HOW DO DISCOUNTED CASH FLOW METHODS WORK?
4. How do discounted cash flow methods work?
■
■ Discounted cash flow methods incorporate compound interest and make compari- sons by converting all cash flows to the same point in time—namely the present value.
■
■ Net Present Value (NPV) analysis is a capital investment analysis method that mea- sures the net difference between the present value of the investment’s net cash inflows and the investment’s cost.
• Discount rate is management’s minimum desired rate of return on a capital invest- ment and is used to select the present value factors used when calculating the net present value of a project.
• Decision rule: If the NPV is positive, invest in the capital asset.
• The profitability index computes the number of dollars returned for every dollar invested, with all calculations performed in present value dollars. It is useful to rank projects of different sizes.
Future value = Amount of each cash inflow * Annuity FV factor for i = ?, n = ?
Profitability index = Present value of net cash inflows / Initial investment
Annuity PV factor (i = ?, n= given) = Initial investment / Amount of each cash inflow Future value = Present value * FV factor for i = ?, n= ?
■
■ To calculate the future value of a lump sum, use the following equation:
■
■ To calculate the future value of an annuity, use this equation:
■
■ Internal rate of return (IRR) is the rate of return, based on discounted cash flows, of a capital investment. It is the interest rate that makes the NPV of the investment equal to zero.
• If net cash inflows are equal:
• Determine the annuity PV factor using this equation:
• Use the Present Value of an Ordinary Annuity of $1 table to find the factor closest to the result to estimate the IRR.
• If net cash inflows are unequal, use the following methods:
• A trial-and-error method can be used to estimate the IRR.
• To find an exact IRR, use a business calculator or spreadsheet software, such as Excel.
• Decision rule: If the IRR meets or exceeds the required rate of return, invest in the asset.
■
■ Review Exhibit 26-12 for a comparison of the four capital investment analysis methods.
■
■ Sensitivity analysis allows managers to evaluate differences when underlying assumptions change.
CHAPTER 26
Check your understanding of the chapter by completing this problem and then looking at the solution. Use this practice to help identify which sections of the chapter you need to study more.
Dyno-max is considering buying a new water treatment system for its plant in Austin, Texas. The company screens its potential capital investments using the payback and accounting rate of return methods. If a potential investment has a payback of less than four years and a minimum 12% accounting rate of return, it will be considered further. The data for the water treatment system follow:
Cost of water treatment system $ 48,000
Estimated residual value 0
Estimated annual net cash inflow (each year for 5 years) from anticipated environmental cleanup savings
13,000
Estimated useful life 5 years
Requirements
1. Compute the water treatment system’s payback. (See Learning Objective 2) 2. Compute the water treatment system’s ARR. (See Learning Objective 2)
3. Should Dyno-max turn down this investment proposal or consider it further? (See Learning Objective 2)
Total operating income during operating life
Total net cash inflows during operating life of the asset ($13,000 per year * 5 years) Less: Total depreciation during operating life of the asset ($48,000 - $0)
Divide by: Asset’s operating life in years Average annual operating income from asset
$ 65,000 48,000 17,000
÷5 years
$ 3,400 Payback= Amount invested
Expected annual net cash inflow
= $48,000
$13,000 = 3.7 years (rounded)
ARR = $3,400
($48,000 + $0) / 2 = $3,400
$24,000 = 0.142 = 14.2%
> Check Your Understanding 26-1
> Solution
Requirement 1
Requirement 2
Requirement 3
Decision: The water treatment system proposal passes both initial screening tests. The pay- back is slightly less than four years, and the accounting rate of return is higher than 12%.
Dyno-max should further analyze the proposal using a method that incorporates the time value of money.
CHAPTER 26
Check your understanding of the chapter by completing this problem and then looking at the solution. Use this practice to help identify which sections of the chapter you need to study more.
Recall from Check Your Understanding 26-1 that Dyno-max is considering buying a new water treatment system. The investment proposal passed the initial screening tests (payback and accounting rate of return) so the company now wants to analyze the proposal using the discounted cash flow methods. Recall that the water treatment system costs $48,000, has a five-year life, and has no residual value. The estimated net cash inflows from environmental cleanup savings are $13,000 per year over its life. The company’s required rate of return is 16%.
Requirements
1. Compute the water treatment system’s NPV. (See Learning Objective 4)
2. Find the water treatment system’s IRR (exact percentage is not required). (See Learning Objective 4)
3. Should Dyno-max buy the water treatment system? Why? (See Learning Objective 4)
Years
CashNet Inflow
Annuity PV Factor
(i = 16%, n = 5) Present Value 1–5
0
Present value of annuity $13,000 3.274 Initial investment
Net present value
$ 42,562 (48,000)
$ (5,438)
Annuity PV factor (i = ?, n = 5) = Initial investment / Amount of each cash inflow
= $48,000 / $13,000
= 3.692
> Check Your Understanding 26-2
> Solution
Requirement 1
Requirement 2
Because the cash flows occur for five years, we look for the PV factor 3.692 in the row marked n = 5 on the Present Value of Ordinary Annuity of $1 table (Appendix A, Table A-2). The PV factor is 3.605 at 12% and 3.791 at 10%. Therefore, the water treatment system has an IRR that falls between 10% and 12%. (Optional: Using a business calculator or Excel, we find an 11.04% internal rate of return.)
Requirement 3
CHAPTER 26
1. What is the second step of capital budgeting?
a. Gathering the money for the investment b. Identifying potential projects
c. Getting the accountant involved d. All of the above
2. Which of the following methods does not consider the investment’s profitability?
a. ARR b. Payback c. NPV d. IRR
3. Suppose Francine Dunkelberg’s Sweets is considering investing in warehouse-man- agement software that costs $550,000, has $75,000 residual value, and should lead to cost savings of $130,000 per year for its five-year life. In calculating the ARR, which of the following figures should be used as the equation’s denominator (average amount invested in the asset)?
a. $275,000 b. $237,500 c. $625,000 d. $312,500
4. Your rich aunt has promised to give you $2,000 per year at the end of each of the next four years to help you pay for college. Using a discount rate of 12%, the present value of the gift can be stated as
a. PV = $2,000 (PV factor, i = 4%, n = 12).
b. PV = $2,000 (Annuity PV factor, i = 12%, n = 4).
c. PV = $2,000 (Annuity FV factor, i = 12%, n = 4).
d. PV = $2,000 * 12% * 4.
5. Which of the following affects the present value of an investment?
a. The type of investment (annuity versus single lump sum) b. The number of time periods (length of the investment) c. The interest rate
d. All of the above
6. Which of the following is true regarding capital rationing decisions?
a. Companies should always choose the investment with the highest NPV.
b. Companies should always choose the investment with the highest ARR.
c. Companies should always choose the investment with the shortest payback.
d. None of the above
Learning Objective 1
Learning Objective 2
Learning Objective 2
Learning Objective 3
Learning Objective 3
Learning Objective 4
> Key Terms
Accounting Rate of Return (ARR) (p. 1434)
Annuity (p. 1438) Capital Asset (p. 1427) Capital Budgeting (p. 1427) Capital Investment (p. 1427) Capital Rationing (p. 1429)
Compound Interest (p. 1438) Discount Rate (p. 1445) Future Value (p. 1439)
Internal Rate of Return (IRR) (p. 1449)
Net Present Value (NPV) (p. 1445)
Payback (p. 1431) Post-Audit (p. 1429) Present Value (p. 1439) Profitability Index (p. 1448) Simple Interest (p. 1438) Time Value of Money (p. 1437)
> Quick Check
7. In computing the IRR on an expansion at Mountain Creek Resort, Vernon Valley
would consider all of the following except a. present value factors.
b. depreciation on the assets built in the expansion.
c. predicted cash inflows over the life of the expansion.
d. the cost of the expansion.
8. The IRR is
a. the interest rate at which the NPV of the investment is zero.
b. the firm’s hurdle rate.
c. the same as the ARR.
d. None of the above
9. Which of the following is the most reliable method for making capital budgeting decisions?
a. ARR method b. Post-audit method
c. NPV method d. Payback method
10. Ian Corp. is considering two expansion projects. The first project streamlines the company’s warehousing facilities. The second project automates inventory utilizing bar code scanners. Both projects generate positive NPV, yet Ian Corp. only chooses the bar coding project. Why?
a. The payback is greater than the warehouse project’s life.
b. The internal rate of return of the warehousing project is less than the company’s required rate of return for capital projects.
c. The company is practicing capital rationing.
d. All of the above are true.
Check your answers at the end of the chapter.
Learning Objective 4
Learning Objective 4
Learning Objective 4
Learning Objective 4
ASSESS YOUR PROGRESS
> Review Questions
1. Explain the difference between capital assets, capital investments, and capital budgeting.
2. Describe the capital budgeting process.
3. What is capital rationing?
4. What are post-audits? When are they conducted?
5. List some common cash inflows from capital investments.
CHAPTER 26
CHAPTER 26
12. What is the accounting rate of return?
13. How is ARR calculated?
14. What is the decision rule for ARR?
15. Why is it preferable to receive cash sooner rather than later?
16. What is an annuity? How does it differ from a lump sum payment?
17. How does compound interest differ from simple interest?
18. Explain the difference between the present value factor tables—Present Value of $1 and Present Value of Ordinary Annuity of $1.
19. How is the present value of a lump sum determined?
20. How is the present value of an annuity determined?
21. Why are net present value and internal rate of return considered discounted cash flow methods?
22. What is net present value?
23. What is the decision rule for NPV?
24. What is the profitability index? When is it used?
25. What is the internal rate of return?
26. How is IRR calculated with equal net cash inflows?
27. How is IRR calculated with unequal net cash inflows?
28. What is the decision rule for IRR?
29. How can spreadsheet software, such as Excel, help with sensitivity analysis?
30. Why should both quantitative and qualitative factors be considered in capital investment decisions?
> Short Exercises
S26-1 Outlining the capital budgeting process
Review the following activities of the capital budgeting process:
a. Budget capital investments.
b. Project investments’ cash flows.
c. Perform post-audits.
d. Make investments.
e. Use feedback to reassess investments already made.
f. Identify potential capital investments.
g. Screen/analyze investments using one or more of the methods discussed.
Place the activities in sequential order as they occur in the capital budgeting process.
S26-2 Using payback to make capital investment decisions
Carter Company is considering three investment opportunities with the following payback periods:
Project A Project B Project C Payback period 2.7 years 6.4 years 3.8 years Learning Objective 1
Learning Objective 2
CHAPTER 26
Use the decision rule for payback to rank the projects from most desirable to least
desirable, all else being equal.
S26-3 Using accounting rate of return to make capital investment decisions Carter Company is considering three investment opportunities with the following accounting rates of return:
Project X Project Y Project Z
ARR 13.25% 6.58% 10.47%
Use the decision rule for ARR to rank the projects from most desirable to least desirable. Carter Company’s required rate of return is 8%.
S26-4 Using the payback and accounting rate of return methods to make capital investment decisions
Consider how Hunter Valley Snow Park Lodge could use capital budgeting to decide whether the $11,000,000 Snow Park Lodge expansion would be a good investment.
Assume Hunter Valley’s managers developed the following estimates concerning the expansion:
Number of additional skiers per day 121 skiers
Average number of days per year that weather conditions
allow skiing at Hunter Valley 142 days
Useful life of expansion (in years) 7 years
Average cash spent by each skier per day $ 241 Average variable cost of serving each skier per day 83
Cost of expansion 11,000,000
Discount rate 10%
Assume that Hunter Valley uses the straight-line depreciation method and expects the lodge expansion to have a residual value of $600,000 at the end of its seven-year life.
Requirements
1. Compute the average annual net cash inflow from the expansion.
2. Compute the average annual operating income from the expansion.
Note: Short Exercise S26-4 must be completed before attempting Short Exercise S26-5.
S26-5 Using the payback method to make capital investment decisions
Refer to the Hunter Valley Snow Park Lodge expansion project in Short Exercise S26-4.
Compute the payback for the expansion project. Round to one decimal place.
Note: Short Exercise S26-4 must be completed before attempting Short Exercise S26-6.
Learning Objective 2
Learning Objective 2
Learning Objective 2
CHAPTER 26
Note: Short Exercises S26-4, S26-5, and S26-6 must be completed before attempting Short Exercise S26-7.
S26-7 Using the payback and ARR methods to make capital investment decisions
Refer to the Hunter Valley Snow Park Lodge expansion project in Short Exercise S26-4 and your calculations in Short Exercises S26-5 and S26-6. Assume the expansion has zero residual value.
Requirements
1. Will the payback change? Explain your answer. Recalculate the payback if it changes. Round to one decimal place.
2. Will the project’s ARR change? Explain your answer. Recalculate ARR if it changes. Round to two decimal places.
3. Assume Hunter Valley screens its potential capital investments using the following decision criteria:
Maximum payback period 5.0 years
Minimum accounting rate of return 18.00%
Will Hunter Valley consider this project further or reject it?
S26-8 Using the payback and ARR methods to make capital investment decisions
Suppose Hunter Valley is deciding whether to purchase new accounting software. The payback for the $30,050 software package is two years, and the software’s expected life is three years. Hunter Valley’s required rate of return for this type of project is 10.0%.
Assuming equal yearly cash flows, what are the expected annual net cash savings from the new software?
S26-9 Determining present value
Use the Present Value of $1 table (Appendix A, Table A-1) to determine the present value of $1 received one year from now. Assume a 8% interest rate. Use the same table to find the present value of $1 received two years from now. Continue this process for a total of five years. Round to three decimal places.
Requirements
1. What is the total present value of the cash flows received over the five-year period?
2. Could you characterize this stream of cash flows as an annuity? Why or why not?
3. Use the Present Value of Ordinary Annuity of $1 table (Appendix A, Table A-2) to determine the present value of the same stream of cash flows. Compare your results to your answer to Requirement 1.
4. Explain your findings.
S26-10 Determining present value
Your grandfather would like to share some of his fortune with you. He offers to give you money under one of the following scenarios (you get to choose):
1. $7,250 per year at the end of each of the next eight years 2. $49,650 (lump sum) now
3. $98,650 (lump sum) eight years from now
Learning Objective 2
Learning Objective 2
Learning Objective 3
Learning Objective 3
CHAPTER 26
Requirements
1. Calculate the present value of each scenario using an 8% discount rate. Which scenario yields the highest present value? Round to nearest whole dollar.
2. Would your preference change if you used a 10% discount rate?
S26-11 Determining future value
David is entering high school and is determined to save money for college. David feels he can save $6,000 each year for the next four years from his part-time job. If David is able to invest at 7%, how much will he have when he starts college?
Note: Short Exercise S26-4 must be completed before attempting Short Exercise S26-12.
S26-12 Using NPV to make capital investment decisions
Refer to the Hunter Valley Snow Park Lodge expansion project in Short Exercise S26- 4. What is the project’s NPV (round to nearest dollar)? Is the investment attractive?
Why or why not?
Note: Short Exercise S26-4 must be completed before attempting Short Exercise S26-13.
S26-13 Using NPV to make capital investment decisions
Refer to Short Exercise S26-4. Assume the expansion has no residual value. What is the project’s NPV (round to nearest dollar)? Is the investment attractive? Why or why not?
Note: Short Exercise S26-4 must be completed before attempting Short Exercise S26-14.
S26-14 Using IRR to make capital investment decisions
Refer to Short Exercise S26-4. Continue to assume that the expansion has no residual value. What is the project’s IRR? Is the investment attractive? Why or why not?
S26-15 Using NPV to make capital investment decisions
Hicks Company is considering an investment opportunity with the following expected net cash inflows: Year 1, $235,000; Year 2, $195,000; Year 3, $125,000. The company uses a discount rate of 6%, and the initial investment is $365,000. Calculate the NPV of the investment. Should the company invest in the project? Why or why not?
Learning Objective 3
Learning Objective 4
Learning Objective 4
Learning Objective 4
Learning Objective 4
> Exercises
E26-16 Defining capital investments and the capital budgeting process Match each capital budgeting method with its definition.
Methods
1. Accounting rate of return 2. Internal rate of return
3. Net present value 4. Payback
Definitions
Learning Objectives 1, 2, 4
CHAPTER 26
E26-17 Defining capital investment terms
Fill in each statement with the appropriate capital investment analysis method:
Payback, ARR, NPV, or IRR. Some statements may have more than one answer.
a. _____ is(are) more appropriate for long-term investments.
b. _____ highlights risky investments.
c. _____ shows the effect of the investment on the company’s accrual-based income.
d. _____ is the interest rate that makes the NPV of an investment equal to zero.
e. _____ requires management to identify the discount rate when used.
f. _____ provides management with information on how fast the cash invested will be recouped.
g. _____ is the rate of return, using discounted cash flows, a company can expect to earn by investing in the asset.
h. _____ does not consider the asset’s profitability.
i. _____ uses accrual accounting rather than net cash inflows in its computation.
E26-18 Using payback to make capital investment decisions
Consider the following three projects. All three have an initial investment of $800,000.
Net Cash Inflows
Project L Project M Project N
Year Annual Accumulated Annual Accumulated Annual Accumulated 1 $ 100,000 $ 100,000 $ 200,000 $ 200,000 $ 400,000 $ 400,000
2 100,000 200,000 250,000 450,000 400,000 800,000
3 100,000 300,000 350,000 800,000
4 100,000 400,000 400,000 1,200,000
5 100,000 500,000 500,000 1,700,000
6 100,000 600,000
7 100,000 700,000
8 100,000 800,000
Requirements
1. Determine the payback period of each project. Rank the projects from most desirable to least desirable based on payback.
2. Are there other factors that should be considered in addition to the payback period?
E26-19 Using payback to make capital investment decisions
Henry Co. is considering acquiring a manufacturing plant. The purchase price is
$1,200,000. The owners believe the plant will generate net cash inflows of $325,000 annually. It will have to be replaced in six years. Use the payback method to determine whether Henry should purchase this plant. Round to one decimal place.
Learning Objectives 1, 2, 4
Learning Objective 2
Learning Objective 2 3.7 yrs.
CHAPTER 26
E26-20 Using payback to make capital investment decisions
Henry Hardware is adding a new product line that will require an investment of
$1,512,000. Managers estimate that this investment will have a 10-year life and generate net cash inflows of $310,000 the first year, $270,000 the second year, and
$240,000 each year thereafter for eight years. Compute the payback period. Round to one decimal place.
Note: Exercise S26-20 must be completed before attempting Exercise S26-21.
E26-21 Using ARR to make capital investment decisions
Refer to the Henry Hardware information in Exercise E26-20. Assume the project has no residual value. Compute the ARR for the investment. Round to two places.
E26-22 Using the time value of money
Helen wants to take the next four years off work to travel around the world. She estimates her annual cash needs at $31,000 (if she needs more, she will work odd jobs).
Helen believes she can invest her savings at 10% until she depletes her funds.
Requirements
1. How much money does Helen need now to fund her travels?
2. After speaking with a number of banks, Helen learns she will only be able to invest her funds at 6%. How much does she need now to fund her travels?
E26-23 Using the time value of money
Congratulations! You have won a state lottery. The state lottery offers you the follow- ing (after-tax) payout options:
Option #1: $12,000,000 after five years Option #2: $2,150,000 per year for five years Option #3: $10,000,000 after three years
Assuming you can earn 6% on your funds, which option would you prefer?
E26-24 Using NPV to make capital investment decisions
Holmes Industries is deciding whether to automate one phase of its production process. The manufacturing equipment has a six-year life and will cost $910,000.
Projected net cash inflows are as follows:
Year 1 $ 262,000 Year 2 254,000 Year 3 222,000 Year 4 215,000 Year 5 200,000
Learning Objective 2 5.9 yrs.
Learning Objective 2
13.07%
Learning Objective 3 2. $107,415
Learning Objective 3 Option #2 $9,055,800
Learning Objective 4 2. Equip. with refurb. $(18,794) NPV