Study Guide Chapter1 12-13 Agricultural Economics 330 Instructor: David J. Leatham

Study GuideChapter1 12-13

Agricultural Economics 330

Instructor: David J. Leatham

0102030405060708090

1 3 5 7 9 11 13 15

Year

$

Net Returns

Loan Payment

Question 1The 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 inthe 5th year isabout $10 per acre

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.

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%

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.

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.

n=7 F*7 = 100 (1+.04)7 = 131.59

g=real growth rate = 4%

F*n = F*

0 (1+g)n

Question 5Answer

Continued

PeriodReal

Net ReturnsNominal

Net ReturnsAfter-tax

Nominal NR

“n”F*

n Fn = F*n (1+If)n Fn (1-m)

7 131.59 F1 = 131.59(1+.05)7

= 185.16

185.16(1-.3) =129.62

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

Question 5 Answer Continued

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.


Mr. Agirich has calculated the after-tax cash flows as follows:

Component: 0 1 2 3Cost ($800.00)After-tax Net Returns

$0.00 $61.60 $61.60 $61.60

Tax Savings:Depreciation

$0.00 $0.00 $0.00 $0.00

After-taxTerminalValue

$0.00 $0.00 $0.00 $828.00

Net CashFlow from Investment

($800.00) $61.60 $61.60 $889.60

Question 6

Calculate the average tax rate for Aggieland Farms if the meadow land is not purchased.

AnswerAverage tax rate = (4,400/55,000)8%

Question 7

What is the marginal tax rate for Aggieland Farms.

Answer30%

Question 8

Calculate the Net Present Value for the meadow land investment.

04/18/23 Agricultural Finance 14

Discount Rate:After-tax risk-adjusted rate

r = [ rbt + PREM ] (1-m)r = after-tax, risk-adjusted discount raterbt = before-tax, risk-free discount ratePREM = risk premium -- adjustment for riskm = marginal tax rate

r = [.08 + .04 ] (1-.30)r = 0.12 (1-.30)r = .084 or 8.4%

Calculate NPV

NPV = -800 + 61.6[USPV8.4%,3] + 0 + 828 (1+0.084)-3

NPV = -800 +157.61 +0 + 650.04 = 7.65

NPV = -C0 +NR(1-m)[USPVr,N] +mD [USPVr,N] + TVat (1+r)-N

NPV = $ 7.65 per acreNPV = $765 for the 100 acres

Question 9

Calculate the maximum bid price per acre of meadow land.

Maximum Bid Price

C = $810

NPV = 0 = -C + PV (after-tax net returns)+[TV-(TV-C)m] (1+r)-N

NPV = 0 = -C + 157.61+[840-(840-C).30] (1+.084)-3

Maximum Bid Price of land is $810 per acre

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.

Annual Principal Payment = 700/15 = 46.67

Loan Amortization ScheduleEqual Principal Payment

Interest Beginning Interest Principal Total Loan TaxRate Period Principal Payment Payment Payment Balance Savings(1) (2) (3) (4)=(1)*(3) (5) (6)=(4)+(5) (7)=(3)-(5) (8)=(4)*tax

0 $700.0010.50% 1 $700.00 $73.50 $46.67 $120.17 $653.33 $22.0510.50% 2 $653.33 $68.60 $46.67 $115.27 $606.67 $20.5810.50% 3 $606.67 $63.70 $46.67 $110.37 $560.00 $19.11

Financial Feasibility

Component: 0 1 2 3

Cash Flow frominvestment

-800 61.60 61.60 889.60

Loan Amount 700.00

Loan Payment -120.17 -115.27 -110.37

Tax Savings fromInterest

22.05 20.58 19.11

Balloon Payment of Loan Principal

0.00 0.00 -560.00

Net Cash Flowsafter debt flows

-100.00 -36.52 -33.09 238.34

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

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.

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%

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.

Calculate CashFlows

First, calculate real net returnsSecond, calculate nominal net returns


Calculate Real Net Returns

F*n = F*

0 (1+g)n

g=real growth rate

n=1 F*

1 = 88 (1+.02)1 = 89.76

n=2 F*

2 = 88 (1+.02)2 = 91.56

n=3 F*

3 = 88 (1+.02)3 = 93.39


PeriodReal

Net ReturnsNominal


Nominal NR

“n”F*

n Fn = F*n (1+If)n Fn (1-m)

1 89.76 F1 = 89.76(1+.03)1

= 92.45

92.45 (1-.30) =64.72

2 91.56 F2= 91.56(1+.03)2

= 97.14

97.14(1-.30) =67.00

3 93.39 F3 = 93.39(1+.03)3

=102.05

102.05 (1-.30)=

71.43

Calculate Nominal Net Returns


PeriodComponent 0 1 2 3 PVCost

NR(1-m) 64.72 67.00 71.43

mD

TV(at)

NCF NPV

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

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%.

Question 12.A

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

Answer

r*.

..

1 0 084

1 031 0 0524

r* = 5.24%

Question 12.B

Calculate the real annuity equivalent for the purchased baler

-6,282 = A* e [USPV5.24,3]

A* e = $-2,317

Question 12.C

Calculate the real annuity equivalent for the leased baler.

Lease Payments

Before Tax Payments $3,300

Tax Savings 3,300 * .3 = 990

Lease Payments after-tax3,300-990 =2,310 or3,300(1-.3) = 2,310


NPV = -3,300 -2310 [USPV8.4%,2] + 990 (1+0.084)-3

NPV = -3,300 - 4,096.9 + 777.23 = -6,619.7


NR(1-m) -3,300 -2,310 -2,310 +990 -6,619.7

mD

TV(at)

NCF -6,619.7

Calculate Net Present Value


V0 = A [USPVr,N] Present Value of an Uniform Annuity

-6,619.7= Ae [USPV5.24%, 3]

0 3

-6,619.7

r = 5.24 %1 2

A A A

Annuity Equivalent for Leasing New Tractor

Ae = -2,441.7

i% PV PMT FV

5.24 -6,619.7 Ae3 0

N

Question 12.D

Should Mr. Agirich buy or lease the baler?

AnswerBuy

Ae(buy) = -2,317

Ae(lease = -2,441

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.


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


PeriodComponent 0 1 2 3

Principal 15,459.18

Payment -6,216.37 -6,216.37 -6,216.37

Fee -150

Stock -309.18 309.18

NCF 15,000.00 -6,216.37 -6,216.37 -5,907.19

Loan Payment (A)15,459.18=A[USPV10%,3]A=-6,216.37

PCA


0

15,000

r = ? %1 3

-6,216.37 - 6,216.37

309.18

Calculate Actuarial Rate (Yield)

15,000 = 6,216.36 [USPVr,3] - 309.18 (1+r)-3

Use Calculator

r = 10.86%

i% PV PMT FV

? 15,000 -6,216.373 309.18

N

2

- 6,216.37


Calculate APR & Effective Rate

Calculate APRAPR = 0.1086* 1 = 0.1086 or 10.86%

Calculate Effective Rate ie = [1+0.1086] -1 =0.1086 or 10.86%

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.

C = 1,918.5

NPV = 0 = -C + PV (after-tax net returns)+[TV-(TV-C)m] (1+r)-N

NPV = 0 = -C + 798.65+[3,000-(3,000-C).30] (1+.091)-10

Maximum Bid Price of land is $1,918.5 per acre

Question 10Answer After-tax risk adjusted discount

rate = [.1 + .03](1-.3) = 0.091 or 9.1%

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.

Discount rate = 0.12(1-.4) = .072 or 7.2%

Real Discount Rate (r*)

r* .

..

1 072

1 051 0 02095

20,000 = Ae* [USPV2.095%, 15]

Real Annuity Equivalent = Ae* = 1,576.6

Question 14Answer

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 yearlease 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?

Question 15

Lease Widget


NR(1-m) -4,200 -4,200 -4,200

mD

TV(at)

NCF NPV

D=0

NR(1-m)= -6,000(1-.30) = -4,200

TVat = 0

mD=0

r = 0.14(1-.3) = 0.098 or 9.8%

NPV = - 4,200 - 7,309 = -11,508


NR(1-m) -4,200 -4,200 -4,200 -7,309

mD

TV(at)

NCF -11,508

NPV = -4,200 + -4,200 [USPV9.8%,2]


-11,508= Ae [USPV9.8%, 3]

3 9.8 -11,508 Ae0 Ae = -4,612

N i PV PMT FV

0 3

-11,508

r = 9.8 %1 2

A A A

Annuity Equivalent for Leasing Widget

Buy Widget

PeriodComponent 0 1 2… 4 PVCost -20,000

NR(1-m)

mD 600 600 600

TV(at) 6,400

NCF NPV

D=20,000/10 = 2,000

NR(1-m)= 0

TVat = 4,000 - [4,000 -(20,000 - 8,000)].3 = 6,400

mD=2,000(.3) = 600

NPV = -20,000 + 600 [USPV9.8%,4]+6,400(1+.098)-4

NPV = -20,000 + 1,910 + 4,403= -13,687

PeriodComponent 0 1 2… 4 PVCost -20,000 -20,000

NR(1-m)

mD 600 600 600 1,910

TV(at) 6,400 4,403

NCF -13,687


-13,687 = Ae [USPV9.8%, 4]

4 9.8 -13,687 Ae0 Ae = -4,299

N i PV PMT FV

0 4

-13,687

r = 9.8 %1 2

...A A A

Annuity Equivalent for the Used Tractor

Widget NPV Annuity Equivalent

Buy -13,687 -4,299Lease -11,508 -4,611

Choose to buy the Widget


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 A&M 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.

Investment DescriptionMr. Agirich has calculated the nominal after-tax cash flows as follows:

Component: 0 1 2 3

Cost (Land) ($300,000)

Cost (Machinery) (45,000)After-tax Net Returns (Land) $28,000 $28,000 $28,000After-tax Net Returns (Machinery) ($1,400) ($1,400) ($1,400)Tax Savings: Depreciation $1,929 $1,929 $1,929After-tax TerminalValue (Land) $342,000After-tax TerminalValue (Machinery) $35,714Net Cash Flow fromInvestment ($345,000) $28,529 $28,529 $406,243

Question 16

Calculate the average tax rate for Aggieland Farms if the PICK-EM FRESH investment is not purchased.

AnswerAverage tax rate = (5,000/75,000)6.67%

Question 17

What is the marginal tax rate for Aggieland Farms.

Answer30%

Question 18

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


Discount Rate:After-tax risk-adjusted rate

r = [ rbt + PREM ] (1-m)r = after-tax, risk-adjusted discount raterbt = before-tax, risk-free discount ratePREM = risk premium -- adjustment for riskm = marginal tax rate

r = [.08 + .07 ] (1-.30)r = 0.15 (1-.30)r = .10.5 or 10.5%

Calculate NPV

NPV = -300k + 28k[USPV10.5%,3] + 0 + 342k (1+0.105)-3

-45k - 1.4k[USPV10.5%,3] + 1,929[USPV10.5%,3] + 35,714 (1+0.105)-3

NPV = -300k+69,023.46+253,477.42 -45k -3,451.17+4754.17+26,470.07

= 5,273.94

NPV = -C0 +NR(1-m)[USPVr,N] +mD [USPVr,N] + TVat (1+r)-N

-C0 +NR(1-m)[USPVr,N] +mD [USPVr,N] + TVat (1+r)-N

Question 19

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

Maximum Bid Price

NPV = 0 = -CL + PV (after-tax net returns to land)+[TVL-(TVL-CL)m] (1+r)-N

-CM + PV (after-tax net returns to Machinery)+PV (Tax Savings: Depreciation)+[TVM-(TVM-CM)m] (1+r)-N

NPV = 0 = -CL + 69,023+[360k-(360k-CL).30] (1+.105)-3

-45k-3,451+4,754+26,470

Maximum Bid Price of land is $306,762

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.

280k=A[USPV12%,15]

A=41,110.79

Loan Amortization Schedule

Interest Beginning Total Interest Principal Loan TaxRate Period Principal Payment Payment Payment Balance Savings(1) (2) (3) (4) (5)=(1)*(3) (6)=(4)-(5) (7)=(3)-(6) (8)=(5)*tax

0 $280,000.0012.00% 1 $280,000.00 $41,110.79 $33,600.00 $7,510.79 $272,489.21 $10,080.00

12.00% 2 $272,489.21 $41,110.79 $32,698.71 $8,412.08 $264,077.13 $9,809.61

12.00% 3 $264,077.13 $41,110.79 $31,689.26 $9,421.53 $254,655.60 $9,506.7812.00% 4 $0.00 $0.00 $0.00 $0.00 $0.00 $0.0012.00% 5 $0.00 $0.00 $0.00 $0.00 $0.00 $0.0012.00% 6 $0.00 $0.00 $0.00 $0.00 $0.00 $0.0012.00% 7 $0.00 $0.00 $0.00 $0.00 $0.00 $0.0012.00% 8 $0.00 $0.00 $0.00 $0.00 $0.00 $0.0012.00% 9 $0.00 $0.00 $0.00 $0.00 $0.00 $0.0012.00% 10 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

Financial Feasibility

Component: 0 1 2 3

Cash Flow from investment -345000.00 28529.00 28529.00 406243.00

Loan Amount 280000.00

Loan Payment -41110.79 -41110.79 -41110.79

Tax Savings from Interest 10080.00 9809.61 9506.78

Balloon Payment of Loan Principal 0.00 0.00 -254655.60

Net Cash Flows after debt flows -65000.00 -2501.79 -2772.18 119983.39

Question 20.B


B. How much is the financing gap in the second year? Answer: $2,772.18

Question 20.C


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.

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.

Problem 20.C.1 continued

PEACHTREE BankAPR = 11.25%Effective Interest Rate

ie = [1+(0.1125/12)]12 -1 = 11.85%=11.85%

AGROCASH BankAPR = 12%

Effective Interest Rate ie = [1+(0.12)] -1 = 12%

PEACHTREE Bank has the Least Cost

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.

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%.

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 returnsSecond, calculate nominal net returns


Calculate Real Net Returns

F*n = F*

0 (1+g)n

g=real growth rate

n=1 F*

1 = 40k (1+.05)1 = 42k

n=2 F*

2 = 40 (1+.05)2 = 44.1k

n=3 F*

3 = 40 (1+.05)3 = 46.31k


PeriodReal

Net ReturnsNominal


Nominal NR

“n” F*n Fn = F*

n (1+If)n Fn (1-m)

1 42 F1 = 42(1+.03)1

= 43.26

43.26 (1-.30) =30.28

2 44.1 F2= 44.1(1+.03)2

= 46.79

46.79(1-.30) =32.75

3 46.31 F3 = 46.31(1+.03)3

=50.60

50.6 (1-.30) =35.42

Calculate Nominal Net Returns



NR(1-m) 30.28 32.75 35.42

mD

TV(at)

NCF NPV

PV(After-tax Net Returns) = 30.28(1+.105)-1 +32.75(1+. 105)-2

+35.42(1+. 105)-3

PV = 27.403+26.822+26.252 = 80.477k or $80,477

Question 21.B

B. By how much was the NPV understated before correcting for this mistake?

Answer80,477-69,023=11,454

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%.

Question 22.A

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

Answer

0728.01

03.1

105.01*

r

r* = 7.28%

-17,227 = A* e [USPV7.28%,3]

A* e = $-6,598

Question 22.B

7.B Calculate the real annuity equivalent for the purchased tractor and sprayer.From question 3:NPV = -45,000-3,451+4754+26,470 = -17,227

Question 22.C

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

Lease Payments

Before Tax Payments $10,000

Tax Savings 10,000 * .3 = 3,000

Lease Payment after tax deduction10,000-3,000 = 7,000 or10,000(1-.3) = 7,000


NPV = -10,000 -7,000 [USPV10.5%,2] + 3,000 (1+0.105)-3

NPV = -10,000 - 12,068 + 2,223 = -19,844


NR(1-m) -10,000 -7,000 -7,000 +3,000 -19,844

mD

TV(at)

NCF -19,844

Calculate Net Present Value



-19,844= Ae [USPV7.28%, 3]

0 3

-19,844

r = 7.28 %1 2

A A A

Annuity Equivalent for Leasing New Tractor

Ae = -7,600

i% PV PMT FV

7.28 -19,844 Ae3 0

N

Question 22.D

Should Mr. Agirich buy or lease the tractor and sprayer?

AnswerBuy

Ae(buy) = -6,598

Ae(lease = -7,600

Question 23

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


Question 23 --Answer

Characteristics of Farm LandDurable and ImmobileLegal Restriction on useSpecial taxationLow ownership turnover --2-3% a year


Question 23 continued

Characteristics of Farm LandValue influenced by special factors:

Excess machinery capacityClose proximity to existing operationsNonmonetary factors: love of farming, rural lifestyleProximity to urban growthEnvironmental ConcernsRecreational ValueMineral, Oil, and Resource Rights

Documents

Study Guide Chapter1 12-13 Agricultural Economics 330 Instructor: David J. Leatham