Corpfin Mod 11: Accounting Income and Economic Income

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NEAS	NEAS posted 19 Years Ago #2612 #
Supreme Being Group: Administrators Posts: 4.3K, Visits: 1.3K	Corporate Finance, Module 11, “Maximizing Net Present Value” Accounting Income and Economic Income (The attached PDF file has better formatting.) Suppose the initial investment is $100,000. The cash inflows are zero for the first four years and $200,000 for the last year. The opportunity cost of capital is 10%. We use pro-rata depreciation over the five years. A. What is the accounting income each year? B. What is the economic income each year? Part A: Using the definitions in the textbook, the accounting depreciation is $20,000 each year. The accounting income is –$20,000 for each of the first four years and +$180,000 for the fifth year. Part B: The present value at inception of the final cash flow is $200,000 / 1.15 = $124,184. The economic income is $124,184 × 10% = $12,418 the first year, and so forth. Year Beginning PV Ending PV Economic Income 1 $124,184 $136,603 $12,418 2 $136,603 $150,263 $13,660 3 $150,263 $165,289 $15,026 4 $165,289 $181,818 $16,529 5 $181,818 $200,000 $18,182 Question: The accounting income makes sense. The first four years, the initial investment depreciates but the first gets no cash; all the cash comes the last year. The economic income is not related to the actual transfers of cash. Answer: This type of project is not uncommon; sometimes the accounting pattern makes sense and sometimes the economic income pattern makes sense. Let’s use an example where the pattern of economic income makes sense, and where GAAP adopts a similar pattern. Illustration: Sara, an elderly and ill woman, needs a full time nurse. She has five more years to live, and she hires Hagar to take care of her for these five years, with payment of $200,000. In addition, Hagar receives food and board and a market based compensation as a live-in nurse; her work effort and the wages and not included in our illustration. Hagar spends $100,000 of her own money on the round-trip camel fare from Egypt to Canaan. Hagar’s opportunity cost of capital is 10% per annum. The net present value is $24,184, so it is a positive NPV project. Hagar recognizes the $24,184 at inception, when she and Sara agree on the terms of employment. The $100,000 investment is a five year investment, so the economic income that compensates for this investment is spread over five years. The accounting income is the reverse. If the camel fare is depreciated over five years, or $20,000 a year, the return on the investment for the five years is ● Year 1: –$20,000 / $100,000 = –20.00% ● Year 2: –$20,000 / $80,000 = –25.00% ● Year 3: –$20,000 / $60,000 = –33.33% ● Year 4: –$20,000 / $40,000 = –50.00% ● Year 5: +$180,000 / $20,000 = 900.00% If the entire camel fare is written off the first year, the returns are –100% the first year, zero for the intervening three years, and +∞ the last year. Question: The economic income increases from year to year; shouldn’t it stay the same? Answer: In deflated terms, the economic income is the same from year to year. A nominal dollar is worth less and less each year, so it seems as though the economic income increases from year to year. Question: Hagar and Sara is just a heuristic example. Do we see this in real life? Answer: This is common in the pharmaceutical industry, commercial aircraft (design and building) industry, and any industry with long lead times. A firm may spend $1 billion developing a new drug or a new aircraft. It gets a large return after ten years if the product is successful; it gets nothing if the product is not successful. Attachments CorpFinance.Module11.econ.inc.pdf (596 views, 46.00 KB) Edited 6 Years Ago by NEAS 0
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Amy	Amy posted 19 Years Ago #3890 #
Forum Newbie Group: Forum Members Posts: 2, Visits: 1	On part A: Why isn't the accounting income for year 5 = 200,000 - 20,000 = 180,000? [NEAS: Thank you; typo is corrected now.] Amy 0
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student	student posted 19 Years Ago #4496 #
Forum Newbie Group: Forum Members Posts: 1, Visits: 1	Amy, You are right, it should be $180,000. The reason why: assuming a straight line depreciation for the $100,000, the book depreciation per year is $20,000; then 1st year: BV_0=100,000, BV_1=80,000, C_1=0 so the accounting income is C_1+(BV_1-BV_0)= -20,000, the book depreciation; 2nd year: BV_1=80,000, BV_2=60,000, C_2=0 so the accounting income is C_2+(BV_2-BV_1)= -20,000, the book depreciation; the reasoning for years 3 and 4 is similar, so the accounting income for each of these two years is also -20,000; 5th year: BV_4=20,000, BV_5=0, and C_5=200,000, so the accounting income is C_5+(BV_5-BV_4)=200,000-20,000=180,000. I hope this helps. 0
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NEAS	NEAS posted 18 Years Ago #6021 #
Supreme Being Group: Administrators Posts: 4.3K, Visits: 1.3K	Economic Depreciation Cash Flows Jacob: Which cash flows do we consider for economic depreciation? And what present value factors do we use? Rachel: Suppose the cash flows are at time t (t = 0, 1, 2, …), where time t is the end of year t. Economic depreciation in year N is the present value right after the cash flow at time N-1 minus the present value right after the cash flow at time N. ~ The cash flow at time N is included in the beginning present value but not the ending present value. ~ The remaining cash flows are discounted for one more year at the beginning of the year than at the end of the year. These two principles are used in many economic depreciation problems. Accounting vs Economic Depreciation Jacob: How does economic depreciation relate to accounting depreciation? I’ve taken an accounting course in college, and depreciation is unrelated to cash flows. Rachel: The firm uses up its assets over time. Accounting depreciation is a charge to income for the assets that are used up. Cash accounting: The entire cost of the asset is a charge to income when it is bought. Accrual accounting: The cost of the asset is charged to income over its useful life. Illustration: A firm buys a machine on January 1, 20X0, for $100,000 and depreciates the machine over ten years. Each year it writes off $10,000 as a charge to income. The depreciation schedule should match the use of the item. Jacob: What is the rationale for a depreciation schedule? Rachel: Assets represent a source of future cash flows. As time goes by, the future cash flows have less value, so the asset depreciates. In the illustration above, the asset has ten years of future cash flows at inception. A year later, it has nine years of future cash flows. Jacob: What is the rationale for economic depreciation? How does economic depreciation differ from accounting depreciation? Rachel: Economic depreciation differs from accounting depreciation two ways: (1) present values vs nominal values; (2) market value vs book value Economic depreciation uses the present value of future cash flows, not the nominal value. Accountants depreciate the book value (ledger value) of an asset, which is its cost. Economists depreciate the market value of an asset, which is the present value of its future cash flows at the appropriate capitalization rate. Cash Flow Patterns Jacob: Do accountants use the cash flow patterns? Rachel: In theory, accountants use the pattern of future cash flows, but not the amount of future cash flows. Illustration: An asset bought for $30,000 on January 1, 20X5, has a useful life of two years. Its future cash flows will be twice as high in 20X5 as in 20X6. In theory, the accountant should depreciate two thirds of the cost in 20X5 ($20,000) and one third of the cost in 20X6 ($10,000). In practice, we can’t estimate future cash flows from each asset over its entire life, so we use standard depreciation schedules (straight line, double declining, etc.). Definitions of Depreciation Jacob: The accountant defines depreciation as writing off the value of an asset as it is used up. Should we depreciate the cost of the asset? What does this have to do with future cash flows? Rachel: The economist doesn’t care about the cost of the asset. Once the asset is bought, its purchase price is a sunk cost. It is past history, unrelated to the value of the asset. Jacob: How does the economist define depreciation? Rachel: Depreciation is the change in the market value of the asset over time. The asset can be anything, whether tangible (buildings machinery) or intangible (customer lists, patents, projects). Jacob: By change in value, I presume you mean decrease in value. Rachel: For most assets (projects), the present value of future cash flows decreases over time. For some scenarios, the present value of the future cash flows increases. A policyholder buys a single premium life insurance policy with a $100,000 face value. As each year goes by, the present value of the future cash flow increases, because the date of death become closer. 0
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NEAS	NEAS posted 6 Years Ago #16321 #
Supreme Being Group: Administrators Posts: 4.3K, Visits: 1.3K	+x NEAS - 12/13/2006 1:17:50 PM Economic Depreciation Cash Flows Jacob: Which cash flows do we consider for economic depreciation? And what present value factors do we use? Rachel: Suppose the cash flows are at time t (t = 0, 1, 2, …), where time t is the end of year t. Economic depreciation in year N is the present value right after the cash flow at time N-1 minus the present value right after the cash flow at time N. ~ The cash flow at time N is included in the beginning present value but not the ending present value. ~ The remaining cash flows are discounted for one more year at the beginning of the year than at the end of the year. These two principles are used in many economic depreciation problems. Accounting vs Economic Depreciation Jacob: How does economic depreciation relate to accounting depreciation? I’ve taken an accounting course in college, and depreciation is unrelated to cash flows. Rachel: The firm uses up its assets over time. Accounting depreciation is a charge to income for the assets that are used up. Cash accounting: The entire cost of the asset is a charge to income when it is bought. Accrual accounting: The cost of the asset is charged to income over its useful life. Illustration: A firm buys a machine on January 1, 20X0, for $100,000 and depreciates the machine over ten years. Each year it writes off $10,000 as a charge to income. The depreciation schedule should match the use of the item. Jacob: What is the rationale for a depreciation schedule? Rachel: Assets represent a source of future cash flows. As time goes by, the future cash flows have less value, so the asset depreciates. In the illustration above, the asset has ten years of future cash flows at inception. A year later, it has nine years of future cash flows. Jacob: What is the rationale for economic depreciation? How does economic depreciation differ from accounting depreciation? Rachel: Economic depreciation differs from accounting depreciation two ways: (1) present values vs nominal values; (2) market value vs book value Economic depreciation uses the present value of future cash flows, not the nominal value. Accountants depreciate the book value (ledger value) of an asset, which is its cost. Economists depreciate the market value of an asset, which is the present value of its future cash flows at the appropriate capitalization rate. Cash Flow Patterns Jacob: Do accountants use the cash flow patterns? Rachel: In theory, accountants use the pattern of future cash flows, but not the amount of future cash flows. Illustration: An asset bought for $30,000 on January 1, 20X5, has a useful life of two years. Its future cash flows will be twice as high in 20X5 as in 20X6. In theory, the accountant should depreciate two thirds of the cost in 20X5 ($20,000) and one third of the cost in 20X6 ($10,000). In practice, we can’t estimate future cash flows from each asset over its entire life, so we use standard depreciation schedules (straight line, double declining, etc.). Definitions of Depreciation Jacob: The accountant defines depreciation as writing off the value of an asset as it is used up. Should we depreciate the cost of the asset? What does this have to do with future cash flows? Rachel: The economist doesn’t care about the cost of the asset. Once the asset is bought, its purchase price is a sunk cost. It is past history, unrelated to the value of the asset. Jacob: How does the economist define depreciation? Rachel: Depreciation is the change in the market value of the asset over time. The asset can be anything, whether tangible (buildings machinery) or intangible (customer lists, patents, projects). Jacob: By change in value, I presume you mean decrease in value. Rachel: For most assets (projects), the present value of future cash flows decreases over time. For some scenarios, the present value of the future cash flows increases. A policyholder buys a single premium life insurance policy with a $100,000 face value. As each year goes by, the present value of the future cash flow increases, because the date of death become closer. 0
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Jennifer Blythe	J Jennifer Blythe posted 5 Years Ago #16489 #
J Junior Member Group: Forum Members Posts: 19, Visits: 140	If Economic Income is defined as CF - Economic Depreciation, then why isn't the economic income for year 5 = 200,000 + 18,182 = 218,182? 0
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NEAS	NEAS posted 5 Years Ago #16490 #
Supreme Being Group: Administrators Posts: 4.3K, Visits: 1.3K	+x Jennifer Blythe - 5/8/2019 8:04:55 PM If Economic Income is defined as CF - Economic Depreciation, then why isn't the economic income for year 5 = 200,000 + 18,182 = 218,182? Economic depreciation is the negative of the change in the present value. 0
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Jennifer Blythe	J Jennifer Blythe posted 5 Years Ago #16491 #
J Junior Member Group: Forum Members Posts: 19, Visits: 140	Yes, but the solution offered didn't include the cash flow for year 5 in computation of economic income. I am not sure why. 0
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NEAS	NEAS posted 5 Years Ago #16493 #
Supreme Being Group: Administrators Posts: 4.3K, Visits: 1.3K	+x Jennifer Blythe - 5/8/2019 10:07:05 PM Yes, but the solution offered didn't include the cash flow for year 5 in computation of economic income. I am not sure why. Cash flow = 200,000; economic depreciation = – (0 – 181,818) = 181,818 (the ending present value is zero after the cash flow is received); economic income = 200,000 – 181,818 = 18,182. 0
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