13.6 Comprehensive Examples of Investment Decisions Flashcards
Don Adams Breweries is considering an expansion project with an investment of $1,500,000. The equipment will be depreciated to zero salvage value on a straight-line basis over 5 years. The expansion will produce incremental operating revenue of $400,000 annually for 5 years. The company’s opportunity cost of capital is 12%. Ignore taxes.
What is the IRR of the investment?
A. 19.17%
B. 16.32%
C. 10.43%
D. 12.68%
C. 10.43%
First, calculate the annual earnings and cash flows:
Operating revenues $400,000
Less: Depreciation 300,000
Book income 100,000
Cash flow 400,000
IRR is calculated by trial and error. Calculate the NPV at different discount rates.
NPV at 10% = ($400,000 × Discount factor for 10%, 5 years) – $1,500,000 = $400,000 × 3.791 – $1,500,000 = $16,400
NPV at 11% = $400,000 × 3.696 – $1,500,000 = $(21,600)
Thus, IRR lies between 10% and 11%. By interpolation, the actual IRR appears to be 10.43% {10 + [$16,400 ÷ ($16,400 + $21,600)}.
NOTE: The NPV tables do not contain the factor for 11%. You can deduce the answer using the factor for 12%, but you cannot interpolate.
Don Adams Breweries is considering an expansion project with an investment of $1,500,000. The equipment will be depreciated to zero salvage value on a straight-line basis over 5 years. The expansion will produce incremental operating revenue of $400,000 annually for 5 years. The company’s opportunity cost of capital is 12%. Ignore taxes.
What is the NPV of the investment?
A. $0
B. $(58,000)
C. $(116,000)
D. $1,442,000
B. $(58,000)
First, calculate the annual earnings and cash flows:
Operating revenues $400,000
Less: Depreciation (300,000)
Book income $100,000
Cash flow $400,000
The cash flows associated with the investment are then discounted accordingly:
Amount Discount Factor Present Value
Year 0 initial investment $(1,500,000) 1 $(1,500,000)
Years 1-5 cash flow 400,000 3.605 1,442,000
Net present value $ (58,000)
McLean, Inc., is considering the purchase of a new machine that will cost $150,000. The machine has an estimated useful life of 3 years. Assume that 30% of the depreciable base will be depreciated in the first year, 40% in the second year, and 30% in the third year. The new machine will have a $10,000 resale value at the end of its estimated useful life. The machine is expected to save the company $85,000 per year in operating expenses. McLean uses a 40% estimated income tax rate and a 16% hurdle rate to evaluate capital projects.
Discount rates for a 16% rate are as follows:
Present Value of $1
Year 1 .862
Year 2 .743
Year 3 .641
Present Value of an Ordinary Annuity of $1
Year 1 .862
Year 2 1.605
Year 3 2.246
What is the net present value of this project?
A. $15,842
B. $13,278
C. $40,910
D. $9,432
B. $13,278
The NPV method discounts the expected cash flows from a project using the required rate of return. A project is acceptable if its NPV is positive. The future cash inflows consist of $85,000 of saved expenses per year minus income taxes after deducting depreciation. In the first year, the after-tax cash inflow is $85,000 minus taxes of $16,000 {[$85,000 – ($150,000 × 30%) depreciation] × 40%}, or $69,000. In the second year, the after-tax cash inflow is $85,000 minus taxes of $10,000 {[$85,000 – ($150,000 × 40%) depreciation] × 40%}, or $75,000. In the third year, the after-tax cash inflow (excluding salvage value) is again $69,000. Also in the third year, the after-tax cash inflow from the salvage value is $6,000 [$10,000 × (1 – 40%)]. Accordingly, the total for the third year is $75,000 ($69,000 + $6,000). The sum of these cash flows discounted using the factors for the present value of $1 at a rate of 16% is calculated as follows:
$69,000 × .862 = $ 59,478
$75,000 × .743 = 55,725
$75,000 × .641 = 48,075
Discounted cash inflows $163,278
Thus, the NPV is $13,278 ($163,278 – $150,000 initial outflow).
McLean, Inc., is considering the purchase of a new machine that will cost $150,000. The machine has an estimated useful life of 3 years. Assume that 30% of the depreciable base will be depreciated in the first year, 40% in the second year, and 30% in the third year. The new machine will have a $10,000 resale value at the end of its estimated useful life. The machine is expected to save the company $85,000 per year in operating expenses. McLean uses a 40% estimated income tax rate and a 16% hurdle rate to evaluate capital projects.
Discount rates for a 16% rate are as follows:
Present Value of $1
Year 1 .862
Year 2 .743
Year 3 .641
Present Value of an Ordinary Annuity of $1
Year 1 .862
Year 2 1.605
Year 3 2.246
The payback period for this investment would be
A. 2.94 years.
B. 1.76 years.
C. 2.09 years.
D. 1.14 years.
C. 2.09 years.
The payback period is the number of years required for the cumulative undiscounted net cash inflows to equal the original investment. The future net cash inflows consist of $69,000 in Years 1 and 3, and $75,000 in Year 2. After 2 years, the cumulative undiscounted net cash inflow equals $144,000. Thus, $6,000 ($150,000 – $144,000) is to be recovered in Year 3, and payback should be complete in approximately 2.09 years [2 years + ($6,000 ÷ $69,000 net cash inflow in third year)].
