A: (-$2000, $500, $600, $700, $800)
B: (-$2000, $950, $850, $400, $300)
If A and B are mutually exclusive and required rate of return is 5%, which should be accepted? Calculate the NPV
1. Enter Cash Flows
2. NPV>I>ENTER
3. arrow down to NPV>CPT
A. 283.26, B. 268.08
A: (-$2000, $500, $600, $700, $800)
B: (-$2000, $950, $850, $400, $300)
If A and B are mutually exclusive and required rate of return is 12%, which should be accepted? Calculate the NPV
1. Enter Cash Flows
2. NPV>I>ENTER
3. arrow down to NPV>CPT
A. -68.50, B. 1.2
A: (-$2000, $500, $600, $700, $800)
B: (-$2000, $950, $850, $400, $300)
At what discount rate will we be indifferent?
1. Use A-B as the cash flow
2. IRR>CPT
IRRdelta = 6.07%
Compute the IRR for investments with the following cash flows in years 0, 1 and 2:
(-$60, $155, -$100)
($60, -$155, $100).
How do you interpret the results in terms of the IRR criterion?
There will be two IRR solutions since two sign changes in cash flow
IRR = 25% for each. There will be a second solution 33.3%, but we will not be asked to find that on the test, just know there are two.
cash flows in years 0, 1 and 2:
(-$60, $155, -$100)
($60, -$155, $100).
Calculate the modified internal rate of return. Use a discount rate of 10%.
1: Calculate the PV of the cash outflows using the required rate of return.
2: Calculate the FV of the cash inflows at the last year of the project’s time line using the required rate of return.
3: Calculate the MIRR: N, PV = sum outflows, PMT = 0, FV = sum of inflows, CPT I/Y
A. 9.33%, B. 10.68%
Consider the following abbreviated financial statements for a proposed investment:
What is the average accounting return for the proposed investment?
1. Find average of net incomes
2. Find average Net book value including time 0. Gross Book value - accumulated depreciation
3. AAR = Ave NI/ Ave Net Book Value
Find IRR assuming k = 11% Initial Investment (160)
Years (0,1,2,3,4)
Sales (NA,95,90,97,80)
Cost (NA, 33,30,25,10)
Dep (NA,40,40,40,40)
Tax (NA,11,10,16,15)
NI (NA,11,10,16,15).
1. CF0 = (initial investment)
2. C01-C04 = NI + Dep
3. IRR > CPT
IRR = 12.06%
Calculate the profitability index for the investment. Assume k = 11%. Initial Investment (160),
Years (0,1,2,3,4)
Sales (NA,95,90,97,80)
Cost (NA, 33,30,25,10)
Dep (NA,40,40,40,40)
Tax (NA,11,10,16,15)
NI (NA,11,10,16,15).
1. Find PV of outflows = PV of initial investment
2. Find PV of inflows = PV of C01-C04 (sum of NI + Dep)
3. PI = PVin/PVout
PI = 1.023
yr (0,1,2,3,)
A(-8100,4800,3500,4600)
B(-5700,2200,1500,2900)
Find Payback for each
1. Make timeline with cash flows.
2. Make row with cumulative cash flows.
3. Payback is n + ($ cum in n/ $ CF in n +1)
A. 1.94 yr, B. 2.69 yr
yr (0,1,2,3,)
A(-8100,4800,3500,4600)
B(-5700,2200,1500,2900)
Discount rate is 13%. Find NPV
1. Enter Cash Flows
2. NPV>I>ENTER
3. arrow down to NPV>CPT
A. 2,076.83, B. -568.53
An investment project has annual cash inflows of
$8,900, 7,700, 7,100, 8,000
and discount rate of 12%. Find discounted payback if initial cost is $19,000
1. Make time line with cash flows
2. Row with discounted PV to time 0 under each CF. Set CF as FV, PMT 0 and CPT PV
3. Cumulative of the discounted value
4. Payback is n + ($ cum in n/ $ CF in n +1)
DPB = 3.15 yr
Yr (0,1,2,3,4)
Gross Investment(29,000 29,000 29,000 29,000 29,000)
Depr (0 7,250 14,500 21,750 29000)
Net Inv (29,000 21,750 14,500 7,250 0)
Generated average NI 6,600
Find Average Accounting Return.
1. Average NI is given
2. Find average Net book value including time 0 Average of Net Inv.
3. AAR = Ave NI/ Ave Net Book Value
ARR = 45.52%
Invested $10,000, lasting 3 years.
Yr (0,1,2,3)
Dep (0 4,200 2,400 3,400). Pretax income 2,100 each year which includes depreciation expense. If tax rate is 21%, what is project's Average Accounting Return?
1.NI is Pretax income * (1-tax)
2.Find Net investment for each year. Investment - Dep.
3. Average the Net investment or net book value
4. ARR = Average Net Income / Average Net Investment
ARR = 34.56%
yr (0,1,2,3)
CF (-8,000 3,500 2,500 2,500)
Find IRR
1. Enter Cash Flows
2. IRR > CPT
IRR = 3.29%
Cost $234,000. Expect after-tax cash inflows of $50,000 for five years then scrap equipment. First cash flow at end of the first year. Required return is 16%. What is the projects PI. Should project be accepted?
1. Use Cash flows in to calculate NPV inflow or PV of 50,000 payments.
2. Investment is NPV outflow
3. PI = NPV in/ NPV out
4. Accept if greater than one.
PI = 0.7 so reject.
A project has an initial outlay of $5,500. It has a single payoff of $11,419 at the end of year 7. What is the internal rate of return for the project?
1. Input N 7, PV -5,500, PMT 0 FV 11,419 CPT
I/Y = 11.00
A firm decides that the cost of capital used in a recent capital investment analysis was too low. Which of the following calculations will remain unchanged after re-evaluating the problem with the new higher discount rate?
C. Internal Rate of Return. Internal Rate of Return is calculated using a project’s cash flows and is independent of the discount rate (it is compared to the appropriate cost of capital after it is calculated)
Which of the following capital investment criteria is most closely related to Net Present Value in terms of calculation and economic interpretation?
A.Profitability Index
B.Average Accounting ReturnC.
Discounted Payback Period
D.Return on Assets
E.Payback Period
Answer: A. The Profitability Index is closely related to the Net Present Value criterion. Both involve calculating the present value of all of the cash flows. For NPV the present values of inflows and outflows are added. For PI the NPV is divided by the present value of outflows. Both are consistent with the goal of shareholder wealth maximization.
Which of the following capital investment analysis techniques ignores some of a project’s estimated cash flows?A.Net present valueB.Profitability indexC.PaybackD.Internal rate of return
Answer: C. Payback ignores cash flows that occur after the payback period
For a normal project, what will be the relationship between Payback and Discounted Payback?
A.Payback will be larger than DPB
B.Payback will be smaller than DPB
C.They will be the same for normal projects
D.Not enough information
Answer: B. Discounted payback will be larger than Payback because the discounted cash flows are smaller than the raw cash flows, taking a longer period of time to “chip away” at the initial cost
A project has a cost of $60,000, and annual cash flows as shown. The discount rate is 10%. Calculate NPV
yr (0,1,2,3,4)
(60,000) 18,500 22,000 33,500 55,000
1. Enter Cash Flow
2. NPV > I > enter rate
3. Arrow down CPT NPV
NPV = 37,734.79
A project has a cost of $60,000, and annual cash flows as shown. The discount rate is 10%. Calculate IRR
yr (0,1,2,3,4)
(60,000) 18,500 22,000 33,500 55,000
1. Enter Cash Flow
2. IRR CPT
IRR = 31.43%
A project has a cost of $60,000, and annual cash flows as shown. The discount rate is 10%. Calculate MIRR
y(0,1,2,3,4)
(60,000) 18,500 22,000 33,500 55,000
1. Move outflows to time 0 CPT PV
2. Move inflows to end of project CPT FV
3. Use 1. and 2. for cash flows
MIRR = 24.27%
A project has a cost of $60,000, and annual cash flows as shown. The discount rate is 10%. Calculate PI.
yr(0,1,2,3,4).
(60,000) 18,500 22,000 33,500 55,000
1. Find PV of outflows = PV of initial investment
2. Find PV of inflows = PV of C01-C04
3. PI = PVin/PVoutPI
PI = 1.63
A project has a cost of $60,000, and annual cash flows as shown. The discount rate is 10%. Calculate PB.
y(0,1,2,3,4).
(60,000) 18,500 22,000 33,500 55,000
1. Make timeline with cash flows.
2. Make row with cumulative cash flows.
3. Payback is n + ($ cum in n/ $ CF in n +1)
PB = 2.58 yr
A project has a cost of $60,000, and annual cash flows as shown. The discount rate is 10%. Calculate DPB.
y(0,1,2,3,4)
(60,000) 18,500 22,000 33,500 55,000
1. Make time line with cash flows
2. Row with discounted PV to time 0 under each CF. Set CF as FV, PMT 0 and CPT PV
3. Cumulative of the discounted value4. Payback is n + ($ cum in n/ $ CF in n +1)
DPB = 2.99 yr
A project has a cost of $25,000, and annual cash flows as shown. Calculate the NPV of the project if the discount rate is 12%
(25,000) 8,500 12,000 13,500 15,000
1. Enter Cash Flow
2. NPV > I > enter rate
3. Arrow down CPT NPV
NPV = 11,297.42
Why use NPV?
1. NPV uses cash flows
2. NPV uses all the cash flows of the project
3. NPV discounts the cash flows properly
Advantages and Disadvantages of Payback
Advantages
1. Easy to understand
2. Biased towards liquidity
Disadvantages
1. Ignores the time value of money
2. Requires an arbitrary cutoff point
3. Ignores cash flows beyond the cutoff date
4. Biased against long-term projects, such as research and development, and new projects
Discounted Payback
1. Fixes the time value of money problem of regular payback
2. The other problems remain:
Arbitrary cutoff, Ignores cash flows occurring after the payback
Average Accounting Return
1. Need to have a target cutoff rate
2. Decision Rule: Accept the project if the AAR is greater than a preset rate.
NPV Decision Rule
1. If the NPV is positive, accept the project
2. A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners.
3. Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal.
PB and DPB Strengths and Weaknesses
Strengths:
1. Easy to calculate
2. Intuitive
Weaknesses:
1.PB ignores the time value of money
2.Both methods rely on arbitrary accept/reject benchmarks
3.Both methods ignore cash flows that occur after the payback period. This is perhaps the most serious flaw of all.
Advantages and Disadvantages of AAR
Advantages
1. Easy to calculate
2. Needed information will usually be available
Disadvantages
1. Not a true rate of return; time value of money is ignored
2. Uses an arbitrary benchmark cutoff rate
3. Based on accounting net income and book values, not cash flows and market values
Advantages and Disadvantages of AAR
Advantages:
1. Knowing a return is intuitively appealing
2. It is a simple way to communicate the value of a project to someone who doesn’t know all the estimation details
3. If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task
Disadvantages:
1. unreliable for non-normal cash flows.
2. unreliable for mutually exclusive projects
Profitability Index
1. Measures the benefit per unit cost, based on the time value of money
2. A profitability index of 1.1 implies that for every $1 of investment, we create an additional $0.10 in value
3. This measure can be very useful in situations where we have limited capital
Advantages and Disadvantages of Profitability Index
Advantages
1. Closely related to NPV, generally leading to identical decisions
2. Easy to understand and communicate
3. May be useful when available investment funds are limited
Disadvantages
1. May lead to incorrect decisions in comparisons of mutually exclusive investments (differences in scale)
MIRR steps
1: Calculate the PV of the cash outflows using the required rate of return.
2: Calculate the FV of the cash inflows at the last year of the project’s time line using the required rate of return.
3: Calculate the MIRR: N, PV = sum outflows, PMT = 0, FV = sum of inflows, CPT I/Y
Advantages and disadvantages of MIRR
Advantages:
1. This method “fixes” the reinvestment rate problem with IRR by manually moving cash flows using the cost of capital–Only then do we calculate IRR, which at that point is called MIRR
2. A by-product of fixing the reinvestment rate problem is fixing the non-normal cash flow problem
Disadadvantages
1. MIRR does not fix the problem of choosing between mutually exclusive projects. This problem is inevitable with any rate-based method
Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9% and required payback is 4 years.
What is the payback period?
1. Make timeline with cash flows.
2. Make row with cumulative cash flows.
3. Payback is n + ($ cum in n/ $ CF in n +1)
PB 4 yr
Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9% and required payback is 4 years.
What is the NPV?
1. Enter Cash Flow
2. NPV > I > enter rate
3. Arrow down CPT NPV
NPV = 2,759
Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9% and required payback is 4 years.
What is the IRR?
1. Enter Cash Flow
2. IRR CPT
IRR = 7.93%
What is the NPV for the following projectcash flows at a discount rate of 12.50%?
CF0 (750), CF1 500, CF2 500,CF3 500.
1. Enter Cash Flow
2. NPV > I > enter rate
3. Arrow down CPT NPV
NPV = 440.67
The profitability index for a project costing $18,000 and returning $3,500 annually for five years at an opportunity cost of capital of 8.5% is:
1. PV of inflows N = 5, I/Y = 8.5, PMT = 3,500, CPT PV = - 13,792.24
2. Investment is NPV outflow = -18,000
3. PI = NPV in/ NPV out = 13,792/18,000
PI = 0.7662
A company’s current machine costs $7,750 annually to run. What is the maximum that should be paid to replace the machine with one that will last four years and cost $3,575 annually to operate? The opportunity cost of capital is 15%.
D. accept all projects with positive net present values.
Which of the following changes will increase the NPV of a project?
A. A decrease in the discount rate
What is the maximum that should be invested in a project at time zero if the inflows are estimated at $40,000 annually for three years, and the cost of capital is 9%?
N 3, I/Y 9, PMT 40,000, FV 0, CPT PV
PV = 101,251.78
What is the IRR for a project that costs $100,000 and provides cash inflows of $30,000 for 6 years?
N 6, PV -100,000, PMT 30,000, FV 0, CPT I
IRR = 19.90%
If the IRR for a project is 15%, then the project's NPV would be:
D. negative at a discount rate of 20%.
Since IRR is the discount rate that makes NPV = 0, then at a higher discount rate NPV would be negative.
Evaluate the following project using an IRR criterion, based on an opportunity cost of 10%:
CF0 -6,000, CF1 3,300, CF2 3,300.
A.Accept, since IRR exceeds opportunity cost.
B.Reject, since opportunity cost exceeds IRR.
C.Accept, since opportunity cost exceeds IRR.
D.Reject, since IRR exceeds opportunity cost.
1. Enter cash flow and IRR CPT
IRR = 6.59%, so reject since less than 10%
B.Reject, since opportunity cost exceeds IRR.
Which of the following investment criteria does not take the time value of money into consideration?
D. Book rate of return
If two projects offer the same, positive NPV, then:
B. they add the same amount to the value of the firm
A firm is considering investing in new equipment. After estimating the free cash flows and using the firm's 12 percent required rate of return, the finance department calculates that the present value of the free cash flows is $40,000. They also find that the net present value of the free cash flows for the new equipment is $2. According to the net present value criterion, should the project be accepted?
D. Yes, because the present value of the free cash flows is $40,000.
A firm is considering a project that will require an initial outlay of $35,000. This project has an expected life of five years and will generate free cash flows to the company as a whole of $15,000 at the end of each year over its five-year life. At the end of the fifth and final year, there will be an additional cash inflow of $8,200 from the salvage value. Given a required rate of return of 12 percent, what is the project's payback period, net present value, profitability index, and Internal Rate of Return?
PB = 2.33
NPV = 23,724.54
PI = 1.6778
IRR = 35.1932
A firm can purchase a new assembly machine for $20,000 that will provide annual free cash flows of $5,000 per year for five years, after which time the assembly machine will be sold as junk for $500. Calculate the net present value of the assembly machine if the required rate of return is 10 percent.
NPV = 735.61
A project has an initial outlay of $2,000. It has a single payoff of $3,996.46 at the end of year 4. What is the internal rate of return for the project?
N 4, PV -2,000, PMT 0, FV 3996.46, CPT I/Y
IRR = 18.89
All of the following criteria for capital budgeting decisions adjust for the time value of money except:
B. Payback period.
If a project with conventional cash flows has a payback period less than the project's life,
a. can you definitively state the algebraic sign of the NPV?
b. why or why not
c. if you know the discounted payback period is less than the projects life, what can you say about the NPV?
a. no.
b. NPV could be any sign depending on what the discount rate is compared to the IRR.
c. NPV is positive. Discounted payback includes discount rate.
Suppose a project has conventional cash flows and positive NPV. What can you say about
a. payback
b. discounted payback
c. PI
d. IRR
a. If NPV is positive for a discount rate then it must be positive for a zero discount rate and hence payback (with no discounting) is less then project life.
b. payback period less than project life. Since discounted payback uses same discount rate as NPV.
c. PI > 1 since NPV is positive so PV of inflows is greater than the outflows.
d. IRR must be greater than the required rate. If NPV is positive for a certain discount rate then for NPV to be zero (IRR) the discount rate would need to be higher.
Investment in A is $1M, B is $2M. Both have a unique IRR of 20%. True of False
For any discount rate from 0-20%, project B has an NPV twice as great as A.
False
Are short or long projects more sensitive to NPV
Long since farther out in future cash is more risky.