Study GuideChapter1 12-13.ppt

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1、Study Guide Chapter1 12-13,Agricultural Economics 330 Instructor: David J. Leatham,Question 1,The following graph shows the financing gaps and surplusesper 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

2、 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 woul

3、d 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 f

4、or 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

5、 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 increa

6、se 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 5 Answer,Continued,After-tax, risk adjusted discount rate = .1(1-.3) =

7、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 b

8、e 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

9、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 pr

10、oduced 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

11、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

12、 to pay $0.30 in taxes per $1 of additional taxable income.,Investment Description,Mr. Agirich has calculated the after-tax cash flows as follows:,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%,Question 7

13、,What is the marginal tax rate for Aggieland Farms. Answer 30%,Question 8,Calculate the Net Present Value for the meadow land investment.,10/14/2018,Agricultural Finance,14,Discount Rate: After-tax risk-adjusted rate,r = rbt + PREM (1-m) r = after-tax, risk-adjusted discount rate rbt = before-tax, r

14、isk-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%,Calculate NPV,NPV = -800 + 61.6USPV8.4%,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

15、 = $ 7.65 per acre NPV = $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,Que

16、stion 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 metho

17、d. 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,Financial Feasibility,Question 10,Suppose Aggieland Farms wants to borrow $700 per acre and the local AGROCASH Bank

18、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,Questio

19、n 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

20、. 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 nonint

21、erest 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 o

22、perating 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

23、, calculate real net returns Second, calculate nominal net returns,10/14/2018,Agricultural Finance,26,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 = 93.39,10/14/2018,Agricultural Finance,27,Calculate

24、Nominal Net Returns,10/14/2018,Agricultural Finance,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,Question 12,Aggieland Farms needs another baler for 3 years. Mr. Agirich can buy a John Deere standard square baler for $20,000 and ha

25、s 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

26、 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 inf

27、lation to be 3%.,Question 12.A,Calculate the real after-tax, risk-adjusted discount rate. Answer,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.,Le

28、ase 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) = 2,310,10/14/2018,Agricultural Finance,34,NPV = -3,300 -2310 USPV8.4%,2 + 990 (1+0.084)-3,NPV = -3,300 - 4,096.9 + 777.23 = -6,619.7,Calculate Net Present Value,10/14/2018,A

29、gricultural Finance,35,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,Ae,3,0,N,Question 12.D,Should Mr. Agirich buy or lease the baler? Answer Buy Ae(bu

30、y) = -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 requi

31、rement 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.,10/14/2018,Agricultural Finance,38,P = L + F = 15,000 +150 = 15,459.18(1-s) (1-.02),S = .02(15,45

32、9.18) = 309.18,L = 15,459,18 - 309.18 - 150 =15,000,10/14/2018,Agricultural Finance,39,Loan Payment (A) 15,459.18=AUSPV10%,3 A=-6,216.37,PCA,10/14/2018,Agricultural Finance,40,0,15,000,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

33、,Use Calculator,2,- 6,216.37,10/14/2018,Agricultural Finance,41,Calculate APR & Effective Rate,Calculate APR APR = 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 ho

34、w 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 i

35、f 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

36、Bid Price of land is $1,918.5 per acre,Question 10 Answer,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 a

37、djusted 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*),20,000 = Ae* USPV2.095%, 15,Real Annuity Equivalent = Ae

38、* = 1,576.6,Question 14 Answer,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

39、 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%.

40、 The manager requires at least a 14% pre-tax return on capital. Assume the inflation rateis 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,D=0,NR(1-m)= -6,000(1-.30) = -4,200,TVat = 0,mD=0,r = 0.14(1-.3) =

41、 0.098 or 9.8%,NPV = - 4,200 - 7,309 = -11,508,NPV = -4,200 + -4,200 USPV9.8%,2,V0 = A USPVr,N Present Value of an Uniform Annuity,-11,508= Ae USPV9.8%, 3,3,9.8,-11,508,Ae,0,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,D=20,000/10 = 2,000

42、,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,V0 = A USPVr,N Present Value of an Uniform Annuity,-13,687 = Ae USPV9.8%, 4,4,9.8,-13,687,Ae,0,Ae = -4,299,N,i,PV,PMT,FV,0,4,-13,687,

43、r = 9.8 %,1,2,.,A,A,A,Annuity Equivalent for the Used Tractor,Widget NPV Annuity EquivalentBuy -13,687 -4,299 Lease -11,508 -4,611,Choose to buy the Widget,Investment Description,Aggieland Farms is located in the between Plantersville and Magnolia, Texas. The owner, Mr. Agirich has an opportunity to

44、 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 pl

45、ans 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

46、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

47、 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 se

48、ven 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

49、 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 Description,Mr. Agirich has calculated the nominal after-tax cash flows as follows:,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%,Question 17,What is the marginal tax rate for Aggieland Farms. Answer 30%,