Agricultural Economics 330 Instructor: David J. Leatham

Agricultural Economics 330 Instructor: David J. Leatham
Study Guide Chapter Agricultural Economics 330 Instructor: David J. Leatham

Question 1 Suppose you have an opportunity to purchase an investment for $600 and the investment promises to return $1,000 in five years. Does the yield on this investment increase or decrease if you can buy this investment for $580 instead of $600. Circle one. Increase

Question 2 Suppose you have $10,000 in your savings account and you are investigating the possibility of investing in bonds. If you believe that interest rates are going to go up over the next three years, should you invest in bonds. Justify your answer. Probably not. If interest rate go up, the value of the bonds you purchase will go down. If you wait to buy the bonds at higher interest rates, the price will be lower. If you buy them now, you are locked into the lower interest rate and a decreasing value of the bond.

Question 3 What does a Net Present Value equal to 0, imply about a project’s rate of return. The rate of return on the investment (internal rate of return --IRR) is equal to the required rate of return on the investment (discount rate).

Question 4 Suppose that you have eight annual payments of $3,425 left to pay on a loan with the first payment due in one year. You can borrow money at 9% and the bank is willing to sell back the note for $18,000. Should you buy back this loan? Assume that you would need to borrow the $18,000 if you buy back the loan.

1 2 8 ... r = 9 % 3,425 3,425 3,425 MV Market Value = 3,425 [USPV9%, 8] = 18,957 The market value of this contract is $18,957. You can buy it for $18,000. Buy it back.

Question 5 Suppose the real price of a tractor in 10 years is $55,000. What is the nominal price of the tractor if inflation is 3%? Fn = F*n (1+If)n F10 = 55,000(1+.03)10 = 73,915.4

Question 6 Suppose you are considering an investment that will increase operating receipts by $10,000 and operating expenses by $6,000. Calculate the after-tax net returns if your marginal tax rate is 15% and your required rate of return on investments is 20%. After-tax net returns = (10,000-6,000)(1-.15) =4,000(.85) = 3,400

Question 7 Suppose you are considering an investment that costs $35,000. You plan on selling the investment in five years for $10,000. The IRS will allow you to depreciate this investment over four years. Calculate the tax savings from depreciation in the fourth and fifth year if you use the straight-line method of calculating depreciation and your marginal tax rate is 15%.

Question 7 Answer Annual Depreciation for tax purposes = (35,000/4) = 8,750 Tax savings from depreciation = 8,750*.15 = 1,312.5 Tax savings in the fourth year is $1,312.5 Tax savings in the fifth year is 0 because the investment is depreciated completely (for tax purposes) over the first four years.

Question 8 Suppose you are considering an investment that costs $60,000. You plan on selling the investment in ten years for $20,000. Calculate the present value of the after-tax terminal value if accumulated depreciation is $30,000, your marginal tax rate is 15%, and your required rate of return on investments is 10%.

Question 8 Answer After-tax Terminal Value = 20,000-[20,000-(60,000-30,000)].15 = 21,500 After-tax discount rate = .1(1-.15) = or 8.5% 10 r = 8.5 % V0 21,500 V0 = 21,500 (1+.085)-10 = 9,509.14

Question 9 Suppose that you are considering the purchase of a bond that matures in 12 years. The bond has a par value of $1,000, it pays a coupon of 10 percent (annually), and the coupon is paid semiannually (10s). Coupon payment every six months = (.10*1,000)/2 = $50

... Question 9 Part A Calculate the market value (price) of the bond
today if the bond’s market rate (yield) is 7%. 24 MV r = 7/2 %= 3.5 % 1 2 ... 50 1,000 Market Value = price = 50[USPV3.5%,24] + 1,000 (1+.035)-24 =$1,240.88

... Question 9 Part B Calculate the market value (price) of the bond
in five years if the bond’s market rate is 4%. 10 MV r =4/2 %= 2 % 1 2 ... 50 1,000 Market Value = price = 50[USPV2%,10] + 1,000 (1+.02)-10 =$1,269.48

Question 9 Part C Calculate the Net Present Value and the Internal Rate of Return on this bond investment if the current market rate on this bond is 7%, you expect the market rate to be 4% in 5 years, you plan to sell the bond in five years, and your required rate of return on this investment is 8% (4% semiannually). Is this an acceptable investment? (hint: use the purchase price in part A, and the sell price in part B)

10 - 1,240.88 r =8/2 %= 4 % 1 2 ... 50 1,363.19 NPV = -1, [USPV4%,10] + 1, (1+.04)-10 = -1, , = 85.59

10 - 1,240.88 r =?/2 %= ? % 1 2 ... 50 1,363.19 NPV = 0 = -1, [USPVr%,10] + 1, (1+.r)-10 r = IRR = 4.82% (semiannual rate) r = IRR = 2*4.82 = 9.63% This is an acceptable investment. NPV > 0 and the IRR > 8%.

Question 10 . List the four steps of capital budgeting discussed in class: A. B. C. D

Answer 10 . List the four steps of capital budgeting discussed in class: A. Identify Alternative Investments B. Collect Relevant Information C. Layout Cashflows D. Analysis Profitability, risk, sensitivity, and financial feasibility

Question 11 Suppose you are considering the purchase of an investment and your discount rate is 10%. Also, suppose you calculate that the net present value of this investment is equal to zero. What is the internal rate of return on this investment? Answer 10%

Question 12 Suppose you have an opportunity to purchase an investment today for $500. A. Calculate the yield on this investment if the investment matures in one year and promises to pay $560 at maturity .

Yield = 12%

Question 12 Suppose you have an opportunity to purchase an investment today for $500. B. Calculate the yield on this investment if the investment promises to pay $140 at the end of each year for the next five years.

... 1 2 5 ... r = ? % 140 140 140 -500 V0 = A [USPVr,N] Present Value of an Uniform Annuity 500 = 140 [USPVr%, 5] 5 ? -500 140 r = 12.38% N i% PV PMT FV 9/17/2018 Agricultural Finance

Question 13 Suppose the annual cash revenue from an investment is $9,000 and the annual cash expenses are $3,000. Calculate the annual after-tax net returns if the marginal tax rate is equal to 15%.

Let ATNR=After-tax Net Returns
R= Cash Revenues E=Cash Expenses m=marginal tax rate NR = [R-E] ATNR = [R-E](1-m) = [NR](1-m) ATNR = [9,000-3,000](1-.15) =6,000(.85) =5,100

Question 14 Suppose Mr. Agirich is considering the purchase of a tractor that costs $75,000. He plans on selling the tractor in 10 years for $10,000. The IRS will allow him to depreciate the tractor over seven years. Assume that he uses the straight-line method of calculating depreciation, the marginal tax rate is 28% and the required rate of return on investments is 16%. A. Calculate the present value of tax savings from depreciation over the life of the investment.

Annual Depreciation (D) = 75,000/7
= 10,714.29 Annual Tax Savings = mD = 10, * .28 = 3,000 After-tax discount rate = .16(1-.28) = or 11.52%

... 1 2 7 8 9 10 ... r = % V0 3,000 3,000 3,000 Present Value of Tax Savings from Depreciation = V0 V0 = A [USPVr,N] Present Value of an Uniform Annuity V0 = 3,000 [USPV11.52%, 7] 7 11.52 ? 3,000 V0 = 13,902.2 N i% PV PMT FV

Question 14 Suppose Mr. Agirich is considering the purchase of a tractor that costs $75,000. He plans on selling the tractor in 10 years for $10,000. The IRS will allow him to depreciate the tractor over seven years. Assume that he uses the straight-line method of calculating depreciation, the marginal tax rate is 28% and the required rate of return on investments is 16%. B. Calculate the present value of the after-tax terminal value.

TVat = 10,000-[10,000-(75,000-75,000)].28 =10,000-[10,000].28 =10,000-2,800 =7,200

10 r = 11.52% % -V0 7,200 V0 = Present Value of After-tax Terminal Value V0 = VN (1+r)-N Present Value of a Single Sum V0 = 7,200 ( )-10 10 11.52 V0 7,200 V0 = 2,419.94 N i% PV PMT FV 01/09/80 Agricultural Finance 19

Question 15 Suppose Mr. Agirich is considering the purchase of a
center pivot irrigation system. He estimates that the after-tax net cash flows associated with this investment are as follows. Assume that the marginal tax rate is 28%. A. Calculate the net present value (NPV) if the required rate of return on investments is 18%.

NPV = -3,790.9 After-tax discount rate = 0.18(1-.28)
= or 12.96% NPV = -85, ,000 [USPV12.96%,5] + 59,000( )-6 = -85, , ,399 =-3,790.9 NPV = -3,790.9

center pivot irrigation system. He estimates that the after-tax net cash flows associated with this investment are as follows. Assume that the marginal tax rate is 28%. B. Explain and show how to calculate the internal rate of return (IRR) on this investment (estimate within ½% accuracy).

---------------------- 11.65 0
The internal rate of return (yield) is the rate that makes the pv(cash inflows) = PV(cash outflows), i.e., NPV=0. Search for the answer. NPV = 0 = -85, ,000 [USPVr%,5] + 59,000(1+r)-6 r NPV 11% 1,982 12% -1,037 11.5% 452 The internal rate of return is between 11.5% and 12%. If you continue to search or use a calculator, the IRR is equal to 11.65%.

center pivot irrigation system. He estimates that the after-tax net cash flows associated with this investment are as follows. Assume that the marginal tax rate is 28%. C. Graphically show the relationship between the net present value (NPV) and the discount rate. Use NPV as the vertical axis and discount rate as the horizontal axis. Use at least four data points.

center pivot irrigation system. He estimates that the after-tax net cash flows associated with this investment are as follows. Assume that the marginal tax rate is 28%. D. Is this an acceptable investment? Why?

Answer 15.D This is not an acceptable investment. The NPV is less than zero which implies that the rate of return is less than what was required. In fact, the after-tax required rate of return was 12.96% but the after-tax rate of return was less than 12%.

Question 16 Suppose that you are considering the purchase of a bond that costs $1,060 today and you plan on selling the bond in four years. Assume that the bond matures in 11 years, has a par value of $1,000, pays a coupon of 8 percent (annually), and the coupon is paid semiannually (8s). A. Calculate the market value (price) of the bond in four years if the bond’s market rate is 12%.

... ... MV = 40 [USPV6%, 14] +1,000(1+.06)-14 2*7=14 r = 12/2 = 6 % 1
2*7=14 r = 12/2 = 6 % 1 2 ... 40 1,000 MV Calculate the Market Value (MV). This is an 11 year bond. In four years there will be 7 years left. Market rate = 12/2 = 6% MV = 40 [USPV6%, 14] +1,000(1+.06)-14 14 6 ? 40 1000 MV=814.10 N i% PV PMT FV 01/16/97 Agricultural Finance 28

Question 15 Suppose that you are considering the purchase of a bond that costs $1,060 today and you plan on selling the bond in four years. Assume that the bond matures in 11 years, has a par value of $1,000, pays a coupon of 8 percent (annually), and the coupon is paid semiannually (8s). B. Calculate the yield on this bond investment if you sell the bond in four years from today and the bond’s market rate is 12%.

... ... 1,060 = 40 [USPVr%, 8] +814.1(1+r)-8 2*4=8 r = i/2 = ? % 1 2
2*4=8 r = i/2 = ? % 1 2 ... 40 814.1 -1060 Calculate the Yield (r), Convert to Annual Rate (i) Purchase Price = 1,060, Sale price = $814.1 (see 7.A) 1,060 = 40 [USPVr%, 8] (1+r)-8 8 ? -1,060 40 814.1 r=0.97% & i=1.9% N i% PV PMT FV 01/16/97 Agricultural Finance 34

Question 16 Is an investment profitable if the the total cash inflows are greater than the total cash outflows? Explain

Answer 16 . Not always. This measure and rule ignores the time value of money. If you paid $100 for an investment today and received $ years from now, total cash inflows would be greater than total cash outflows. It may not be profitable in the sense that you probably have other investment opportunities that pay more money i.e., have a higher rate of return.

Question 17 Does the Net Present Value (NPV) increase or decrease when the yield of an investment increases? Explain.

Answer 17 Neither. By definition the yield is the rate that makes the NPV=0. Thus, NPV is always zero when the discount rate is equal to the yield. The NPV is dependent on the discount rate used, not the yield of an investment.

Question 18 Suppose that you have just graduated from TAMU and you have a job paying $38,000 per year. You would like to save $20,000 so that you can make a downpayment on a house in 5 years. How much would you have to put in the bank each month if the bank pays 6 percent on savings accounts (assume you put the money in the bank at the end of the month and interest is compounded monthly)?

... 20,000 = A [USFV0.5%, 60] 5*12=60 1 2 r =6/12=0.5% -A -A -A 20,000
1 2 ... r =6/12=0.5% -A -A -A 20,000 V0 = A [USPVr,N] Present Value of an Uniform Annuity 20,000 = A [USFV0.5%, 60] 60 0.5 ? 20,000 A = $286.66 N i% PV PMT FV

Question 19 Suppose that you have an opportunity to buy a house for $100,000. You have enough money in your bank account to make a $20,000 downpayment. Suppose you borrow $80,000 to buy the house and will repay the loan over 30 years. The annual interest on the loan is eight percent. The bank requires equal monthly payments. A. Calculate the monthly payments.

... 80,000 = A [USPV0.67%, 360] 30*12=360 1 2 r =8/12=0.67% -A -A -A
1 2 ... r =8/12=0.67% -A -A -A 80,000 V0 = A [USPVr,N] Present Value of an Uniform Annuity 80,000 = A [USPV0.67%, 360] 360 0.67 80,000 ? A = $587.01 N i% PV PMT FV

Question 19 Conintued Suppose that you have an opportunity to buy a house for $100,000. You have enough money in your bank account to make a $20,000 downpayment. Suppose you borrow $80,000 to buy the house and will repay the loan over 30 years. The annual interest on the loan is eight percent. The bank requires equal monthly payments. B. How much interest will you pay on this loan if you keep the loan for 30 years?

Interest Total Payments=587.01*360 = Total Interest = 211,324-80,000 =
131,324.2

Question 20 Suppose that you have an opportunity to start a computer business in the shadow of TAMU. You are sure it will be a successful business but you don’t have any money to get it started. Your parents have agreed to lend you $100,000 today so that you can start the business. They will charge you six-percent interest and require that you pay the loan back, principal and interest, at the end of five years. A. How much money will you owe your parents in five years?

5 r = 6% 100,000 -V5 VN = V0 (1+r)N Future Value of a Single Sum V5 = 100,000 (1+.06)5 5 6 100,000 V5 V5 = 133,822.56 N i% PV PMT FV

Question 20 Continued Part B
Suppose at the end of five years you don’t have the money to pay your parents the money you owe them (Part A.). A friendly bank will lend you the money. The annual interest rate is 12 percent. The bank will lend you the money for 10 years and requires equal annual payments. Calculate the annual payments.

10 1 2 ... r =12% -A -A -A 133,822.56 V0 = A [USPVr,N] Present Value of an Uniform Annuity 133, = A [USPV12%, 10] 10 12 133,822 ? A = $23,684.47 N i% PV PMT FV

Question 20 Continued Part C
Suppose at the end of five years you don’t have the money to pay your parents the money you owe them (Part A.). You agree to take out a loan with the local bank to pay your parents as much as you can. The annual interest rate is 12 percent. The bank will lend you the money for 10 years and requires equal annual payments. The maximum annual payment you can make is $10,000. What is the maximum amount of money that you can borrow from the bank?

10 1 2 ... r =12% -10k -10k -10k V0 V0 = A [USPVr,N] Present Value of an Uniform Annuity V0 = 10,000 [USPV12%, 10] 10 12 V0 10,000 V0=56,502.23 N i% PV PMT FV

Question 21 Suppose you have received permission to sell “Snow Cones” on TAMU campus for four years. You can buy a Snow Cone machine for $2,000 and can sell it for $500 in four years. The IRS will allow this machine to be depreciated using straight-line for seven years. You anticipate that you can sell 5,000 Snow Cones per year. You can sell the cones at $0.50 per cone and it will cost you $0.35 per cone to make (including labor). Assume that you require a 14 percent return to capital and your are in the 15 percent tax bracket. A. Layout the cash flows.

Period Component Cost -2,000 Initial Cost

After-tax Net Returns = 750(1-.15) = 637.50
Period Component Cost -2,000 NR(1-m) Operating Revenue = 5,000 * .5 = 2,500 Operating Expense = 5,000 * .35 = 1,750 Net Returns = 2, ,750 = 750 After-tax Net Returns = 750(1-.15) =

Annual Depreciation = 2,000/7 = 285.71
Period Component Cost -2,000 NR(1-m) mD Annual Depreciation = 2,000/7 = Tax Savings: Depreciation = *.15 = 42.86

After-Tax Terminal Value= 500-[500-(2,000-(285.71*4))].15 = 553.57
Period Component Cost -2,000 NR(1-m) mD / Tvat NCF -2, ,233.93 After-Tax Terminal Value= 500-[500-(2,000-(285.71*4))].15 =

Question 21 Continued B. Calculate the Net Present Value and indicate whether not this is an acceptable investment

Period Component Cost -2,000 NR(1-m) mD Tvat NCF -2, ,233.93 After-tax discount rate = 0.14(1-.15) = or 11.9% NPV = -2, [USPV11.9%,4] [USPV11.9%,4] +553.6(1+.119)-4 = -2,000 +1, = Acceptable

Problem 21 Continued Explain and show how to calculate the internal rate of return (IRR) on this investment (estimate within ½% accuracy if time permits).

----------------------- 0.2068 0 IRR = 20.68% This is an after-tax
NPV = -2, [USPV11.9%,4] [USPV11.9%,4] +553.6(1+.119)-4 Set NPV = 0 and solve for r NPV = 0 = -2, [USPVr%,4] [USPVr%,4] +553.6(1+r)-4 r NPV IRR = 20.68% This is an after-tax Internal Rate of Return

Question 22 An increase in the general price level is called __________________. Inflation

Question 23 Explain why the yield on bonds issued by Microsoft is higher than the yield on comparable bonds issued by the U.S. government. Microsoft Bonds are more risky than U.S. Treasury bonds. That is, there is a greater likelihood that Microsoft will default on bonds than the U.S. Government. Because of the greater risk, investors demand a greater profit, thus, a higher yield.

Question 24 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 25 Suppose that new tractors are selling for $85,000 today but you decide to wait five years before buying a new tractor. If the real price of tractors do not change but the inflation rate is 10% per year, how much will you pay for a new tractor in five years? Show all your work.

Question 25 Answer Fn = F*n (1+If)n F5 = 85,000(1+.1) 5 = $136,893

Question 26 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.

Question 26 Answer F*n = F*0 (1+g)n g=real growth rate = 4%
Continued

Question 26 Answer Continued
After-tax, risk adjusted discount rate = .1(1-.3) = 0.07 ot 7% PV(after-tax net return in 7th year = (1+.07)-7 = 80.72

Question 27 Suppose that you borrow $80,000 to buy a tractor and the loan is fully amortized at 12% over eight years. Calculate the tax savings from claiming interest as an expense in the second year. Assume that the pretax discount rate is 14%, the marginal tax rate is 30.3% and inflation is expected to be 6%. Show all your work.

Annual Payment =A 80,000 = A [USPV12%,8] A = 16,104.23
Question Answer Annual Payment =A 80,000 = A [USPV12%,8] A = 16,104.23 Marginal tax Rate = m =30.3% Continued

Question 27 -- Answer Continued
Tax Savings from Claiming Interest in the 2nd year = $2,672.31

Investment Description
Sanderson Farms, Inc., a major poultry producer, has established a major poultry operation in the Brazos Valley. The facility includes a hatchery, a feed mill, and a poultry processing plant with a capacity to process approximately 625,000 birds per week. Sanderson Farms will contract independent growers to support the poultry facility. Growers finance and build their own poultry houses to supply pullets (young breeder hens), hatching eggs, and broilers to Sanderson Farms. Suppose Mr. Agirich, of Aggie Farms, wants to diversify and is considering the construction and operation of two breeder hen houses. The estimated cost of two fully-equipped hen houses is $310,000. Annual revenue is expected to be $88,400. Annual expenses is expected to be $22,100. Mr. Agirich plans on selling the hen houses in three years and expects that he can sell them for $255,000. Mr. Agirich anticipates that his marginal tax rate over the next four years will be 28%. The IRS will allow Aggie Farms to depreciate the hen houses using straight-line over 20 years.

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

Question 1 Mr. Agirich can save $4,340 in taxes in the third year because depreciation is tax deductible. Is the $4,340 real or nominal? Answer Nominal

Question 2.A Suppose Mr. Agirich requires at least a 10% pre-tax, risk-free return on capital investments and a 6% risk premium on projects of comparable risk to the hen houses. A. Calculate the investment’s Net Present Value.

Discount Rate: After-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 = [ ] (1-.28) r = 0.16 (1-.28) r = or 11.52% 9/17/2018 Agricultural Finance

Calculate NPV NPV = -C0 +NR(1-m)[USPVr,N] +mD [USPVr,N] + TVat (1+r)-N
NPV = -310, ,7360[USPV11.52%,3] + 4,340 [USPV11.52%,3] + 257,380 ( )-3 NPV = -310, , , ,573.74 = 1,690.46 NPV = $ 1,690.46

Question 2.B Suppose Mr. Agirich requires at least a 10% pre-tax, risk-free return on capital investments and a 6% risk premium on projects of comparable risk to the hen houses. B. Calculate the minimum after-tax net return that can be earned on this investment per year and still have this investment be an acceptable investment, holding everything else constant.

Break-Even NPV = -310, ,7360[USPV11.52%,3] + 4,340 [USPV11.52%,3] + 257,380 ( )-3 Set NPV = 0 and Solve for the After-tax Net Return (ATNR) 0 = -310,000 + ATNR [USPV11.52%,3] + 4,340 [USPV11.52%,3] + 257,380 ( )-3 0 = -310,000 + ATNR [USPV11.52%,3] +10, ,573.74

Break-Even 0 = -310,000 + ATNR [USPV11.52%,3] +10,510.53 + 185,573.74
Note: V0 = 1 [USPV11.52%,3] = [USPV11.52%,3] 0 = -310,000 + ATNR (2.4218) +10, ,573.74 ATNR = 47,038 If the after-tax net returns per year are below $47,038, the NPV<0, thus this investment would be unacceptable.

Question 2.C Suppose Mr. Agirich requires at least a 10% pre-tax, risk-free return on capital investments and a 6% risk premium on projects of comparable risk to the hen houses. C. Graphically show the relationship between the after-tax net return and the Net Present Value. Use at least three points on the graph (hint: use information from problems 2.A and 2.B for two of the points).

Sensitivity Analysis NPV = -310,000 + ATNR (2.4218) +10, ,573.74 NPV = ATNR (2.4218) - 113,915.73 ATNR NPV 46,750 (696) 47,038 0 47,736 1,690

Sensitivity Analysis

Question 2.D Suppose Mr. Agirich requires at least a 10% pre-tax, risk-free return on capital investments and a 6% risk premium on projects of comparable risk to the hen houses. D. Suppose that Mr. Agirich made a mistake when calculating the after-tax net returns. Suppose that the projected annual revenues of $88,400 and annual expenses of $22,100 are estimated as real dollars. Assume that Mr. Agirich expects that inflation will be 3% and the annual revenue and annual expenses will increase at the rate of inflation over the life of the investment. Calculate the present value of the after-tax net returns over the three year life of the investment.

Real Net Returns = 88, ,100 = 66,300 9/17/2018 Agricultural Finance

Present Value of After-Tax Net Returns
PV(ATNR) = 49,168 (1.1152)-1 +50,643 (1,1152)-2 +52,162(1.1152)-3 = 44, , ,609.36 = 122,418

Question 3.A Suppose a bank has offered to lend Mr. Agirich $248,000. The loan will be fully amortized at a 10% interest rate over five years (annual payments). A. Calculate the annual loan payment.

... V0= A [USPVr,N] Present Value of an Uniform Annuity
5 248,000 r = 10 % 1 2 ... -A V0= A [USPVr,N] Present Value of an Uniform Annuity 75,000= A [USPV10%,5] where A = loan payment 5 10 248,000 -A AA=65,421.78 N i% PV PMT FV 9/17/2018 Agricultural Finance

Question 3.B Suppose a bank has offered to lend Mr. Agirich $248,000. The loan will be fully amortized at a 10% interest rate over five years (annual payments). B. Calculate the annual tax savings from claiming interest as a tax deduction in each of the first three years.

Question 3.C Suppose a bank has offered to lend Mr. Agirich $248,000. The loan will be fully amortized at a 10% interest rate over five years (annual payments). ) C. Calculate the net cash flow after debt for this investment.

Financial Feasibility

Question 3.D Suppose a bank has offered to lend Mr. Agirich $248,000. The loan will be fully amortized at a 10% interest rate over five years (annual payments). D. Is there a potential liquidity problem if Mr. Agirich invests in the hen houses? Explain..

Potential Liquidity Problem
Must have $62,000 in cash for the down payment Must be able to generate $6,402 in the first year and $7,539 the second year from other parts of the business. If not, the investment is financially infeasible.

Question 3.E Suppose a bank has offered to lend Mr. Agirich $248,000. The loan will be fully amortized at a 10% interest rate over five years (annual payments). E. How can Mr. Agirich determine if this investment is financially feasible?

Financially Feasible A Projected Cash Flow Statement can be used to determine if enough surplus cash can be generated from other parts of the business to meet the cash deficits caused by the purchase of the hen houses. If so, the investment is financially feasible. If not, Mr. Agirich will not be able to invest in the hen houses even though it would be profitable.

Question 4 Suppose Mr. Agirich decides to keep the hen houses 10 years before selling them. Also suppose that a bank will lend him $248,000. The loan will be fully amortized at a 11% interest rate over 12 years (annual payment). Calculate the loan balance at the end of the tenth year after the scheduled annual payment.

V0= A [USPVr,N] Present Value of an Uniform Annuity
1 2 3 r = 11 % -38,198.8 - 38,198.8 BV V0= A [USPVr,N] Present Value of an Uniform Annuity Book Value= 38,198.8 [USPV11%,2] where BV = Loan Balance 2 11 BV -38,198.8 BV = 65,416.3 N i% PV PMT FV 9/17/2018 Agricultural Finance

Yield monitoring systems, which are installed on combines, use the Global Positioning System (GPS) and a mechanical yield monitor to link crop yield to a given location in a field. Many farmers have purchased monitor-equipped combines ($8,000) but do not have the knowledge or desire to create yield maps from the data collected. It is estimated that a farmer can increase net returns per acre by $10-$15 per acre by using yield maps correctly via increased yields and reduced input costs. Suppose Mr. Agirich of Aggie Farms is an expert in using yield monitoring systems and using yield maps to enhance farm income. Mr. Agirich believe he can make money if he sets up a consulting firm that helps other farmers make yield maps and provides instruction on how to use the yield maps. Securing a good customer base will be essential for this to be a profitable venture. Mr. Agirich believes that farmers will pay $3.00 per acre for this service and he believes that he can obtain a clientele base that will pay him to process 31,000 acres.

Investment Description (cont.)
Mr. Agirich estimates that he will have to produce an average of five different maps per thousand acres per year. With the yield mapping software Aglink it takes less than 30 minutes to produce one map. The initial cost of starting this business is $11,000 that includes yield mapping software, computer equipment, legal fees, and office supplies. Mr. Agirich anticipates that his marginal tax rate over the next four years will be 28%. The IRS will allow Aggie Farms to depreciate the start-up cost using straight-line over four years. Annual expenses are expected to be $91,000 including salaries, office rental, utilities, internet services, mail, advertising and travel costs. Mr. Agirich plans on selling this business to his son in three years for $20,000.

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

Question 1 Suppose Mr. Agirich expects inflation to be 4% over the next three years and requires a 10% return on investments. Calculate the real tax savings from depreciation in the third year. Answer Fn*=Fn(1+If)n Fn*=770(1+.04)3 =

Question 2.A Suppose Mr. Agirich requires at least a 5% pre-tax, risk-free return on capital investments and a 20% risk premium on projects of comparable risk to the yield-mapping business. The interest rate on loans is 15%. A. Calculate the investment’s Net Present Value.

Discount Rate: After-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 = [ ] (1-.28) r = 0.25 (1-.28) r = .18 or 18% 9/17/2018 Agricultural Finance

Calculate NPV NPV = -C0 +NR(1-m)[USPVr,N] +mD [USPVr,N] + TVat (1+r)-N
NPV = -11, ,440[USPV18%,3] [USPV18%,3] + 15,170 (1+.18)-3 NPV = -11,000 +3, , ,232.93 = 3,038.07 NPV = $ 3,

Question 2.B Suppose Mr. Agirich requires at least a 5% pre-tax, risk-free return on capital investments and a 20% risk premium on projects of comparable risk to the yield-mapping business. The interest rate on loans is 15%. B. As stated above, Mr. Agirich expects to process 31,000 acres for clients and get paid $3 per acre. Calculate the least number of acres that can be processed and still have this investment be an acceptable investment, holding everything else constant.

Break-Even NPV = -11,000 + 1,440[USPV18%,3] + 770 [USPV18%,3]
+ 15,170 (1+.18)-3 Set NPV = 0 and Solve for the After-tax Net Return (ATNR) 0 = -11,000 + NR(1-.28) [USPV18%,3] [USPV18%,3] + 15,170 (1+.18)-3 0 = -11,000 + NR(1-.28) [USPV18%,3] +1, ,232.93

Break-Even 0 = -11,000 + NR(1-.28) [USPV18%,3] +1,674.19 + 9,232.93
Note: V0 = 1 [USPV11.52%,3] = [USPV11.52%,3] 0 = -11,000 + NR(1-.28) [2.1743] +1, ,232.93 NR = 59.34

Break-Even NR=Price per Acre * Acres Processed 59.33 = ($3 *AP)-91,000
If the number of acres processed (AP) per year are below 30,353, the NPV<0, thus this investment would be unacceptable.

Question 2.C Suppose Mr. Agirich requires at least a 5% pre-tax, risk-free return on capital investments and a 20% risk premium on projects of comparable risk to the yield-mapping business. The interest rate on loans is 15%. C. Graphically show the relationship between the acres processed and the Net Present Value. Use at least three points on the graph.

Sensitivity Analysis (hint: use information from problems 2.A and 2.B for two of the points). NPV = -11,000 + [(3*AP)-91,000](1-.28) [2.1743] +1, ,232.93 NPV = *AP - 142,553 ATNR NPV 30,000 (1,658) 30,353 0 31,000 3,038

Sensitivity Analysis

Question 2.D Suppose Mr. Agirich requires at least a 5% pre-tax, risk-free return on capital investments and a 20% risk premium on projects of comparable risk to the yield-mapping business. The interest rate on loans is 15%. D. Suppose that Mr. Agirich made a mistake when calculating the after-tax net returns. Suppose that the projected revenue per acre of $3 and annual expenses of $91,000 are estimated as real dollars. Assume that Mr. Agirich expects that inflation will be 4% and the annual revenue and annual expenses will increase at the rate of inflation over the life of the investment. Calculate the present value of the after-tax net returns over the three-year life of the investment.

Real Net Returns = (3*31,000) -91,000 = 2,000
9/17/2018 Agricultural Finance

Present Value of After-Tax Net Returns
PV(ATNR) = 1,497.6 (1.18)-1 +1,557.5 (1.18)-2 +1,619.8(1.18)-3 = 1, , = 3,373.58

Question 3.A Suppose a bank has offered to lend Mr. Agirich $10,000. The loan will be fully amortized at a 15% interest rate over two years (annual payments). A. Calculate the annual loan payment.

Question 3.B Suppose a bank has offered to lend Mr. Agirich $10,000. The loan will be fully amortized at a 15% interest rate over two years (annual payments). B. Show a complete amortization schedule for this loan.

Question 3.C Suppose a bank has offered to lend Mr. Agirich $10,000. The loan will be fully amortized at a 15% interest rate over two years (annual payments). ) C. Calculate the net cash flow after debt for this investment.

Financial Feasibility

Question 3.D Suppose a bank has offered to lend Mr. Agirich $10,000. The loan will be fully amortized at a 15% interest rate over two years (annual payments). D. Is there a potential liquidity problem if Mr. Agirich invests in yield-mapping business? Explain.

Potential Liquidity Problem
Must have $1,000 in cash for the down payment Must be able to generate $3,521 in the first year and $3,716 the second year from other parts of the business. If not, the investment is financially infeasible.

Question 3.E Suppose a bank has offered to lend Mr. Agirich $10,000. The loan will be fully amortized at a 15% interest rate over two years (annual payments). E. Suppose it is projected that the net cash flows after debt are negative in the first and second year. How can Mr. Agirich determine if this investment is financially feasible?

Financially Feasible A Projected Cash Flow Statement can be used to determine if enough surplus cash can be generated from other parts of the business to meet the cash deficits caused by the purchase of the yield-mapping business. If so, the investment is financially feasible. If not, Mr. Agirich will not be able to invest in the yield-mapping business even though it would be profitable.

Question 4 Suppose Mr. Agirich decides to keep the yield-mapping business 12 years before selling it. Also suppose that a bank will lend him $10,000. The loan will be fully amortized at a 15% interest rate over 20 years (annual payment). Calculate the loan balance at the end of the twelfth year after the scheduled annual payment.

V0= A [USPVr,N] Present Value of an Uniform Annuity
1 8 r = 15 % - 1,597.61 - 1, 1,597.61 BV V0= A [USPVr,N] Present Value of an Uniform Annuity Book Value= 1,597.61[USPV15%,8] where BV = Loan Balance 8 15 BV - 1,597.61 BV = 7,169 N i% PV PMT FV 9/17/2018 Agricultural Finance

Agricultural Economics 330 Instructor: David J. Leatham

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