understated before
  correcting for this mistake?
• Answer
• 80,477-69,02311,454

79
Question 22

• Suppose that Mr. Agirich is considering leasing a
  tractor and sprayer instead of purchasing it.
  Mr. Agirich has talked with the local John Deere
  dealership and the dealership has agreed to lease
  Mr. Agirich a tractor and sprayer. The financial
  lease is a 3 year lease with annual lease
  payments of 10,000 paid at the beginning of each
  year. The lease payment is tax deductible but is
  claimed at the end of the year instead of at the
  beginning of the year when the lease payment is
  made. The leased tractor and sprayer are the
  same as the tractor and sprayer that would be
  purchased and must be operated and maintained the
  same. Cashflows common with the purchase and
  lease arrangement were omitted. Assume that the
  discount rate is the same as the discount rate
  used in evaluating the PICK-EM FRESH investment.
  Also assume that Mr. Agirich expects inflation to
  be 3.

80
Question 22.A

• Calculate the real after-tax, risk-adjusted
  discount rate.
• Answer

r 7.28
81
Question 22.B

• 7.B Calculate the real annuity equivalent for
  the purchased tractor and sprayer.
• From question 3
• NPV -45,000-3,451475426,470 -17,227

-17,227 A e USPV7.28,3
A e -6,598
82
Question 22.C

• 7.C Calculate the real annuity equivalent for
  the leased tractor and sprayer.

83
Lease Payments

• Before Tax Payments
• 10,000
• Tax Savings
• 10,000 .3 3,000
• Lease Payment after tax deduction
• 10,000-3,000 7,000 or
• 10,000(1-.3) 7,000

84
Calculate Net Present Value
NPV -10,000 -7,000 USPV10.5,2 3,000
(10.105)-3
NPV -10,000 - 12,068 2,223 -19,844
85
Annuity Equivalent for Leasing New Tractor
0
1
2
3
r 7.28
A
A
A
-19,844
V0 A USPVr,N Present Value of an Uniform
Annuity
-19,844 Ae USPV7.28, 3
Ae -7,600
7.28
-19,844
Ae
3
0
i
PV
PMT
FV
N
86
Question 22.D

• Should Mr. Agirich buy or lease the tractor and
  sprayer?
• Answer
• Buy
• Ae(buy) -6,598
• Ae(lease -7,600

87
Question 23

• 8. List and discuss the characteristics of
  farmland and the special factors affecting the
  value of land.

88
Question 23 --Answer

• Characteristics of Farm Land
• Durable and Immobile
• Legal Restriction on use
• Special taxation
• Low ownership turnover --2-3 a year

89
Question 23 continued

• Characteristics of Farm Land
• Value influenced by special factors
• Excess machinery capacity
• Close proximity to existing operations
• Nonmonetary factors love of farming, rural
  lifestyle
• Proximity to urban growth
• Environmental Concerns
• Recreational Value
• Mineral, Oil, and Resource Rights