1. FIN 360: Corporate Finance
Topic 11: Cost of Capital and the Basics of Capital Budgeting
Larry Schrenk, Instructor

2. Overview Cost of Capital Decision Rules in Capital Budgeting
Sources of Capital
Weighted Average Cost of Capital (WACC)
WACC Example
Decision Rules in Capital Budgeting
The Decision Rules:
Payback Period
Discounted Payback Period
Net Present Value (NPV)
Internal Rate of Return (IRR)
Modified Internal Rate of Return (MIRR)
Some Additional Issues

3. Sources of Capital Internal External Pecking Order Capital as ‘Cost’
Retained Earnings
External
Debt
Equity
Pecking Order
Capital as ‘Cost’

4. Weighted Average Cost of Capital (WACC)
Interpretation
Average Cost to Firm of Capital
Uses
Firm Cost of Capital
Discounting for Projects
Cautions:
Risk
Financing

5. WACC Formula Weights (Weighted Average) Required Returns Tax Effect
wi = weight of asset
ri = return on asset
tc = corporate tax rate
Weights (Weighted Average)
Required Returns
Tax Effect

6. Weights

7. Weights Two Goals Decisions Forecast Relate to Project
Firm versus Project Weights
Book versus Market
Past versus Future
Actual versus Target

8. Required Returns Bonds (rd) Preferred Stock (rp) Common Stock (rs)
Current YTM on Firm’s Bonds
Return on Firm’s Bond Grade, e.g., AA
Preferred Stock (rp)
Implied Discount Rate from Market
Common Stock (rs)
CAPM
Alternate Model

9. Tax Effect Key Effect Required Return on Bond Dividends: Not Deducible
Interest Payments: Deducible
Effect
Dividends: $1 costs $1
Interest Payments: $1 costs $1(1- tc)
If tc = 30%, $1( ) = $0.70
Required Return on Bond
rd(1- tc)

10. WACC Goal
Minimize Cost
Cost of Capital
Debt Ratio

11. Debt Trade-Off Why not All Debt Financing? Trade-Off Tax Subsidy
Financial Distress

12. Tax Effects and Financial Distress
Present value of tax shield on debt
Value of firm with debt subsidy
Value of firm with debt subsidy and financial distress
Maximum firm value
Present value of financial distress costs
Value of firm with no debt subsidy
Value of Firm D*
Debt

13. WACC Example Investment Amounts Common Stock = $50,000 Bonds = $25,000
Preferred Shares = $25,000
Bond
Price = $990
Coupon Rate = 8%
Period = Semiannual
Maturity = 25 Years
Par Value = $1,000
Preferred Share
Price = $85
Dividend = $8
Common Stock
Risk-Free Rate (rf) = 5%
Return on Market (rM) = 12%
Beta (b) = 1.1
Corporate Tax Rate
(tc) = 35%

14. WACC Example Overview Calculate Weights, wd, wp, ws
Calculate Cost of Equity Capital, rs, using CAPM.
Calculate Cost of Preferred Capital, rs, using Market Implied Discount Rate
Calculate Cost of Debt Capital, rd, using YTM.
Calculate WACC.

15. WACC Example: Weights

16. WACC Example: Cost of Debt
Price = $990
Coupon Rate = 8%
Period = Semiannual
Maturity = 25 Years
Par Value = $1,000
Yield to Maturity (YTM)
P/Y = 2; N = 50; I/Y = 8.09%;
PV = 990; PMT = -40; FV = -1,000

17. WACC Example: Cost of Preferred
Price = $85
Dividend = $8
Implied Discount Rate

18. WACC Example: Cost of Equity
rf = 5%
rM = 12%
b = 1.1
CAPM

19. WACC Example: Result wd = 0.25; wp = 0.25; ws = 0.50 rd = 8.09%
rp = 9.41%
rs = 12.70%
tc = 35%

20. Decision Rules in Capital Budgeting
Goal: Only do projects that increase firm value
Criteria:
C1) Recognize the time value of money.
C2) Incorporate all relevant free cash flows.

21. Decision Rules in Capital Budgeting
Avoid (if possible):
C3) Arbitrary assumptions,
C4) The need for data that has great uncertainty,
C5) Excessive complexity of calculation, and
C6) Technical problems.

22. The Five Decision Rules

23. Data
r = 10% 1 2 3 4
-1,000
300
200
400
700

24. Payback Period
Rule
Do project if total cash flow within the payback period > the required investment.

25. Payback Period EXAMPLE: 3 Year Payback Period Calculation
= 900 < 1,000
Result: $ < $1, Bad Project 1 2 3 4
-1,000
300
200
400
700

26. Calculate Payback Period
Find payback period:
= 900 < 1,000 < 1,600 =
Period is between 3 and 4 years
Amount left to be paid in year 4 = 1,000 – 900 = 100
Cash flow in year 4 = 700
Payback point in year 4 = 100/700 =
Payback Period = years 1 2 3 4
-1,000
300
200
400
700

27. Payback Period Evaluation Result: Fails C1) Fails (no discounting)
C2) Fails (not after payback period)
C3) Fails (length of payback period)
C4) Passes
C5) Passes
C6) Passes
Result: Fails

28. Discounted Payback Period
Rule
Do project if present value of the cash flows within the payback period > the required investment.

29. Discounted Payback Period
EXAMPLE (r = 10%):
3 Year Discounted Payback Period Calculation:
Result: $ < $1, Bad Project 1 2 3 4
-1,000
300
200
400
700

30. Calculate Discounted Payback Period
Find discounted payback period:
= < 1,000 < 1, =
Period is between 3 and 4 years
Amount left to be paid in year 4 = 1,000 – =
Cash flow in year 4 =
Payback point in year 4 = / =
Discounted Payback Period = years 1 2 3 4
-1,000
300
200
400
700
272.73
165.29
300.53
478.11

31. Discounted Payback Period
Evaluation
C1) Passes
C2) Fails (not after payback period)
C3) Fails (length of payback period)
C4) Passes
C5) Passes
C6) Passes
Result: Fails

32. T-P-S
If the payback period approach says a project is good, then the discounted payback period will always agree.
True
False
If the discounted payback period approach says a project is good, then the payback period will always agree.

33. Net Present Value (NPV)
Rule
Do project if NPV is positive.

34. Net Present Value (NPV)
NPV is:
The present value of all cash flows (including any required investments).

35. Net Present Value (NPV)
EXAMPLE (r = 10%):
NPV Calculation:
Result: $ > 0 Good Project 1 2 3 4
-1,000
300
200
400
700

36. Net Present Value (NPV)
Evaluation
C1) Passes
C2) Passes
C3) Passes
C4) Require estimating long term cash flows
C5) Moderate complexity
C6) Passes
Result: G) Passes

37. T-P-S
If you apply the discounted payback period, but include all relevant cash flows, would this be an acceptable method?
Yes No
It would depend on other factors.

38. NPV on Calculator
What is the NPV of a cash flow that costs $1000 and has the following cash flows: 200, -300, 1,200 (r = 18%)?
Press CF, Input 1000, Press +/-, Press Enter
Press , Input 200, Press Enter
Press , Press Enter (Default Frequency is 1)
Press , Input 300, Press +/-, Press Enter
Press , Input 1200, Press Enter
Press NPV,
Input 18, Press Enter
Press , CPT to get , i.e., $ NOTE: Similar to Mixed CF calculation.

39. NPV on Calculator
What is the NPV of a cash flow that costs $1000 and has the following cash flows: 200, -300, 1,200 (r = 18%)?
=npv(18,-1000,{ 200, -300, 1200}
Answer =

40. Internal Rate of Return (IRR)
Rule
Do project if IRR > required rate of return (r).

41. Internal Rate of Return (IRR)
IRR is:
The discount rate that makes present value of all cash flows (including any required investments) equal to zero.

42. IRR Diagram = + + + = IRR is the discount rate that makes
C1/(1+IRR)
PV(C4) +
C2/(1+IRR)2
PV(C3) +
C3/(1+IRR)3
PV(C2) +
C4/(1+IRR)4
PV(C1) =
IRR is the discount rate that makes
Total PV = |C0 |
Total PV =
|-C0|

43. Internal Rate of Return (IRR)
EXAMPLE (r = 10%):
IRR Calculation:
Result: 18.1% > 10% Good Project 1 2 3 4
-1,000
300
200
400
700

44. Internal Rate of Return (IRR)
Evaluation
C1) Passes
C2) Passes
C3) Passes
C4) Requires estimating long term cash flows
C5) Moderate complexity
C6) Technical Problems
1) Reinvestment Rate Assumption
2) Multiple IRR Results
3) Project Comparisons
Result: G) Passes (assuming the technical problems do not occur)

45. IRR on Calculator
What is the IRR of a cash flow that costs $1000 and has the following cash flows: 200, -300, 1,200?
Press CF, Input 1000, Press +/-, Press Enter
Press , Input 200, Press Enter
Press , Press Enter (Default Frequency is 1)
Press , Input 300, Press +/-, Press Enter
Press , Input 1200, Press Enter
Press IRR, , CPT to get 3.34, i.e., 3.34%

46. IRR on Calculator =irr(-1000,{ 200, -300, 1200} Answer = 3.34%
What is the IRR of a cash flow that costs $1000 and has the following cash flows: 200, -300, 1,200?
=irr(-1000,{ 200, -300, 1200}
Answer = 3.34%

47. Modified Internal Rate of Return
Rule
Do project if MIRR > required rate of return (r).
MIRR is the discount rate that makes
the present value of all cash outflows
equal to
the present value of the terminal value.

48. ‘Modification’
Allows the reinvestment rate of cash flows to be specified.
Allows the reinvestment rate of cash flows to be different than the discount rate.

49. MIRR Diagram = MIRR is the discount rate that makes PV(Total FV) =|C0|+
C3(1+rRI)
FV(C3) +
C2(1+rRI)2
FV(C2) +
C1(1+rRI)2
|-C0|
FV(C1) = =
PV(Total FV)
Total FV
Total FV
(1+MIRR)4

50. Modified Internal Rate of Return
Steps:
1) Determine all cash flows.
2) Find the ‘terminal value’, i.e., the future value, of all cash inflows.
3) Find the present value of all cash outflows.
4) Find the MIRR which is the discount rate that makes the present value of all cash outflows equal to the present value of the terminal value.

51. Modified Internal Rate of Return
EXAMPLE (r = 10%):
MIRR Step 1: Determine Cash Flows
Above 1 2 3 4
-1,000
300
200
400
700

52. Modified Internal Rate of Return
EXAMPLE (r = 10%):
MIRR Step 2: Calculate Terminal Value (TV), i.e., the future value of cash inflows. 1 2 3 4
-1,000
300
200
400
700

53. Modified Internal Rate of Return
EXAMPLE (r = 10%):
MIRR Step 3: Find the present value of all cash outflows.
The only cash outflow is at t = 0 and its present value is -1,000. 1 2 3 4
-1,000
300
200
400
700

54. Modified Internal Rate of Return
EXAMPLE (r = 10%):
MIRR Step 4: Find the MIRR that makes the present value of all cash outflows equal to the present value of the terminal value.
Result: 15.53% > 10% Good Project 1 2 3 4
-1,000
300
200
400
700

55. Modified Internal Rate of Return
Evaluation
C1) Passes
C2) Passes
C3) Passes
C4) Requires estimating long term cash flows
C5) Most complexity
C6) Passes
Result: G) Passes

56. Summary of the Five Rules
Undertake Projects when:
Payback Period: Payback period cash flow > investment
Discounted Payback Period: Discounted payback period cash flow > investment
NPV: NPV > 0
IRR: IRR > r
MIRR: MIRR > r

57. Some Additional Issues

58. Some Additional Issues
Comparing NPV and IRR
Using Decision Rules to Compare or Select among Projects
Sign Changes in the Cash Flows and Multiple IRR’s

59. Comparing NPV, IRR, and MIRR
Assuming no technical problems occur, NPV and IRR always give the same and the correct answer about whether or not to do one specific project.

60. Comparing Projects
The IRR and MIRR rules cannot be used to compare projects or select among projects since they do not meaningfully compare the absolute advantage of one project over another.
Instead, the NPV rule must be used to compare or select among projects.

61. Comparing Projects EXAMPLE (r = 10%): Period 1 2 3 4 5 A -1,000 300
200
400
700 B
-100 40 30 50 80

62. Comparing Projects
IRRA
IRRB

63. Comparing Projects
NPVA
NPVB

64. Comparing Projects Results
IRRA = 18.1% < IRRB = 29.6%
NPVA = $ > NPVB = $53.36
Question: Would you rather have a higher rate of return or a higher dollar return?
In the end it is the dollar return that counts
Project A increases firm value by $
Project B increases firm value by $53.36.
Project A is worth $ more than B!

65. Sign Changes and Multiple IRR’s
What is the IRR of the following cash flow? 1 2 3 4 -3 20
-16
-32 32

66. Sign Changes and Multiple IRR’s
There are multiple correct answers!
This is possible whenever there is more than one sign change in the cash flows!

67. Sign Changes and Multiple IRR’s
The line crosses the x-axis at each IRR.