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Q1: Process for Making StrategicInvestment Decisions
• The process used to compare and analyze long-term investment projects is called capital budgeting.
• The capital budgeting process includes the following stages:• Identify decision alternatives.• Identify relevant cash flows.• Apply the appropriate quantitative techniques.• Perform sensitivity analysis.• Identify and analyze qualitative factors.• Consider quantitative and qualitative factors and make
Joseph Leasing is considering an investment in a new apartment building. The Lindie Lane building will cost $450,000 and the net annual cash inflows are expected to be $45,000 for 7 years. At the end of the 7th year, Joseph expects to be able to sell Lindie Lane building for $400,000. Joseph demands a minimum required rate of return of 8% on all invest-ments. Assume all cash inflows occur at the end of each year. Compute the NPV of the Lindie Lane building. Is it an acceptable investment?
PV of cash inflows:Annuity of cash inflows:
$45,000 x PV annuity factor of 5.206 $234,270Sale of building:
$400,000 x PV of $1 factor of 0.583 233,200467,470
Joseph Leasing is also looking at the purchase of a lot with a double-wide trailer on it. The cost is $65,000 and the expected net cash inflows are $6,800 per year for 10 years. At the end of the 10th year, Joseph expects to be able to sell the lot and trailer for $45,000. Compute the NPV of the trailer investment. Is it an acceptable investment?
Yes, the NPV > 0, so the invest-
ment is acceptable
Yes, the NPV > 0, so the invest-
ment is acceptable
PV of cash inflows:Annuity of cash inflows:
$6,800 x PV annuity factor of 6.710 $45,628Sale of lot and trailer:
Compare the two investments for Joseph using the profitability index, and describe to him what the index means. Which investment (or both) should he make?
The Lindie Lane yields
a slightly greater PV
for each invested
dollar than does the trailer.
The Lindie Lane yields
a slightly greater PV
for each invested
dollar than does the trailer.
Profitability index
Lindie Lane building:PV of cash inflows 467,470PV of cash outflows 450,000
Trailer:PV of cash inflows 66,463PV of cash outflows 65,000
= 1.0388
= 1.0225
If Joseph has sufficient capital, he should invest in both unless he has alternatives that have even greater profitability indices.If Joseph has sufficient capital, he should invest in both unless he has alternatives that have even greater profitability indices.
• The uncertainty about future cash flows increases the further the cash flow is in the future, but NPV analysis uses only one discount rate for all future periods.
• Individuals providing information about the future cash flows are likely to have a vested interest in the project’s acceptance.
• The IRR method computes the discount rate required to set the NPV to zero.
• For projects with equal annual cash inflows where the only cash outlay is the initial investment, the IRR can be determined by computing the PV of an annuity factor and solving for the interest rate.
PV of an annuity factor=Initial investment
Annual cash inflow
• Then the discount rate is found by locating the column for the PV factor, given n.
Graham Enterprises is considering the purchase of a new machine. The cost is $100,000 and the machine is expected to generate cost savings of $17,700 each year for 10 years. The machine is not expected to have any salvage value at the end of its life. Assume the cost savings are realized at the end of the year. Graham requires a 10% rate of return on all new investments. Compute the IRR for the proposed machine. Should Graham purchase the machine?
Since the machine’s IRR exceeds Graham’s minimum rate of return, the machine is an acceptable investment, but of course
should still be compared to other, potentially better, investments.
Since the machine’s IRR exceeds Graham’s minimum rate of return, the machine is an acceptable investment, but of course
should still be compared to other, potentially better, investments.
5.650=$100,000 $17,700
Locate the 5.65 factor in the present value of an annuity table, using n = 10 years and note that it is found in the 12% column, so the IRR = 12%.
• The payback method computes the number of years before the initial investment is recovered.
• If cash inflows are the same each year and the project has only one initial outlay, the payback period is computed as:
Payback period in years = Initial investmentAnnual cash inflow
• For projects where annual cash inflows are not equal, the payback period is computed by merely counting the years required before the initial investment is recovered.
Graham Enterprises is considering the purchase of a new machine. The cost is $100,000 and the machine is expected to generate cost savings of $17,700 each year for 10 years. The machine is not expected to have any salvage value at the end of its life. Compute the payback period for the proposed machine.
Notice that the payback period is the same as the PV factor computed in the IRR example.
Notice that the payback period is the same as the PV factor computed in the IRR example.
Cophil, Inc. is considering the purchase of a new machine. There are two alternatives, and the cash flow information is given below. Compute the payback period for each and comment on your findings.
The payback method shows Machine B to be preferable to Machine A, but ignores the
large cash inflows of Machine A that occur after the payback period.
The payback method shows Machine B to be preferable to Machine A, but ignores the
large cash inflows of Machine A that occur after the payback period.
The payback period for Machine B is 2 years. The
payback period for Machine A is 3.5 years ($60,000 covered after 3 years, and $40,000 is
• The accrual accounting rate of return computes the project’s rate of return using operating income in place of cash flows.
• This method is widely used because the financial accounting information is readily available, but is is flawed because it ignores the time value of money.
Q5: Accrual Accounting Rate of ReturnMethod Example
Blanche Manufacturing is considering the purchase of a new machine. The cost is $100,000 and it is expected to last 5 years and have no salvage value. The machine is expected to generate cost savings of $32,000 per year. Ignoring income tax effects, compute the accrual accounting rate of return for this investment.
Q7: Capital Budgeting and IncomeTax Considerations (NPV) Example
Colby Products is considering the purchase of a new machine. The cost is $180,000 and it is expected to last 6 years and have no salvage value. The machine is expected to generate cost savings of $50,000 per year. Colby’s tax rate is 30% and its discount rate is 10%. For simplification, suppose that Colby uses straight-line depreciation for both books and taxes. Compute the IRR of this machine.
Cash inflows after taxes [$50,000 x (1 – 30%)] $35,000
Tax savings from depreciation [$30,000 x 30%] 9,000
Net after-tax annual cash inflows $44,000
NPV = $44,000 x PV factor of an annuity - $180,000
Q7: Capital Budgeting and IncomeTax Considerations (IRR) Example
Colby Products is considering the purchase of a new machine. The cost is $180,000 and it is expected to last 6 years and have no salvage value. The machine is expected to generate cost savings of $50,000 per year. Colby’s tax rate is 30% and its discount rate is 10%. For simplification, suppose that Colby uses straight-line depreciation for both books and taxes. Compute the IRR of this machine.
Cash inflows after taxes [$50,000 x (1 – 30%)] $35,000
Tax savings from depreciation [$30,000 x 30%] 9,000
Net after-tax annual cash inflows $44,000
PV of an annuity factor = 4.091=$180,000
$44,000
Locate the 4.091 factor in the present value of an annuity table, using n = 6 years and note that it is found between the 12% & 13%
Q7: Capital Budgeting and IncomeTax Considerations (Payback) Example
Colby Products is considering the purchase of a new machine. The cost is $180,000 and it is expected to last 6 years and have no salvage value. The machine is expected to generate cost savings of $50,000 per year. Colby’s tax rate is 30% and its discount rate is 10%. For simplification, suppose that Colby uses straight-line depreciation for both books and taxes. Compute the payback period of this machine.
Cash inflows after taxes [$50,000 x (1 – 30%)] $35,000
Tax savings from depreciation [$30,000 x 30%] 9,000
Q7: Capital Budgeting and Income Tax Considerations (Accrual Accounting ROR)
ExampleColby Products is considering the purchase of a new machine. The cost is $180,000 and it is expected to last 6 years and have no salvage value. The machine is expected to generate cost savings of $50,000 per year. Colby’s tax rate is 30% and its discount rate is 10%. For simplification, suppose that Colby uses straight-line depreciation for both books and taxes. Compute the accrual accounting rate of return of this machine.
Cash inflows after taxes [$50,000 x (1 – 30%)] $35,000
Tax savings from depreciation [$30,000 x 30%] 9,000
Net after-tax annual increase in operating income $44,000
• In the real method of NPV analysis, future cash flows are state in real dollars (without considering changes in the purchasing power of the dollar) and a real rate of interest is used as the discount rate.
• In the nominal method of NPV analysis, future cash flows and the terminal project value must be inflated to future dollars and a nominal rate of interest is used as the discount rate.
Stiles, Inc. is considering the purchase of a new machine. The cost is $400,000 and it is expected to last 6 years and have a salvage value of $80,000. Stiles’ tax rate is 30%, the risk-free rate is 3%, the expected inflation rate is 2%, and Stiles believes that a risk premium of 5% for this machine is appropriate. The machine qualifies as 5-year MACRS property for tax purposes, which means that the depreciation deduction is taken over 6 years at 20%, 32%, 19.2%, 11.52%, 11.52%, and 5.76% of asset cost, respectively. Compute the depreciation tax shield in real dollars for this machine.
Stiles, Inc. is considering the purchase of a new machine. The cost is $400,000 and it is expected to last 6 years and have a salvage value of $80,000. Stiles’ tax rate is 30%, the risk-free rate is 3%, the expected inflation rate is 2%, and Stiles believes that a risk premium of 5% for this machine is appropriate. The machine qualifies as 5-year MACRS property for tax purposes, which means that the depreciation deduction is taken over 6 years at 20%, 32%, 19.2%, 11.52%, 11.52%, and 5.76% of asset cost, respectively. Compute the depreciation tax shield in nominal dollars for this machine.
Compute the tax on the gain on the sale of the machine, in nominal dollars.
= (1.02)6
$400,000 cost less depreciation taken
of $400,000
Disposal value $80,000Inflation factor 1.12616Inflated disposal value $90,093Tax basis of asset $0Gain on sale $90,093Tax rate 30%Taxes on gain $27,028
Disposal value $80,000Inflation factor 1.12616Inflated disposal value $90,093Tax basis of asset $0Gain on sale $90,093Tax rate 30%Taxes on gain $27,028