1. Asset Valuation Methods
Byers

2. Time Value of Money Basics
The basic idea behind the time value of money is that $1 today is worth more than $1 promised next year
Factors to consider:
Size of the cash flows
Time between the cash flows
Rate of return
Opportunity cost
Interest rate
Required rate of return
Discount rate

3. Organizing Cash Flows
A helpful tool for analysis of cash flows is the time line, which shows the magnitude of cash flows at different points in time
Cash we receive is called an inflow and is represented by a positive number
Cash that leaves us is called an outflow and is represented by a negative number

4. Single-period Future Value
You invest $100 today in an account earning 5% per year. Compute the future value in one year.
Value in one year = Today’s cash flow + Interest earned
= $100+ ($100 x 0.05)
= $100 x ( )
= $105
In general: FV = PV x (1 + r)T

5. Compounding and Future Value
In the example above, suppose you leave the money invested for two years. What is the future value?
Value in 2 years = $100 x ( )2
= $110.25
The total interest of $10.25 represents $10 earned on the original $100 investment plus $0.25 earned on the $5 first year’s interest
This represents compounding, i.e. earning interest on interest

6. Time Value in Excel: Future Value

7. Suppose we leave the deposit for five years
FV = $100 x (1.05)5 = $127.63
Financial calculator solution:
INPUT 5 N
I/YR PV
PMT FV
OUTPUT
127.63

9. Future Value in Excel

10. Using the built-in Excel function

11. Present Value
Watching money grow into the future (compounding) makes intuitive sense. Why would anyone care about finding the present value of a future cash flow, which uses the opposite process, called discounting?
It may surprise you to learn that much of finance involves the application of present value. Finance is about valuing things, and that often means finding the present value of future cash flows.

12. In general: PV = FV /(1 + r)T
This process is called discounting.
Notice that this isn’t a new equation. It is really the same as the future value equation we saw before (just rearranged to solve for PV instead of FV)

13. Present Value
Suppose we discount a $100 deposit for two years at a discount rate of 5 percent?
PV = $100 / (1.05)2 = $90.70
Suppose we discount for five years?
PV = $100 / (1.05)5 = $78.35

14. Time Value in Excel: Present Value

15. Excel solution to PV examples

16. Using Excel’s built-in PV function

17. Solving for the Rate
Here’s an example where we need to solve for the interest rate: If we bought a gold coin for $350 three years ago and we can sell it for $475 today, what annual rate of return have we earned?

19. Solving for Time
Suppose your company currently has sales of 350 billion ISK. If the company grows at 7 percent per year, how long will it take before the firm reaches 500 billion ISK in sales?

21. Present Value of Multiple Cash Flows
Example: You are offered cash flows of $100 today, followed by $125 next year and a $150 at the end of the second year. Interest rates are 7%
To find the present value of these cash flows we recognize that we can find their individual present values and add them up
100
125
150
... 1 2 3

22. Present Value Multiple Cash Flows
$100
$125
$150 $0
$125/(1.07)
$116.82
$150/ (1.07)2
$131.02
$0 / (1.07)3
$0.00
$347.84
133

23. Excel: Present Value of Uneven Cash Flows

24. Value
What factors determine a firm’s value?

26. Exercise: Determining the value of a simple project
Set up your spreadsheet

27. A project costs $25 million
A project costs $25 million. It returns cash flows of $10 million, $20 million, and $18 million for the next three years. The required return on projects of this risk is 10 percent. What is the project’s value? What is the return on the project?

29. Capital Investment Analysis Techniques
Net Present Value (NPV)
Internal Rate of Return (IRR)
Payback (PB)
Discounted Payback (DPB)
Average Accounting Return (AAR)
Modified Internal Rate of Return (MIRR)
Profitability Index (PI)

30. Processing Capital Budgeting Decisions
For each of our decision statistics, we need to
Identify how to calculate the decision statistic
Decide on an appropriate benchmark for comparison
Define what relationship between the statistic and the benchmark will dictate project acceptance
For mutually exclusive projects, we will also have to choose between the competing projects

31. Net Present Value
NPV represents the “purest” of the capital budgeting rules
It measures the amount of value created by the project
NPV is completely consistent with the overall goal of the firm: to maximize firm value

32. Calculating NPV is very straightforward
It is simply the sum of the present value of every project cash flow

33. NPV Benchmark
NPV includes all of the project’s cash flows, both inflows and outflows
Since it involves finding the present values of every cash flow using the appropriate cost of capital as the discount rate, anything greater than zero represents the amount of value added above and beyond the required return
Accept project if NPV > 0
Reject project if NPV < 0

34. Example
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 percent
i=12%
(25,000)
8,500
12,000
13,500
15,000

35. 12%
Period
Cash Flow PV
(25,000) 1
8,500
7,589 2
12,000
9,566 3
13,500
9,609 4
15,000
9,533
NPV =
11,297

36. Interpretation: Do we like this project? Yes – it has a positive NPV
If the market agrees with our analysis, the value of our firm will increase by $11,297 due to this project
When will the value-added occur? When the project is complete?
NO – it will occur immediately upon the announcement that we are taking the project

37. NPV Strengths and Weaknesses
NPV not only provides a go/no-go decision, but it also quantifies the dollar amount of the value added
NPV is not a ratio
It works equally well for independent projects and for choosing between mutually- exclusive projects
Accept the project with the highest positive NPV
Weakness
Managers who are unfamiliar with NPV can misinterpret the results
They sometimes insist on comparing NPV to the cost of the project, not understanding that the cost is already incorporated into the NPV

38. What is the Source of Positive NPV?
Competitive Advantage!
Sustainable Competitive Advantage (hopefully)

39. Payback
Answers the question: How long will it take us to recoup our costs?
Has intuitive appeal
Remains popular because it is easy to compute
Built-in assumptions:
Cash flows are normal
Assumes cash flows occur smoothly throughout the year

40. Example Refer to the problem we worked earlier. Compute the payback.
(25,000)
8,500
12,000
13,500
15,000
Cumulative
(25,000)
(16,500)
(4,500)
Payback will occur during the 3rd year
Payback = 2 + 4,500/13,500
= years

41. Accept project if calculated payback < Maximum allowable payback
Payback Benchmark
Firms set some maximum allowable payback
Often set arbitrarily – one of payback’s greatest weaknesses
Accept project if calculated payback < Maximum allowable payback
Reject project if calculated payback > Maximum allowable payback

42. Payback Strengths and Weaknesses
Easy to calculate
Intuitive
Weaknesses:
Payback has severe weaknesses that make it unsuitable to be the primary method used to select projects
Payback ignores the time value of money
Payback relies on arbitrary accept/reject benchmarks
Payback ignores cash flows that occur after the payback period. This is perhaps the most serious flaw of all

43. Discounted Payback
Fixes the time value of money problem of regular payback
The other problems remain:
Arbitrary cutoff
Ignores cash flows occurring after the payback
Method
Convert the raw cash flows to their present value equivalents
Re-compute payback

44. Example Discounted Payback for our project: i=12%
(25,000)
8,500
12,000
13,500
15,000
CF present values
(25,000)
7,589
9,566
9,609
9,533
Cumulative
(25,000)
(17,411)
(7,845)
Discounted Payback will occur during the 3rd year
Discounted Payback = 2 + 7,845/9,609
= years

45. Average Accounting Return
Another attractive, but fatally flawed, approach
Ranking Criteria and Minimum Acceptance Criteria set by management

46. Average Accounting Return
There are many different definitions for average accounting return
The one used in the book is:
Average net income / average book value
Note that the average book value depends on how the asset is depreciated.
Need to have a target cutoff rate
Decision Rule: Accept the project if the AAR is greater than a preset rate.
The example in the book uses straight line depreciation to a zero salvage; that is why you can take the initial investment and divide by 2. If you use MACRS, you need to compute the BV in each period and take the average in the standard way.

47. Consider the ACME Project
Year 0: CF = -165,000
Year 1: CF = 63,120; NI = 13,620
Year 2: CF = 70,800; NI = 3,300
Year 3: CF = 91,080; NI = 29,100
Your required return for assets of this risk is 12%
Cost of the project = $165,000
Straight-line depreciation to zero

48. Computing AAR For The ACME Project
Assume we require an average accounting return of 25%
Average Net Income:
(13, , ,100) / 3 = 15,340
Average Book Value = 165,000 / 2 = 82,500
AAR = 15,340 / 82,500 = .186 = 18.6%
Do we accept or reject the project?
Students may ask where you came up with the 25%, point out that this is one of the drawbacks of this rule. There is no good theory for determining what the return should be. We generally just use some rule of thumb.

49. Average Accounting Return has the distinction of being the only capital investment analysis method that is worse that Payback
At least payback uses cash flows

50. Internal Rate of Return
IRR is the most popular technique to analyze projects
Often referred to as “the return on the project”
Fortunately, IRR is generally consistent with Net Present Value
Problems occur if cash flows are not normal
Problems can occur when choosing among mutually exclusive projects

51. IRR is so closely related to NPV that it is actually defined in terms of NPV
IRR is the discount rate that results in a zero NPV

52. Example
Refer to our previous problem. Calculate the IRR of the project.
i=12%
(25,000)
8,500
12,000
13,500
15,000

53. Period
Cash Flow
(25,000) 1
8,500 2
12,000 3
13,500 4
15,000
IRR =
30.08%

54. Interpretation: Do we like this project?
Yes – the IRR is greater than the required return
Notice that we did not input the discount rate when calculating IRR. IRR is a mathematical solution to a series of numbers. It is only when we compare the IRR to the required return do we insert any economic content into the problem

55. Internal Rate of Return benchmark
Once we calculate IRR, we must compare it to the cost of capital (investors’ required return) to see if the project is acceptable
We only want to invest in projects where the rate we expect to get (IRR) exceeds the rate investors require

56. Problems with IRR IRR will be consistent with NPV as long as:
The project has normal cash flows
Projects are independent

57. For non-normal cash flows there will be multiple IRRs for the same project
IRRs represent the solution to a mathematical series. These solutions are called ‘roots’, and a series will have as many roots as there are sign changes. This is Descartes’ Rule of Signs, discovered in 1637.
For us, this means that there will be as many IRRs as there are sign changes in the cash flows.

58. - + + + + - + + + - - + + - + + Examples:
In our normal project, we have one IRR because we have one sign change
What if a project involves a cleanup at the end? We might have two sign changes (and two IRRs):
What if a project has to shut down in the 3rd year for maintenance, and then starts up again? We might have three sign changes:

59. Differing Reinvestment Rate Assumptions of NPV and IRR
There is yet another problem with IRR relative to NPV. Each method implicitly makes assumptions about what happens to the cash flows that are generated by the project. Both assume that the cash flows are reinvested elsewhere in the firm. But the two methods differ greatly in the assumed rate that the reinvested cash flows earn.

60. NPV assumes that the reinvested cash flows earn the cost of capital (i).
IRR assumes that the cash flows will be reinvested at the IRR of the project
This doesn’t make sense, since the project likely beat out a bunch of other projects in the first place
Also, in a competitive market, it is more realistic to assume that there are more project available at a rate that is near the firm’s cost of capital
NPV’s reinvestment rate assumption is considered to be superior to IRR’s.

61. Modified Internal Rate of Return
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
A by-product of fixing the reinvestment rate problem is fixing the non-normal cash flow problem

62. Example Calculate the MIRR of the following project: 1 2 3 4 5 i = 9%1 2 3 4 5
i = 9%
-10,000
4,000
6,000
-5,000
12,000
15,000

63. INPUT 5 -13,861 N I/YR PV PMT FV OUTPUT 41,497 24.52
Step 1: PV of outflows = -13,861
Step 2: FV of inflows = 41,497
Step 3: Calculate MIRR
MIRR = 24.52%
Exceeds the required return of 9%, so accept project
INPUT 5
-13,861 N
I/YR PV
PMT FV
OUTPUT
41,497
24.52

65. Profitability Index
Measures the benefit per unit cost, based on the time value of money
A profitability index of 1.1 implies that for every $1 of investment, we create an additional $0.10 in value
This measure can be very useful in situations where we have limited capital

66. Profitability Index PI = Very Similar to Net Present Value
PV of Inflows
Initial Outlay
PI =
Instead of Subtracting the Initial Outlay from the PV of Inflows, the Profitability Index is the ratio of Initial Outlay to the PV of Inflows.

67. Example Calculate the PI of our project: i=12%
Recall that the NPV = $11,297
PI = 36,297 / 25,000 =
PI indicates that we should accept the project
i=12%
(25,000)
8,500
12,000
13,500
15,000

68. PI can have problems for mutually exclusive projects of differing size

69. Capital Rationing
Occurs when a company has more good projects than money to invest in them
Best method: NPV
Select set of projects that maximizes total NPV

70. Adjusting the Discount Rate
The risk inherent in the cash flows should be reflected in the discount rate
Average risk project → Firm’s Overall Cost of Capital
Safer project → Lower discount rate
Riskier project → Higher discount rate

71. Now Let’s Solve a Capital Budgeting Problem from Start to Finish
NPV
IRR
Payback
Discounted Payback
MIRR PI