Agricultural Economics 330
Agricultural Finance
Problems: Capital Budgeting
Instructor: Dr. David J. Leatham
Definitions
1. : To liquidate on an installment basis.
2. : An increase in the general price level of prices.
3. : The interest rate stated by a lender on a contract (note).
4. : The process of planning asset expenditures whose returns are expected to extend beyond one year.
5. : The difference between the present value of cash inflows and cash outflows associated with an investment.
6. : The point from which taxable gains or losses are measured.
7. : The present value of cash inflows minus the present value of cash outflows for an investment.
8. : The rate that make the net present value equal to zero.
True or False. Circle the most correct answer. If False, justify your answer.
T F If inflation increases the nominal terminal value of an investment, the annual depreciation that can be claimed as a tax deduction is reduced.
T F An increase in the required rate of return to equity capital will decrease the net present value of an investment.
T F Pre-tax lease payments should be used to calculate the net present value when evaluating a lease agreement.
T F A negative net present value implies a negative yield on an investment and thus should be rejected.
T F If a loan is fully amortized, the annual debt payment is tax deductible.
T F Annual depreciation calculated using straight-line methods reduces a firm's taxable income.
T F A firm that has restrictions on how much money it will borrow (internal or external) should use the interest rate on debt capital as its discount rate.
T F An investment can have a positive net present value but not be financially feasible.
T F An investment can be self liquidating but have a negative net present value.
T F The net present value of an investment will always be positive and the investment will be self liquidating as long as the after-tax cash flows are positive after the initial equity investment.
T F Inflation will not affect the annual depreciation a farmer can claim as a tax deduction after a tractor is purchased.
T F Inflation increases the tax savings a farmer can obtain by claiming depreciation on farm equipment as a tax deductible expense.
T F Lease payments on farm equipment are tax deductible.
T F The book value (tax basis) of leased equipment is the purchase price minus accumulated depreciation.
T F Mutually exclusive investments are unacceptable.
T F When ranking two investments, the investment with the highest annuity equivalent may be acceptable even if the net present value is negative.
T F When ranking two investments, negative annuity equivalents imply that both investments should be rejected.
T F A positive net present value implies that an investment is financially feasible.
T F Nominal interest rates increase if the expected inflation rate increases, holding the real interest rate constant.
T F The yield on an investment is always equal to the discount rate.
T F An investment is not acceptable if the discount rate is greater than the Internal Rate of Return.
T F An investment should always be considered profitable if the total cash inflows is greater than the total cash outflows.
T F The marginal tax rate can be calculated by dividing total tax obligation (money that must be paid to the IRS) by total taxable income.
T F A pre-tax discount rate is converted to an after-tax discount rate by multiplying the pre-tax discount rate by (1-the average tax rate).
T F The tax basis of an asset is calculated by subtracting the projected terminal value of an asset from the original cost.
T F From a bankers perspective, the net present value of a fully amortized loan, by definition, is zero, assuming that the bankers discount rate is the same as the contractual interest rate on the loan.
T F Sensitivity analysis for an investment is performed by setting the discount rate = 0 and solving for one unknown variable.
T F An investment with a net present value of zero is an acceptable investment.
T F An investment's internal rate of return and an investment's yield are the same by definition.
T F A fully amortized loan has equal principal payments over the life of the loan.
T F When adjusting for risk, a risk premium is subtracted from the risk-free discount rate to account for the fact that a more risky investment is worth less than a risk free investment.
T F Allowable depreciation and interest expenses are both multiplied by the marginal tax rate to calculate tax savings.
T F When calculating the annual loan payment for a fully amortized loan, the contractual rate is multiplied by (1-marginal tax rate).
T F Corn prices will always increase at the same rate as inflation.
T F An investment's book value (or taxable basis) is the initial cost minus the annual depreciation in the year the investment is sold.
T F The appropriate discount rate to use is an after-tax discount rate and is calculated by multiplying the pre-tax discount rate by one plus the marginal tax rate.
T F When laying out the cash flows for an investment alternative, the book value (or taxable basis) of an investment is not considered a cash inflow.
T F When laying out the cash flows for an investment alternative, initial equity, operating expenses, depreciation, and loan interest are some of the categories that are added together to obtain total cash outflows.
T F An investment that is not self-liquidating cannot be financially feasible.
T F The depreciable life of an investment may be different that the life of the investment.
Problems
1. Suppose you purchase a combine to custom harvest wheat for $90,000 and you believe you can sell it in five years for $50,000 in real dollars. Calculate the present value of the after-tax terminal value of this combine. Assume that your marginal tax rate is 30%, you expect inflation to be 5% over the next five years, you expect that used combine prices will increase at the rate of inflation, the IRS allows you to depreciate the combine using straight line over seven years, and you require at least an eight percent return on capital and a 2% risk premium on projects of comparable risk.
2. Mr. Agirich is tired of suffering heavy losses from deer damage to his 100-acre orchard. He has read in the Farm Bureau News that a New York apple producer buried a copper stranded wire around his orchard. The wire does not carry electricity, just a harmless radio signal. His dogs were outfitted with special collars containing battery-operated receivers, which give an electronic signal when the dog gets within a certain distance from the fence. The dogs are allowed to roam free in the orchard, thus discouraging deer from feasting on fruit buds and damaging new plantings. Mr. Agirich believes that deer damage costs him $12,000 per year and this would be saved if dogs were allowed to roam in the orchard. The fence should have a 15-year life and is virtually maintenance free. The only regular expense is replacement of dog collars. The cost is about $35 per dog per year. Mr. Agirich believes four dogs would be sufficient and because the dogs would be pets, he will not assign a cost to the dogs. The fence would be worthless after 15 years. Assume it would cost Mr. Agirich $20,000 to put in the fence, Mr. Agirich has other investment opportunities that promise to return 10%, the IRS will allow the fence to be depreciated using straight-line over seven years, and the marginal tax rate is 30% (Ignore risk and inflation).
A. Calculate the present value of the after-tax net returns from this investment if Mr. Agirich plans to keep the fence for 15 years.
B. Calculate the present value of tax savings from depreciating the fence if Mr. Agirich plans to keep the fence for 15 years.
C. Calculate the net present value of this investment if Mr. Agirich plans to keep the fence for 15 years. Is this an acceptable investment?
D. Suppose that Mr. Agirich can borrow $15,000 from the bank and the loan will be fully amortized over 20 years at 8% (annual payments):
(1) Show whether or not Mr. Agirich would have a potential liquidity problem in the first and second year.
(2) Suppose the lender requires that Mr. Agirich pay the remaining principal balance of the loan (balloon payment) at the end of the 15th year. Calculate the balloon payment (hint: the principal balance of a loan is equal to the book value of the loan). Assume the Mr. Agirich has already paid the annual loan payment at the end of the 15th year.
E. Originally Mr. Agirich decided not to assign a cost for keeping the dogs. How much could Mr. Agirich pay for the dogs each year and still have this be an acceptable investment?
3. You have a chance of a lifetime (or at least your "friend" says so). Your friend has just received permission to sell "Snow Cones" on TAMU campus for two years. He wants you to be his partner and this is the deal. You can buy a "Snow Cone" machine for $5,000 and probably sell it for $4,000 in two years. The IRS will allow this machine to be depreciated using straight-line for 5 years. You anticipate that you can sell 7,000 Snow Cones at $0.50 per cone and it will cost you $0.35 per cone to make (including labor). You can borrow $4,000 if the loan is fully amortized over two years at 12 percent. Assume that you have other investment opportunities that promise to yield 10 percent, and you are in the 15 percent tax bracket. [SHOW ALL YOUR WORK]
A. List the relevant information, layout the cash flows, and calculate the net present value.
B. Is this a good investment? Explain?
C. If you take out the loan, will it be self liquidating? Explain?
D. How many snow cones would you have to sell for this investment to break-even (NPV=0) holding everything else constant?
4. Suppose Mr. Agirich has decided to buy or lease a center pivot irrigation system but can’t decide between leasing, or buying a new or used system. Mr. Agirich has determined that the NPV(new)=$4,500 and the NPV(used)=$2,500. Mr. Agirich wants to chose the new system because it has a higher NPV but is not sure because he has heard that NPV is not the correct criterion for investment comparisons if the investments have different economic lives. Suppose Mr. Agirich learns that you have taken a financial management course at TAMU and has asked you to help him decide whether to buy the new or used irrigation system. He provides the additional information:
Mr. Agirich requires at least a 15% pre-tax rate of return on investments, the marginal tax rate is 40%, the expected rate of inflation is 3.8%, the economic life of the new system is 15 years and the economic life of the used system is 6 years.
Should Mr. Agirich buy the new or used irrigation system? Show your work.
5. Mr. Agirich of Aggie Farms has the opportunity to buy a parcel of land next to his base operation. The land sells for $1,000 per acre. The Mr. Agirich anticipates that his marginal tax rate will be 20%. Mr. Agirich requires at least a 12.5% pre-tax return on equity capital. After several days of hard and diligent work, he concludes that the net present value per acre of land is -$50. What is the maximum bid price of the land per acre (i.e., what the most money Mr. Agirich should pay for this land)?
6. You have the opportunity to buy an apartment complex. After spending days gathering information you project that the net annual after-tax cash flows generated by the apartment investment is $12,000 (this will be received each year at the end of the year). You plan to sell the apartment complex in 20 years and you believe that the annual after-tax cash flow in the 20th year will be $138,000 from selling the apartment complex and $12,000 from operations. How much should you be willing to pay for the apartment complex if you require at least a 10% after-tax return on equity capital? Assume that you will not need to borrow money.
7. Mr. Agirich of Aggie Farms has decided to buy or lease a tractor. Mr. Agirich requires at least a 10% after-tax return on equity capital and is in the 15% tax bracket. If Mr. Agirich buys the tractor, he plans to keep it for 8 years. He has already estimated the net present value of buying the tractor to be -$15,000 after omitting the cash flows common with the lease arrangement. The local implement dealership has also agreed to lease a comparable tractor to Aggie Farms. The financial lease is a 3 year lease with annual lease payments of $3,300 paid at the beginning of each year (a lease payment is tax deductible; assume it can be claimed at the beginning of each year). Should Mr. Agirich buy or lease the tractor?
8. Eureka. Your friend has an investment opportunity for you he says you can't pass up. For just $4,000 you can buy a computer, printer and software that will do financial plans for farmers. Your friend will do all the work selling the service and preparing the reports for clients. You have to provide the capital. It is estimated that this business will bring in $14,000 of receipts in real dollars this year and the next (end of year cash flow for two years). The operating expenses is expected to be $12,000 in real dollars each year to pay your friend wages and out-of-pocket expenses. You expect that the computer can be sold in two years for $500 in real dollars. Your lender will lend you $3,000 and the loan will be fully amortized at 10% over 5 years. The outstanding loan balance must be paid as a balloon payment in the year the business is sold. Assume that inflation will be 4% per year, operating receipts, operating expenses, and terminal value will increase at the rate of inflation, the risk-free, pretax discount rate is 12.5%, a 5% risk premium is required for this type of investment, the marginal tax rate is 20%, and the IRS will allow you to depreciate this investment over 6 years (use straight-line). If you plan to liquidate this business in two years, is this an acceptable investment? (A capital budgeting worksheet is attached).
9. Suppose Mr. Agirich is considering the purchase or lease of a mechanical post hole digger. His marginal tax rate is 40% and he requires a pre-tax rate of return of 10%. The useful life of the digger is 5 years. Mr. Agirich calculates the net present value of the digger over the five years to be $-6,000 if it is purchased (cashflows common with leasing were omitted). Mr. Agirich can also obtain the digger through a financial lease. The financial lease is a 5 year lease with annual lease payments of $2,000 paid at the beginning of each year (a lease payment is tax deductible; assume it can be claimed at the beginning of each year). Should Mr. Agirich buy or lease the digger?
10. A farmer buys a tractor for $40,000. If the farmer borrows $35,000 and takes $5,000 from savings to pay the down payment, by how much will the ending cash balance (recorded on the cash flow statement) decrease?
11. Mr. Agirich of Aggie Farms bought a combine 2 years ago for $70,000. He believes he could sale it today for $60,000. He depreciates the combine for accounting purposes using the straight line method over 10 years. State the two basic methods he can use to value the combine today and show the value using the two methods on a simple balance sheet.
12. Calculate the market value of a bond that matures in 10 years, has a par value of $1,000, pays a coupon of 8 percent semiannually (remember the 8% is an annual rate), and has a market rate of 10%. Show time line and factors.
13. Suppose you buy a new tractor for $100,000. What will the after-tax terminal value of this tractor be in 5 years if you can sell the tractor for $60,000 in five years and the IRS will allow you to depreciate the tractor, using straight-line, over 10 years. Assume that your marginal tax rate is 30%.
14. Suppose you borrow $5,000 from the bank. The loan is fully amortized at a 5% interest rate over 10 years and you expect your marginal tax rate to be 20% over the next 10 years. Calculate your tax savings in the second year from the reduction in taxable income due to the interest payment on the loan in the second year. Show all your work.
15. Suppose you borrow $5,000 from the bank. The loan is fully amortized at a 5% interest rate over 10 years and you expect your marginal tax rate to be 20% over the next 10 years. Calculate your tax savings in the second year from the reduction in taxable income due to the interest payment on the loan in the second year. Show your work.
16. Calculate the net present value of an acre of land given the following information.
|Required information |
|per acre of land |
|Purchase Price |$800 |
|Operating Receipts |$1,000 |
|Operating Expenses |$900 |
|Terminal Value |$950 |
|Marginal tax rate |0% |
|Pretax discount rate |10% |
|Life of Investment |15 years |
|Inflation Rate |0% |
17. A farmer has just purchased a tractor for $60,000. He expects to sell the tractor in 10 years for $10,000 in today's dollars (real) but also anticipates that used tractor prices will increase at the current rate of inflation of four percent. If this farmer is in the 15 percent marginal tax bracket and IRS allows tractors to be depreciated over five years, calculate the after-tax nominal terminal value.
18. A farmer is contemplating the purchase of a grain storage bin for $30,000. He plans to calculate the Net Present Value of the investment but is having a hard time deciding what the appropriate discount rate is to use. He has relatively risk-free investment opportunities that promise to pay 8 percent. He also believes that an appropriate risk premium for the storage facility would be 2 percent. If the farmer is in the 15 percent marginal tax bracket, calculate the appropriate discount rate.
19. A farmer has been given the opportunity to become a part owner in a local fertilizer business for $60,000. If the farmer becomes an owner of the fertilizer business, he will receive $5,000 each year from the firm's profits. In addition, the farmer will receive a discount on fertilizer which he believes will reduce his fertilizer costs by $1,600 per year. The farmer plans to retire in 20 years and thinks he can sell his equity in the fertilizer business for $60,000. The initial cost would come from savings.
A. Calculate the Net Present Value.
B. Calculate the Internal Rate of Return.
C. Would this be a good investment if the farmer has other investment alternatives that promise to pay 10 percent? Why?
20. Calculate the net present value (discount rate = 10%) for an investment you can buy for $1,000 and will return the following net cash flows:
| Years | | | | | |
|0 |1 |2 |3 |4 |5 |
| |$300 |$300 |$300 |$300 |$500 |
21. Suppose you buy a tractor for $50,000 today and plan to sell it for $10,000 in 10 years. Also suppose that the IRS will allow you to depreciate the tractor using straight-line over 5 years and your marginal tax rate is 40%. If you require a pre-tax 10.5% return to capital, and a 2.0% risk premium, what is the present value of the tax savings from depreciation over the life of this tractor.
22. Suppose you wish to buy a car today. You have two choices, buy a new car for $10,000 or buy a used car for $6,000. The new car has an economic life of 6 years and you expect that it can be sold at the end of 6 years for $2,000. If you buy the used car, you plan to sell it in 3 years and expect to receive $600. Also, you expect that the used car will require $300 more a year than the new car for maintenance. Assume your marginal tax rate equal to zero. If your opportunity cost of capital is 12%, would you choose the new or used car? (Use the back if you need more space)
23. A farmer is considering the purchase of a tractor for $60,000. He expects to sell the tractor in 10 years for $10,000 in today's (real) dollars.
A. Assuming that used tractor prices will increase at the current rate of inflation of four percent, how much will the farmer receive for the used tractor in nominal dollars at the end of 10 years?
B. Assuming that the farmer is in the 15 percent marginal tax bracket and that the IRS allows tractors to depreciated be over five years (use straight-line depreciation), how much depreciation expense can the farmer claim on his income tax statement in the 5th and 6th year?
C. Given your response in question 1.B, by how much money will the farmer's income taxes owed "Uncle Sam" be reduced in the 5th due to depreciation expenses (Tax Reduction: Depreciation)?
D. Given your responses to questions 1.A and 1.B, please calculate the after-tax nominal terminal value of the tractor.
E. Assuming that the farmer has other investment opportunities that promise to pay 10% (pre-tax) and he is in the 15 percent marginal tax bracket, what is the appropriate discount factor to use when calculating the net present value?
F. Assuming that the farmer decides to borrow $40,000 from a local bank and that the loan would be paid back (fully amortized) at 10 percent over 10 years, what would the annual loan payment be?
G. Given your response to question 1.F, how much interest would be paid the bank in the second year? (Show the amortization schedule for two years)
H. Given your response in question 1.G, by how much money will the farmer's income taxes owed "Uncle Sam" be reduced in the 2nd year due to interest expenses (Tax Reduction: Interest Payment)?
24. Suppose that you would like to borrow $100,000 for one year and two banks agree to lend you the money. Bank B will lend you the money at 12% compounded monthly and bank B will lend you the money at 12.6825% compounded annually. Principal and interest will be paid back as a lump sum at the end of the year if you borrow from bank A or bank B.
A. Calculate the combined principal and interest payment due at the end of the year for each loan.
B. Calculate the amount of interest that you would pay on each loan.
C. Calculate actuarial interest rate for each loan.
D. Calculate the annual percentage rate for each loan.
E. Calculate the effective interest rate for each loan
F. Which bank would you borrow the money from? Why?
25. Mr. Agirich of Aggie Farms is considering the purchase of a hay baler so that his son can custom bale their neighbors hay. Mr. Agirich can borrow money at 10%, requires at least a 11% pre-tax, risk free return on equity capital, requires a 4% risk premium on projects of comparable risk, has a marginal tax rate of 20%, and anticipates inflation to be 3%. Mr. Agirich estimates the after-tax net cash flows to be as follows:
|Present (0) |Year 1 |Year 2 |Year 3 |Year 4 |Year 5 |
|-$10.000 |$2,500 |$2,500 |$2,500 |$2,500 |$2,500 |
SHOW ALL WORK!
A. What is the appropriate discount rate to use when calculating the net present value?
B. Calculate the net present value.
26. Calculate the nominal value of a 5 year old hay baler if a 5 year old hay baler is valued at $5,000 today and you expect that the price of used equipment will increase at the rate of inflation. Assume that the inflation rate will be 6% over this period of time.
27. Assume that you borrow $10,000 to buy a new car. The loan is fully amortized over four years at 12% interest. Payments will be monthly. Your marginal tax rate is 15%.
Note: USPV.01,48=37.9739.
A. Calculate the interest and principal payments for the first and second months of the loan.
B. Calculate the total interest you will pay on this loan if you make all the payments over the four years.
Essay
1. Discuss under what conditions it is acceptable to omit common cash flows when calculating annuity equivalents.
2. A young farmer has an opportunity to buy a parcel of land next to his homestead and after calculating the net present value he believes it is a good investment. Explain why the farmer may choose not to buy the land.
3. Discuss why a farmer may choose to lease equipment instead of buying.
4. List the four major steps for Investment Decisions
5. Briefly explain why a young farmer may choose not to buy land even if a land investment has a positive net present value.
6. List the four steps of capital budgeting discussed in class:
A.
B.
C.
D.
7. Briefly explain what is meant by the term “maximum bid price of land.”
8. Briefly explain why common cash flows can be omitted when comparing two mutually exclusive investments.
9. Show the formula for calculating the real rate of interest as a function of the nominal rate of interest and the expected inflation rate.
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