Homework Questions pg 67-68

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Southern Arkansas University *

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4043

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Finance

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Feb 20, 2024

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Sarah Barkhimer Ag Finance February 9, 2024 Homework Questions pg. 67-68 1. A cattle rancher had average total assets of five million dollars and average total liabilities of two million dollars during the preceding year. Her cost of debt for that year was 7.5% and she estimates her cost of equity to be 10%. What was this rancher’s weighted average cost of capital expressed as a percentage? a. K c = w d K d + w e K e b. w d = total liabilities/total assets = $2,000,000/$5,000,000 = 0.4 c. w e = total owner’s equity/total assets = $3,000,000/$5,000,000 = 0.6 i. assets = liabilities + owner’s equity ii. Owner’s equity = assets – liabilities iii. $5,000,000 - $2,00,000 = $3,000,000 d. K d = 7.5% = 0.075 e. K e = 10% = 0.1 f. K c = (0.4)(0.075) + (0.6)(0.1) = 0.03+0.06 = 0.09 = 9% 2. Calculate the payback period for a dry-bean harvester that required an initial cash outlay of $250,000. The after-tax net cash flows from this harvester will be $60,000 during the first year; $50,000 for each of the second, third, and fourth years; and $30,000 for the fifth, sixth, seventh, and eighth years. In year eight, the harvester can be sold for an after-tax salvage value of $40,000. Year Annual Net Cash Flows Running Total 1 $60,000 $60,000 2 $50,000 $110,000 3 $50,000 $160,000 4 $50,000 $210,000 5 $30,000 $240,000 6 $30,000 $270,000 7 $30,000 $300,000 8 $30,000 $330,000 a. The payback period for a dry-bean harvester will be 6 years because the money spent on the harvester will be recouped after the sixth year. 3. What is the simple rate of return on an almond hulling business you can buy for $1,500,000 that will generate a net income of $200,000 per year. a. Simple rate of return = net income /initial investment = $200,000/$1,500,000 = 0.1333 = 13.3%

Sarah Barkhimer Ag Finance February 9, 2024 4. A farm building costs $54,000 to build today and will earn after-tax net cash flows of $16,000 per year for five years. There is no salvage value on the building at the end of the five-year life, and the farmers’ cost of capital is 9%. a. What is its net present value? i. Original Investment $54,000 Cash Flow NPV Value 9% Present Value Year 1 $16,000 0.9174 14,678.40 Year 2 $16,000 0.8417 13,467.20 Year 3 $16,000 0.7722 12,355.20 Year 4 $16,000 0.7084 11,334.40 Year 5 $16,000 0.6499 10,398.40 Total 62,233.60 Less Initial Cost -54,000 NPV $8,233.60 b. What is the benefit-cost ratio of this building at a cost of capital of 9%? i. Benefit Cost Ratio = Present Value of Future Benefits/Initial Investment = (NPV + Initial Investment)/Initial Investment ii. ($8,233.60+$54,000)/$54,000 = 1.15 c. Calculate the internal rate of return on this building. Use the trial- and-error method and show all of your iterative steps. i. Since 9% gave us an NPV of $8,233.6, our first trial-and- error number will be 13%. We will plug it into the table from part A. Original Investmen t Cash Flow NPV Value 13% Present Value Original Investme nt Cash Flow NPV Value 15% Present Value Year 1 $16,000 0.885 14,160 Year 1 $16,000 0.8696 13,913.60 Year 2 $16,000 0.7831 12,529.60 Year 2 $16,000 0.7561 12,097.60

Sarah Barkhimer Ag Finance February 9, 2024 Year 3 $16,000 0.6931 11,089.60 Year 3 $16,000 0.6575 10,520 Year 4 $16,000 0.6133 9,812.80 Year 4 $16,000 0.5718 9,148.80 Year 5 $16,000 0.5428 8,684.80 Year 5 $16,000 0.4972 7,955.20 Total $56,276.8 Total 53635.2 Less Initial Cost -54,000 Less Initial Cost -54000 NPV $2,276.8 NPV -364.80 Since our NPV is way too high with 13%, but too low with 15%. We can assume the IRR will be approximately 14.5%. 5. What is the internal rate of return (to the nearest one-half percent) on an investment costing $500,000 and having expected future after-tax net cash flows of: Year Net Cash Flow ($) 1 100,000 2 150,000 3 150,000 4 300,000 (includes salvages) Use the trial-and-error method and write out all your work. Hint: start at 10%. Original Investme nt Cash Flow NPV Value 10% Present Value Original Investment Cash Flow NPV Value 12% Present Value Year 1 $100,000 0.9091 90,910 Year 1 $100,000 0.8929 89,290 Year 2 $150,000 0.8264 123,960 Year 2 $150,000 0.7972 119,580 Year 3 $150,000 0.7513 112,695 Year 3 $150,000 0.7118 106,770 Year 4 $300,000 0.683 204,900 Year 4 $300,000 0.6355 190,650 Total 532,465 Total 506,290 Less Initial Cost -500,000 Less Initial Cost -500,000 NPV 32,465 NPV 6,290 Original Investment Cash Flow NPV Value 13% Present Value Year 1 $100,000 0.885 88,500 Year 2 $150,000 0.7831 117,465

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Sarah Barkhimer Ag Finance February 9, 2024 Year 3 $150,000 0.6931 103,965 Year 4 $300,000 0.6133 183,990 Total 493,920 Less Initial Cost -500,000 NPV -6,080 Based on the work shown in these tables, we can estimate our IRR will be approximately 12.5%. 6. Your father has inherited lots of money, and he has always wanted to own a farm. He is considering the purchase of several farm properties. Additionally, your father expects to sell the farm and retire after owning the farm for a full fifteen years. One of the farms he is looking at has a purchase price of $800,000, after-tax development costs of $40,000 per year for the first five years, and after-tax net cash inflows of $35,000 per year for years six through fifteen. To determine the selling price of the farm at the end of the fifteenth year, assume that the farm will increase in value at a rate of 5% per year. Using a 7% cost of capital, calculate the net present value and benefit- cost ratio of this farm investment. Show your work. Explain whether or not and why you should keep this farm among your investment alternatives. i. Original Investmen t $800,000 Cash Flow NPV Value 7% Present Value Original Investmen t Cash Flow NPV Value 7% Present Value Year 1 40,000 0.9346 37,384 Year 9 35,000 0.5439 19,036.50 Year 2 40,000 0.8734 34,936 Year 10 35,000 0.5083 17,790.50 Year 3 40,000 0.8163 32,652 Year 11 35,000 0.4751 16,628.50 Year 4 40,000 0.7629 30,516 Year 12 35,000 0.444 15,540 Year 5 40,000 0.713 28,520 Year 13 35,000 0.415 14,525 Year 6 35,000 0.6663 23,320.50 Year 14 35,000 0.3878 13,573 Year 7 35,000 0.6227 21,794.50 Year 15 35,000 0.3624 12,684 Year 8 35,000 0.582 20,370 Total 339,271 Less Initial Cost -800,000

Sarah Barkhimer Ag Finance February 9, 2024 NPV -460,730 BCR = ( NPV + Initial Investment)/Initial Investment = (-460,730 +800,000) / 800,000 = 0.424 Since the NPR is a negative number, and the BCR is so low, t his would not be a good investment. 7. Within a recent tax year, a farmer has taxable cash revenues of $120,000, taxable cash expenses of $70,000, and depreciation expenses of $24,000. The applicable tax rate was 36%. With the tax savings from depreciation included, what was the total after-tax cash flow for this year? a. $120,000 - $70,000 - $24,000 = $26,000 b. ($26,000)(1 - .36) = $16,640 c. $120,000 - $70,000 + $16,640 =$ 66,640 8. An agricultural accounting firm needs three new copy machines. If it leases the copiers on a five-year lease, five rental payments of $21,000 each will be made at the beginnings of the years. The firm is in the 30% tax bracket and has cost of capital at 9%. a. Prepare a table similar to table 4.3 to find the present value of the cash flows for the lease option. Year Rent Tax Benefit 30% Net Cash Flow Present Value Factor 9% Present Value (1) (2) (3) (4) (5) (6) 1 -21,000 +6300 -14,700 0.9174 -13,485.78 2 -21,000 +6300 -14,700 0.8417 -12,372.99 3 -21,000 +6300 -14,700 0.7722 -11,351.34 4 -21,000 +6300 -14,700 0.7084 -10,413.48 5 -21,000 +6300 -14,700 0.6499 -9,533.53 Present Value of Cash Flows -57,156.82

Sarah Barkhimer Ag Finance February 9, 2024 b. The accounting firm could purchase the copiers on credit. The original cost for all three machines is $82,500, and the total down payment will be $22,500. Amortized loan payments of $15,828each will be made at the ends of years one through five, and the loan carries an interest rate of 10%. Depreciation expense in years one through six will be: $12,375, $21,038, $14,726, $13,745, $13,745, and $6,872, respectively. The tax rate is once again 30%, and the cost of capital is 9%. Prepare a table similar to table 4.4 to find the present value of the cash flows for the credit purchase option. Year Principal Interest Depreci ation Tax Benefit Net Cash Flow Present Value Factor Present Value (1) (2) (3) (4) (5) (6) (7) (8) 0 -9,000 1 -15,828 12,375 0.9174 2 -15,828 21,038 0.8417 3 -15,828 17,726 0.7722 4 -15,828 13,745 0.7084 5 -15,828 13,745 0.6499 6 -15,828 6,872 0.9174 Present Value of cash flows c. Discuss which option the accounting firm should choose – leasing the copiers or buying them on credit. Include any other factors that might influence their decision in your discussion.

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