Chapter 2: Capital-Budgeting Principles and Techniques
Chapter 2: Capital-Budgeting Principles and Techniques
QUESTIONS
1. a. What is the relationship between accounting income and economic profit?
Answer: Accounting income is calculated by taking revenues and subtracting all cash and non-
cash expenses (such as depreciation). Accounting income also often recognizes losses for tax
purposes as well, even though the economic loss may have taken place at another time.
Economic profit is the sum of the present values of all the cash flows net of expenses generated
by the firm’s actions. Economic profit measures true increments to value, but is hard to
measure. Accounting profit is correlated with economic profit, but not perfectly so. Accounting
profit can be measured much more easily.
b. What is the relationship between accounting rate of return and economic rate of return?
Answer: The accounting rate of return is the ratio of after-tax profit to average book investment.
Economic rate of return is the ratio of after-tax economic profit to the market value of the
investment. Economic profit equals cash accruals to the asset combined with changes in its
market value.
2. In 1991, AT&T laid a transatlantic fiber optic cable costing $400 million that can handle
80,000 calls simultaneously. What is the payback on this investment if AT&T uses just half
its capacity while netting one cent per minute on calls?
Answer: $210 Million per year assuming the half capacity is for 24 hours a day, 365 days per
year. The annual payback is then 53%.
3. The satisfied owner of a new $15,000 car can be expected to buy another ten cars from the
same company over the next 30 years (an average of one every three years) at an average
price of $15,000 (ignore the effects of inflation). If the net profit margin on these cars is 20
percent, how much should an auto manufacturer be willing to spend to keep its customers
satisfied? Assume a 9 percent discount rate.
Answer: At a 20 percent profit margin, the auto company will earn an annuity of about $3,000
every three years for the next 30 years. Discounted at 9 percent, this annuity is worth $9,402,
assuming that the first new car is purchased three years from today. Hence, an investment to
keep customers satisfied will have a positive NPV as long as the amount spent is less than
$9,402. Thus, a car company should be willing to spend up to $9,402 in present value terms to
keep its customers satisfied. A trick is available to calculate the present value of this annuity.
Recognize that an annuity received every three years for 30 years and discounted at 9 percent is
equivalent to a 10-year annuity discounted at 29.5029 percent since each cash flow term is
discounted at (1.09)3 = 1.295029.
,Chapter 2: Capital-Budgeting Principles and Techniques
4. Demonstrate that the following project has internal rates of return of 0 percent, 100 percent,
and 200 percent.
Year 1 2 3 4
Cash flow –$1,200 +7,200 –13,200 +7,200
Answer: To demonstrate that an IRR calculation is valid, compute the net present value at the
IRR. A valid IRR yields NPV = 0.
Year Cash Flow PV@0% PV@100% PV@200%
1 -1,200 -1,200 -600 -400.00
2 +7,200 +7,200 +1,800 +800.00
3 -13,200 -13,200 -1,650 -488.89
4 +7,200 +7,200 +450 +88.89
Total 0 0 0 0
5. During 1990, Dow Chemical generated the following returns on investment in its different
business units:
Business Unit Return on Investment
(%)
Plastics 16.6
Chemicals/Performance 16.7
Products
Consumer Specialties 12.7
Hydrocarbons/Energy 5.2
Other 1.6
Dow Chemical overall 11.8
Given these returns, which of the business units should Dow invest additional capital in? What
additional information would you need in order to make that decision?
Answer: These figures tell you what Dow earned in 1990. In order to decide on future
investments, you need the following information:
1. Whether these returns are representative of those expected to be earned in the
future in these different divisions. What matters for investment decisionmaking are
projected future returns, not past returns. To the extent that these returns vary widely
from year to year—which they do in the chemical business—historical return data for
,Chapter 2: Capital-Budgeting Principles and Techniques
one year are meaningless. One reason these data may be misleading is that they are based
on historical cost figures for investment. You really want to calculate returns on the
replacement cost of assets. Inflation will cause asset values to be understated, which will
lead the return on investment to be overstated.
2. The cost of capital for these divisions. Each division is likely to have its own risk
and, hence, its own cost of capital. A high return could just indicate a high degree of risk
and, therefore, a high required return. What matters is the projected return relative to the
cost of capital. A high projected return that is less than the risk-adjusted cost of capital
will yield a negative NPV investment. Conversely, a low projected return that exceeds
the cost of capital will yield a positive NPV investment.
3. The marginal return on investment in each division. Even if the figures for, say,
the plastics and chemical/performance products divisions exceed their cost of capital and
are representative of those expected to be earned in the future, that does not
automatically justify additional investment in those divisions. These figures tell us the
average ROI; for investment purposes you need the marginal ROI. That is, what matters
for investment purposes is not the return on past investments but the return on future
investments. As we have seen, many companies (e.g., Monsanto, Philip Morris) have
divisions that yield high returns on past investments but very low returns on incremental
investments.
4. The extent to which these divisions sell to one another. Dow Chemical is a
vertically-integrated company. Its hydrocarbons/energy unit sells to its downstream
plastics unit, which in turn sells to its consumer specialties unit. Thus, the profitability of
these units depends critically on the prices at which these internal transactions take place.
For example, the hydrocarbons/energy unit may be showing a low ROI simply because it
sells petroleum to the plastics unit at a below-market price. That is, the hydrocarbons unit
may be very profitable but its profits are showing up in the plastics unit in the form of a
low price on raw materials. This is a form of cross-subsidization. Disentangling the true
profitability of the different units of a vertically-integrated company like Dow turns out
to be a very difficult task, but it is a necessary one for capital budgeting purposes. What
matters is how profitable investments are from the standpoint of the overall company, not
from the standpoint of the units undertaking those investments.
5. The returns associated with specific assets and activities within each division.
What matters from an investment standpoint is not just how well each division can be
expected to do in the future but how well specific projects within each division can be
expected to do. For example, certain products within the profitable plastics division may
be earning a 40% return while others are only earning a 2% return. Similarly, certain
R&D investments may be expected to yield a high return relative to their riskiness,
whereas others have little chance of a significant payoff. At the same time, the low-return
hydrocarbons/energy division may have some very high-return projects, which are
masked by a lot of value-destroying activities elsewhere. Without detailed data on the
, Chapter 2: Capital-Budgeting Principles and Techniques
returns associated with each division’s various activities, customers, and products, one
can’t say where investment dollars would be best spent.
CHAPTER 2: PROBLEMS
1. A firm is considering investing in a project with the following cash flows:
Year 1 2 3 4 5 6 7 8
Net cash 2,00 3,00 4,00 3,50 3,00 2,00 1,00 1,00
flow ($) 0 0 0 0 0 0 0 0
The project requires an initial investment of $12,500, and the firm has a required rate of
return of 10 percent. Compute the payback, discounted payback, and net present value, and
determine whether the project should be accepted.
Answer: Payback period = 4 years exactly.
Discounted payback period (r = 10%) = 5.84 years.
Net Present Value (r = 10%) = $1164.70. The project should be accepted.
Intermediate Calculations:
Cash PV Cumulative
Cash Flows -12,500.00
1 2,000.00 1,818.18 1,818.18
2 3,000.00 2,479.34 4,297.52
3 4,000.00 3,005.26 7,302.78
4 3,500.00 2,390.55 9,693.33
5 3,000.00 1,862.76 11,556.09
6 2,000.00 1,128.95 12,685.04
7 1,000.00 513.16 13,198.20
8 1,000.00 466.51 13,664.70
2. The Pennco Oil Co. must decide whether it is financially feasible to open an oil well off the
coast of China. The drilling and rigging cost for the well is $5,000,000. The well is expected
to yield 585,000 barrels of oil a year at a net profit to Pennco of $5 a barrel for four years.
The well will then be effectively depleted but must be capped and secured at a cost of
$4,000,000. Pennco requires an annual rate of return of 14 percent on its investment
projects. Should Pennco open the well? (Assume all of a year’s production occurs at the end
of the year.)
Answer:
Net annual profit = 585,000($5.00) = $2.925M.
PV(Production) = $2.925M _ PVIFAr=14%,n=4 = 2.925M _ 2.9137 = $8.523M.
PV(Capping) = $4.000M _ PVIFr=14%,n=4 = 4 _ 0.5921 = $2.368M.
Chapter 2: Capital-Budgeting Principles and Techniques
QUESTIONS
1. a. What is the relationship between accounting income and economic profit?
Answer: Accounting income is calculated by taking revenues and subtracting all cash and non-
cash expenses (such as depreciation). Accounting income also often recognizes losses for tax
purposes as well, even though the economic loss may have taken place at another time.
Economic profit is the sum of the present values of all the cash flows net of expenses generated
by the firm’s actions. Economic profit measures true increments to value, but is hard to
measure. Accounting profit is correlated with economic profit, but not perfectly so. Accounting
profit can be measured much more easily.
b. What is the relationship between accounting rate of return and economic rate of return?
Answer: The accounting rate of return is the ratio of after-tax profit to average book investment.
Economic rate of return is the ratio of after-tax economic profit to the market value of the
investment. Economic profit equals cash accruals to the asset combined with changes in its
market value.
2. In 1991, AT&T laid a transatlantic fiber optic cable costing $400 million that can handle
80,000 calls simultaneously. What is the payback on this investment if AT&T uses just half
its capacity while netting one cent per minute on calls?
Answer: $210 Million per year assuming the half capacity is for 24 hours a day, 365 days per
year. The annual payback is then 53%.
3. The satisfied owner of a new $15,000 car can be expected to buy another ten cars from the
same company over the next 30 years (an average of one every three years) at an average
price of $15,000 (ignore the effects of inflation). If the net profit margin on these cars is 20
percent, how much should an auto manufacturer be willing to spend to keep its customers
satisfied? Assume a 9 percent discount rate.
Answer: At a 20 percent profit margin, the auto company will earn an annuity of about $3,000
every three years for the next 30 years. Discounted at 9 percent, this annuity is worth $9,402,
assuming that the first new car is purchased three years from today. Hence, an investment to
keep customers satisfied will have a positive NPV as long as the amount spent is less than
$9,402. Thus, a car company should be willing to spend up to $9,402 in present value terms to
keep its customers satisfied. A trick is available to calculate the present value of this annuity.
Recognize that an annuity received every three years for 30 years and discounted at 9 percent is
equivalent to a 10-year annuity discounted at 29.5029 percent since each cash flow term is
discounted at (1.09)3 = 1.295029.
,Chapter 2: Capital-Budgeting Principles and Techniques
4. Demonstrate that the following project has internal rates of return of 0 percent, 100 percent,
and 200 percent.
Year 1 2 3 4
Cash flow –$1,200 +7,200 –13,200 +7,200
Answer: To demonstrate that an IRR calculation is valid, compute the net present value at the
IRR. A valid IRR yields NPV = 0.
Year Cash Flow PV@0% PV@100% PV@200%
1 -1,200 -1,200 -600 -400.00
2 +7,200 +7,200 +1,800 +800.00
3 -13,200 -13,200 -1,650 -488.89
4 +7,200 +7,200 +450 +88.89
Total 0 0 0 0
5. During 1990, Dow Chemical generated the following returns on investment in its different
business units:
Business Unit Return on Investment
(%)
Plastics 16.6
Chemicals/Performance 16.7
Products
Consumer Specialties 12.7
Hydrocarbons/Energy 5.2
Other 1.6
Dow Chemical overall 11.8
Given these returns, which of the business units should Dow invest additional capital in? What
additional information would you need in order to make that decision?
Answer: These figures tell you what Dow earned in 1990. In order to decide on future
investments, you need the following information:
1. Whether these returns are representative of those expected to be earned in the
future in these different divisions. What matters for investment decisionmaking are
projected future returns, not past returns. To the extent that these returns vary widely
from year to year—which they do in the chemical business—historical return data for
,Chapter 2: Capital-Budgeting Principles and Techniques
one year are meaningless. One reason these data may be misleading is that they are based
on historical cost figures for investment. You really want to calculate returns on the
replacement cost of assets. Inflation will cause asset values to be understated, which will
lead the return on investment to be overstated.
2. The cost of capital for these divisions. Each division is likely to have its own risk
and, hence, its own cost of capital. A high return could just indicate a high degree of risk
and, therefore, a high required return. What matters is the projected return relative to the
cost of capital. A high projected return that is less than the risk-adjusted cost of capital
will yield a negative NPV investment. Conversely, a low projected return that exceeds
the cost of capital will yield a positive NPV investment.
3. The marginal return on investment in each division. Even if the figures for, say,
the plastics and chemical/performance products divisions exceed their cost of capital and
are representative of those expected to be earned in the future, that does not
automatically justify additional investment in those divisions. These figures tell us the
average ROI; for investment purposes you need the marginal ROI. That is, what matters
for investment purposes is not the return on past investments but the return on future
investments. As we have seen, many companies (e.g., Monsanto, Philip Morris) have
divisions that yield high returns on past investments but very low returns on incremental
investments.
4. The extent to which these divisions sell to one another. Dow Chemical is a
vertically-integrated company. Its hydrocarbons/energy unit sells to its downstream
plastics unit, which in turn sells to its consumer specialties unit. Thus, the profitability of
these units depends critically on the prices at which these internal transactions take place.
For example, the hydrocarbons/energy unit may be showing a low ROI simply because it
sells petroleum to the plastics unit at a below-market price. That is, the hydrocarbons unit
may be very profitable but its profits are showing up in the plastics unit in the form of a
low price on raw materials. This is a form of cross-subsidization. Disentangling the true
profitability of the different units of a vertically-integrated company like Dow turns out
to be a very difficult task, but it is a necessary one for capital budgeting purposes. What
matters is how profitable investments are from the standpoint of the overall company, not
from the standpoint of the units undertaking those investments.
5. The returns associated with specific assets and activities within each division.
What matters from an investment standpoint is not just how well each division can be
expected to do in the future but how well specific projects within each division can be
expected to do. For example, certain products within the profitable plastics division may
be earning a 40% return while others are only earning a 2% return. Similarly, certain
R&D investments may be expected to yield a high return relative to their riskiness,
whereas others have little chance of a significant payoff. At the same time, the low-return
hydrocarbons/energy division may have some very high-return projects, which are
masked by a lot of value-destroying activities elsewhere. Without detailed data on the
, Chapter 2: Capital-Budgeting Principles and Techniques
returns associated with each division’s various activities, customers, and products, one
can’t say where investment dollars would be best spent.
CHAPTER 2: PROBLEMS
1. A firm is considering investing in a project with the following cash flows:
Year 1 2 3 4 5 6 7 8
Net cash 2,00 3,00 4,00 3,50 3,00 2,00 1,00 1,00
flow ($) 0 0 0 0 0 0 0 0
The project requires an initial investment of $12,500, and the firm has a required rate of
return of 10 percent. Compute the payback, discounted payback, and net present value, and
determine whether the project should be accepted.
Answer: Payback period = 4 years exactly.
Discounted payback period (r = 10%) = 5.84 years.
Net Present Value (r = 10%) = $1164.70. The project should be accepted.
Intermediate Calculations:
Cash PV Cumulative
Cash Flows -12,500.00
1 2,000.00 1,818.18 1,818.18
2 3,000.00 2,479.34 4,297.52
3 4,000.00 3,005.26 7,302.78
4 3,500.00 2,390.55 9,693.33
5 3,000.00 1,862.76 11,556.09
6 2,000.00 1,128.95 12,685.04
7 1,000.00 513.16 13,198.20
8 1,000.00 466.51 13,664.70
2. The Pennco Oil Co. must decide whether it is financially feasible to open an oil well off the
coast of China. The drilling and rigging cost for the well is $5,000,000. The well is expected
to yield 585,000 barrels of oil a year at a net profit to Pennco of $5 a barrel for four years.
The well will then be effectively depleted but must be capped and secured at a cost of
$4,000,000. Pennco requires an annual rate of return of 14 percent on its investment
projects. Should Pennco open the well? (Assume all of a year’s production occurs at the end
of the year.)
Answer:
Net annual profit = 585,000($5.00) = $2.925M.
PV(Production) = $2.925M _ PVIFAr=14%,n=4 = 2.925M _ 2.9137 = $8.523M.
PV(Capping) = $4.000M _ PVIFr=14%,n=4 = 4 _ 0.5921 = $2.368M.
