13.4 Payback and Discounted Payback Flashcards
A characteristic of the payback method (before taxes) is that it
A. Incorporates the time value of money.
B. Neglects total project profitability.
C. Uses accrual accounting inflows in the numerator of the calculation.
D. Uses the estimated expected life of the asset in the denominator of the calculation.
B. Neglects total project profitability.
The payback method calculates the number of years required to complete the return of the original investment. This measure is computed by dividing the net investment required by the average expected cash flow to be generated, resulting in the number of years required to recover the original investment. Payback is easy to calculate but has two principal disadvantages: (1) It ignores the time value of money, and (2) it does not consider returns after the payback period. Thus, it ignores total project profitability.
The length of time required to recover the initial cash outlay of a capital project is determined by using the
A. Discounted cash flow method.
B. Payback method.
C. Weighted net present value method.
D. Net present value method.
B. Payback method.
The payback method measures the number of years required to complete the return of the original investment. This measure is computed by dividing the net investment by the average expected cash inflows to be generated, resulting in the number of years required to recover the original investment. The payback method gives no consideration to the time value of money, and there is no consideration of returns after the payback period.
A company has a payback goal of 3 years on new equipment acquisitions. A new sorter is being evaluated that costs $450,000 and has a 5-year life. Straight-line depreciation will be used; no salvage is anticipated. The company is subject to a 40% income tax rate. To meet the company’s payback goal, the sorter must generate reductions in annual cash operating costs of
A. $60,000
B. $100,000
C. $150,000
D. $190,000
D. $190,000
Given a periodic constant cash flow, the payback period is calculated by dividing cost by the annual after-tax cash inflows, or cash savings. To achieve a payback period of 3 years, the annual increment in net cash inflow generated by the investment must be $150,000 ($450,000 ÷ 3-year targeted payback period). This amount equals the total reduction in cash operating costs minus related taxes. Depreciation is $90,000 ($450,000 ÷ 5 years). Because depreciation is a noncash deductible expense, it shields $90,000 of the cash savings from taxation. Accordingly, $60,000 ($150,000 – $90,000) of the additional net cash inflow must come from after-tax net income. At a 40% tax rate, $60,000 of after-tax income equals $100,000 ($60,000 ÷ 60%) of pre-tax income from cost savings, and the outflow for taxes is $40,000. Thus, the annual reduction in cash operating costs required is $190,000 ($150,000 additional net cash inflow required + $40,000 tax outflow).
Which one of the following is an advantage of the use of the payback method for capital budgeting?
A. Cash flows after the payback period are considered.
B. More liquid projects are rated higher.
C. The time value of money is considered.
D. The effects of accrual accounting conventions are considered.
B. More liquid projects are rated higher.
More liquid projects are rated higher.
A proposed capital budgeting project has a discounted payback period of 5 years when a 10% cost of capital is used. The project has cash flows that will be positive for Years 1 through 7. The undiscounted payback period of the project is
A. More than 7 years.
B. Between 5 and 7 years.
C. Less than 5 years.
D. 2 years.
C. Less than 5 years.
Undiscounted payback periods are always quicker than the discounted payback periods because the cash flows are larger.
The company is contemplating the purchase of a new glass-cutting machine to lessen the throughput time on production of picture frames. The new glass-cutting machine will cost $750,000. The company has calculated the annual cash savings of using the machine over the next 7 years:
Annual After-Tax Cash Flow Savings / PV of $1 at 10%
Year 1: $180,000 / .909
Year 2: 210,000 / .826
Year 3: 190,000 / .751
Year 4: 170,000 / .683
Year 5: 150,000 / .621
Year 6: 100,000 / .564
Year 7: 20,000 / .513
If their cost of capital is 10% and the company uses discounted cash flow analysis, how many years will the machine need to last to pay for itself?
A. 4 years
B. 5 years
C. 6 years
D. 7 years
D. 7 years
A manufacturer is analyzing a capital investment project that is forecasted to produce the following cash flows and net income:
After-Tax Cash flow / Net income
Year 0: ($20,000) / $ 0
Year 1: 6,000 / 2,000
Year 2: 6,000 / 2,000
Year 3: 8,000 / 2,000
Year 4: 8,000 / 2,000
The manufacturer’s payback period for this project will be
A. 2.5 years.
B. 3.3 years.
C. 3.0 years.
D. 2.6 years.
The payback period for this project can be calculated as follows:
After-Tax Cash Flows / Remaining Investment
Year 0: $ – / $20,000
Year 1: 6,000 / 14,000
Year 2: 6,000 / 8,000
Year 3: 8,000 / 0
The Keego Company is planning a $200,000 equipment investment that has an estimated 5-year life with no estimated salvage value. The company has projected the following annual cash flows for the investment:
Projected Cash Inflows / Present Value of $1
Year 1: $120,000 / .91
Year 2: 60,000 / .76
Year 3: 40,000 / .63
Year 4: 40,000 / .53
Year 5: 40,000 / .44
Totals $300,000 / 3.27
Assuming that the estimated cash inflows occur evenly during each year, the payback period for the investment is
A. 4.91 years.
B. 2.50 years.
C. 1.96 years.
D. 1.67 years.
B. 2.50 years.
The payback period is the number of years required to complete the return of the original investment. The principal problems with the payback method are that it does not consider the time value of money and the inflows after the payback period. The inflow for the first year is $120,000, the second year is $60,000, and the third year is $40,000, a total of $220,000. Given an initial investment of $200,000, the payback period must be between 2 and 3 years. If the cash inflows occur evenly throughout the year, $20,000 ($200,000 – $120,000 – $60,000) of cash inflows are needed in year 3, which is 50% of that year’s total. Thus, the answer is 2.5 years.
A company is considering the purchase of five construction cranes for its recently awarded construction project. The cranes cost $20,000 each. These cranes are projected to provide a total cash saving of $190,000 over the next 8 years. The projected cash savings by year is shown below
Year / Cash Savings
0 / -
1 / $35,000
2 / 32,000
3 / 28,000
4 / 26,000
5 / 24,000
6 / 20,000
7 / 15,000
8 / 10,000
The payback period is closest to
A. 4.0 years.
B. 3.0 years.
C. 3.2 years.
D. 3.4 years.
C. 3.2 years.
The initial investment in the cranes is $100,000 (5 cranes × $20,000 each). Through the end of Year 3, the total cumulative cash savings is $95,000 ($35,000 + $32,000 + $28,000). Given an estimated cash savings in Year 4 of $26,000, the remaining $5,000 will be collected approximately within the first fifth of Year 4 ($5,000 ÷ $26,000). Thus, the payback period is closest to 3.2 years.
A company is analyzing the opportunity to expand into a new market. The expansion would require an initial investment of $261,600. Cash flows for the new market expansion are forecasted to be $120,000 for each of the next 3 years. The company has a cost of capital of 8%. The discounted payback period for the new market expansion would be
A. 2.8 years.
B. 2.0 years.
C. 2.5 years.
D. 2.2 years.
C. 2.5 years.
The discounted payback period for an investment, assuming an 8% discount, can be found by accumulating each year’s discounted net cash flows until the initial investment is recovered.
$120,000 × 0.92593 = $111,111.60
120,000 × 0.85734 = 102,880.80
120,000 × 0.79383 = 95,259.60
$309,252.00
Thus, the answer is greater than 2 years. After 2 years, an additional $47,607.60 [$261,600 – ($111,111.60 + $102,880.80)] is needed. Consequently, the discounted payback period is approximately 2.5 years [2 + ($47,607.60 ÷ $95,259.60 third year discounted cash flow)].
Yipann Corporation is reviewing an investment proposal. The initial cost, as well as other related data for each year, are presented in the schedule below. All cash flows are assumed to take place at the end of the year. The salvage value of the investment at the end of each year is equal to its net book value, and there will be no salvage value at the end of the investment’s life.
Year 0
Initial Cost and Book Value: $105,000
Annual Net After-Tax Cash Flows: $0
Annual Net Income: $0
Year 1
Initial Cost and Book Value: 70,000
Annual Net After-Tax Cash Flows: 50,000
Annual Net Income: 15,000
Year 2
Initial Cost and Book Value: 42,000
Annual Net After-Tax Cash Flows: 45,000
Annual Net Income: 17,000
Year 3
Initial Cost and Book Value:21,000
Annual Net After-Tax Cash Flows:40,000
Annual Net Income: 19,000
Year 4
Initial Cost and Book Value: 7,000
Annual Net After-Tax Cash Flows: 35,000
Annual Net Income: 21,000
Year 5
Initial Cost and Book Value: 0
Annual Net After-Tax Cash Flows: 30,000
Annual Net Income: 23,000
Yipann uses a 24% after-tax target rate of return for new investment proposals. The discount factors for a 24% rate of return are given.
Year / PV of $1 Received at the EOP / PV of an Annuity of $1
1 / .81 / .81
2 / .65 / 1.46
3 / .52 / 1.98
4 / .42 / 2.40
5 / .34 / 2.74
6 / .28 / 3.02
7 / .22 / 3.24
The traditional payback period for the investment proposal is
A. More than 5 years.
B. .875 years.
C. 1.833 years.
D. 2.250 years
D. 2.250 years
The payback period is the time required to recover the initial investment. The net cash inflows used to determine the payback period are not discounted. The initial cost was $105,000, and inflows during the first 2 years were $95,000 ($50,000 + $45,000). Thus, the first $10,000 ($105,000 – $95,000) of the third year’s net cash inflows will complete the recovery of the initial investment. This amount is one-fourth of the third year’s inflows. Hence, the payback period is 2.25 years.
A proposed capital budgeting project requires an initial investment of $95,000. The subsequent annual cash flows from the project of $40,000 are expected to last for 7 years and be received at the end of each year. If the cost of capital is 20%, the discounted payback period of the project is
A. Less than 2 years.
B. Between 3 and 4 years.
C. Between 4 and 5 years.
D. Between 2 and 3 years.
B. Between 3 and 4 years.
The discounted payback period for an investment, assuming a 20% discount, can be found by accumulating each year’s discounted net cash flows until the initial investment is recovered.
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 payback period of the project?
A. 2 years.
B. 5 years.
C. 3.75 years.
D. 2.14 years.
C. 3.75 years.
The payback period in this case is equal to the investment divided by the annual operating cash flows ($400,000) that result from that investment. Thus, the payback period is 3.75 years ($1,500,000 ÷ $400,000).
The Dickins Corporation is considering the acquisition of a new machine at a cost of $180,000. Transporting the machine to Dickins’ plant will cost $12,000. Installing the machine will cost an additional $18,000. It has a 10-year life and is expected to have a salvage value of $10,000. Furthermore, the machine is expected to produce 4,000 units per year with a selling price of $500 and combined direct materials and direct labor costs of $450 per unit. Federal tax regulations permit machines of this type to be depreciated using the straight-line method over 5 years with no estimated salvage value. Dickins has a marginal tax rate of 40%.
What is the approximate payback period on Dickins’ new machine?
A. 2.22 years.
B. 1.33 years.
C. 1.54 years.
D. 1.05 years.
C. 1.54 years.
The company will receive net cash inflows of $50 per unit ($500 selling price – $450 variable costs), a total of $200,000 per year for 4,000 units. This amount will be subject to taxation. However, for the first 5 years, a depreciation deduction of $42,000 per year ($210,000 ÷ 5 years) will be available. Thus, annual taxable income will be $158,000 ($200,000 – $42,000). At a 40% tax rate, income tax expense will be $63,200, and the net cash inflow will be $136,800 ($200,000 – $63,200). When annual cash inflows are uniform, the payback period is calculated by dividing the initial investment ($210,000) by the annual net cash inflows ($136,800). Dividing $210,000 by $136,800 produces a payback period of 1.54 years.
A company uses straight-line depreciation for both tax and financial reporting purposes. The following data relate to Machine No. 108, which cost $400,000 and is being written off over a 5-year life.
Year / Operating Income / Savings in Cash Operating Costs
1 / $150,000 / $230,000
2 / 200,000 / 280,000
3 / 225,000 / 305,000
4 / 225,000 / 305,000
5 / 175,000 / 255,000
All of these amounts are on a before-tax basis. The company is subject to a 40% income tax rate. The company strives for a 12% rate of return. The traditional payback period for Machine No. 108 would be
A. 2.14 years.
B. 2.58 years.
C. 2.44 years.
D. 3.41 years.
A. 2.14 years.
The after-tax payback for the first 3 years would be calculated as follows:
Taxable Income Tax Net cash flow
$150,000 × 40% = $60,000 $170,000
200,000 × 40% = 80,000 200,000
225,000 × 40% = 90,000 215,000
By the end of 2 years, the total recovery would be $370,000 ($170,000 + $200,000). Subtracting $370,000 from the $400,000 initial cost leaves $30,000 to be recovered in Year 3. The $30,000 represents 14% of the Year 3 inflows of $215,000. Thus, the total payback period would be 2.14 years.
A firm is considering an investment in a capital project. The sole outlay will be $800,000 at the outset of the project, and the annual net after-tax cash inflow will be $216,309.75 for 6 years. The present value factors at the firm’s 8% cost of capital are
Year: PV Factors
1: .926
2: .857
3: .794
4: .735
5: .681
6: .630
What is the breakeven time (BET)?
A. 6.00 years.
B. 5.00 years.
C. 4.57 years.
D. 3.70 years.
C. 4.57 years.
Breakeven time is a more sophisticated version of the payback method. Breakeven time is defined as the period required for the discounted cumulative cash inflows on a project to equal the discounted cumulative cash outflows (usually the initial cost). Thus, it is the time necessary for the present value of the discounted cash flows to equal zero. This period begins at the outset of a project, not when the initial cash outflow occurs. Accordingly, the BET is calculated as follows:
Year: After-Tax Cash Flow / PV of Inflow / Cumulative PV
1: $216,309.75 / $200,302.83 / $200,302.83
2: 216,309.75 / 185,377.46 / 385,680.29
3: 216,309.75 / 171,749.94 / 557,430.23
4: 216,309.75 / 158,987.67 / 716,417.90
5: 216,309.75 / 147,306.94
Amount required in Year 5:
$800,000 – $716,417.90 = $83,582.10
BET = 4 years + ($83,582.10 ÷ $147,306.94) = 4.57 years
Henderson, Inc., has purchased a new fleet of trucks to deliver its merchandise. The trucks have a useful life of 8 years and cost a total of $500,000. Henderson expects its net increase in after-tax cash flow to be $150,000 in Year 1, $175,000 in Year 2, $125,000 in Year 3, and $100,000 in each of the remaining years.
Based on a 6% annual interest rate, what is the discounted payback period for Henderson’s fleet of trucks?
A. 4.25 years.
B. 3.98 years.
C. 5.0 years.
D. 3.5 years.
A. 4.25 years.
The discounted payback period for an investment, assuming a 6% discount, can be found by accumulating each year’s discounted net cash flows until the initial investment is recovered.
$150,000 × .94339 = $141,508.50
175,000 × .88999 = 155,748.25
125,000 × .83962 = 104,952.50
100,000 × .79209 = 79,209.00
$481,418.25
Thus, the answer is something greater than four years. After four years, an additional $18,581.75 ($500,000 – $481,418.25) is needed. The calculation for the fifth year is $74,726 ($100,000 × .74726). Consequently, the discounted payback period is approximately 4.25 years [4 + ($18,581.75 ÷ $74,726)].
A company is planning to purchase a furnace that would cost $20,000 and save the company $4,000 pre-tax annually. It has an estimated useful life of seven years with no salvage value. The company would depreciate the furnace using the straight-line method. The company has an effective income tax rate of 30%. Assuming no change in working capital, the payback period for the furnace is
A. 4.12 years.
B. 7.14 years.
C. 5.00 years.
D. 5.47 years.
D. 5.47 years.
The payback period for an investment, ignoring the time value of money, can be found by accumulating each year’s net cash flows until the initial investment is recovered. Annual cash inflow consists of after-tax annual savings and depreciation tax shield. After-tax annual savings are $2,800 [$4,000 × (1 – 30%)]. The annual depreciation tax shield is $857 [($20,000 ÷ 7 years) × 30%]. Total annual cash inflow is $3,657. Therefore, dividing the $20,000 initial investment by the $3,657 annual cash inflow gives a payback time of 5.47 years.
Rex Company is considering an investment in a new plant, which will entail an immediate capital expenditure of $4,000,000. The plant is to be depreciated on a straight-line basis over 10 years to zero salvage value. Operating income (before depreciation and taxes) is expected to be $800,000 per year over the 10-year life of the plant. The opportunity cost of capital is 14%. Assume that there are no taxes.
What is the discounted payback period for the investment?
A. 7.1 years.
B. 9.2 years.
C. 11.7 years.
D. 5.5 years.
B. 9.2 years.
The discounted payback period is the number of years needed to get the PV of the cash flows to equal the initial investment. At a 14% discount rate, this occurs at 9.2 years. The inflows during the first 9 years are $3,956,800 ($800,000 × 4.946). The remaining amount from the initial investment that must be recovered in the tenth year is $43,200 ($4,000,000 – $3,956,800). This amount is one-fifth of the tenth year’s discounted inflow [$43,200 ÷ ($800,000 × .270)]. Thus, the discounted payback period is 9.2.
Despite its shortcomings, the traditional payback period continues to be a popular method to evaluate investments because, in part, it
A. Provides some insight into the risk associated with a project.
B. Focuses on income rather than cash flow.
C. Furnishes information about an investment’s lifetime performance.
D. Ignores the time value of money.
A. Provides some insight into the risk associated with a project.
To some extent, the traditional payback method measures risk. The longer the project takes to payoff, the riskier it is.
