Study Guide Chapter1 10-11

1. Study GuideChapter1 10-11 Agricultural Economics 330 Instructor: David J. Leatham

2. 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

3. 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.

4. 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).

5. 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.

6. 0 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.

7. 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

8. 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

9. 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%.

10. Question 7Answer 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.

11. 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%.

12. Question 8Answer After-tax Terminal Value = 20,000-[20,000-(60,000-30,000)].15 = 21,500 After-tax discount rate = .1(1-.15) = 0.085 or 8.5% 0 10 r = 8.5 % V0 21,500 V0 = 21,500 (1+.085)-10 = 9,509.14

13. 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

14. 0 1 2 24 ... r = 7/2 %= 3.5 % 50 50 50 MV Question 9Part A Calculate the market value (price) of the bond today if the bond’s market rate (yield) is 7%. 1,000 Market Value = price = 50[USPV3.5%,24] + 1,000 (1+.035)-24 =$1,240.88

15. 0 1 2 10 ... r =4/2 %= 2 % 50 50 50 MV Question 9Part B Calculate the market value (price) of the bond in five years if the bond’s market rate is 4%. 1,000 Market Value = price = 50[USPV2%,10] + 1,000 (1+.02)-10 =$1,269.48

16. Question 9Part 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)

17. 0 1 2 10 ... r =8/2 %= 4 % 50 50 50 - 1,240.88 1,363.19 NPV = -1,240.88 + 50[USPV4%,10] + 1,363.19 (1+.04)-10 = -1,240.88 + 1,326.47 = 85.59

18. 0 1 2 10 ... r =?/2 %= ? % 50 50 50 - 1,240.88 1,363.19 NPV = 0 = -1,240.88 + 50[USPVr%,10] + 1,363.19 (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%.

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

20. 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

21. 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%

22. 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 .

23. Yield = 12%

24. 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.

25. ... 0 1 2 5 ... r = ? % 140 140 140 -500 V0 = A [USPVr,N] Present Value of an Uniform Annuity 500= 140 [USPVr%, 5] r = 12.38% 5 ? -500 140 0 i% N PV PMT FV Agricultural Finance

26. 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%.

27. 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

28. 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.

29. Annual Depreciation (D) = 75,000/7 = 10,714.29 Annual Tax Savings = mD = 10,714.29 * .28 = 3,000 After-tax discount rate = .16(1-.28) =0.1152 or 11.52%

30. ... 0 1 2 7 8 9 10 ... r = 11.52 % V0 3,000 3,000 0 0 0 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] V0 = 13,902.2 7 11.52 ? 3,000 0 i% N PV PMT FV

31. 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.

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

33. 0 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 (1+.1152)-10 V0 = 2,419.94 10 11.52 V0 0 7,200 i% N PV PMT FV 19 01/09/80 Agricultural Finance

34. 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%.

35. After-tax discount rate = 0.18(1-.28) = 0.1296 or 12.96% NPV = -85,000 + 15,000 [USPV12.96%,5] + 59,000(1+.1296)-6 = -85,000 + 52,810 + 28,399 =-3,790.9 NPV = -3,790.9

36. 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%. B. Explain and show how to calculate the internal rate of return (IRR) on this investment (estimate within ½% accuracy).

37. 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 + 15,000 [USPVr%,5] + 59,000(1+r)-6 r NPV 12.96 -3790 11% 1,982 12% -1,037 11.5% 452 ---------------------- 11.65 0 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%.

38. 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%. 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.

40. 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%. D. Is this an acceptable investment? Why?

41. 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%.

42. 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%.

43. ... 0 1 2 2*7=14 ... r = 12/2 = 6 % MV 40 40 40 1,000 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 • MV=814.10 14 • 6 ? 40 1000 i% N PV PMT FV 28 01/16/97 Agricultural Finance

44. 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%.

45. ... 0 1 2 2*4=8 ... r = i/2 = ? % -1060 40 40 40 814.1 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] +814.1(1+r)-8 • r=0.97% & i=1.9% 8 • ? -1,060 40 814.1 i% N PV PMT FV 34 01/16/97 Agricultural Finance

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

47. Answer 16 • . Not always. This measure and rule ignores the time value of money. If you paid $100 for an investment today and received $101 10 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.

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

49. 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.

50. 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)?