MANAGERIAL FINANCE 410
LECTURE NOTE 8
I.
Capital Budgeting (CB)
A.
Defn.: Evaluation of long-term investment projects/ opportunities.
B.
Typically involve purchase or replacement of fixed assets. May also include analysis of long-term projects like R&D investment or advertising campaigns. Note:
Even Marketing or Engineering departments may be involved in CB process.
II. Quantitative Evaluation Techniques
A.
Four Principal Approaches
1.
Net Present Value
2.
Internal Rate of Return
3.
Modified Internal Rate of Return
B.
Steps in the Evaluation Process
1.
Identification of Cash Flows and Timing a.
Include only incremental flows. b.
Relevant cash flows should be after-tax.
2.
Application of Analysis Method
3.
Decision, Implementation & Evaluation
C.
Cash Flow Identification (Three types, generally.)
1.
Initial Cash Flows

Paid now to undertake project

Includes purchase price and install costs

Possible (after-tax) salvage value of old machine if replacement.
2.
Interim Operating Cash Flows a.
Need to deduct depreciation as non-cash, deductible expense to calculate taxable income. b.
Then add depreciation back since it is a non-cash
1

expense. c.
May need to account for incremental increase/ decrease in net working capital. d.
Note: These cash flows will necessarily include both incremental inflows offset against outflows.
3.
Terminal Cash Flows: a.
Estimate of asset’s (salvage) value at project termination. b.
Taxes due to asset sale at market vs. book value.

Sale at BV (= MV)

no tax effect.

Sale above BV

Recapture of depreciation, leads to added tax liability.

Sale below BV

Loss on sale, generates tax credit.

Sale above purchase price

Sale minus purchase equals capital gain. CG may be taxed at rate more favourable than ordinary income.
Difference between Purchase price and BV taxed as recapture of depreciation. c.
Cash flows (inflows and/or outflows) due to project termination.
III. Net Present Value and Internal Rate of Return
Evaluation of Bond Investments
A.
Net Present Value: As you will all surely recall from
FIN 381 Net Present Value is considered to be THE best capital budgeting technique, given the assumptions involved in its calculation.
B.
It is calculated as shown in equation (8.1) below. The decision rule is to accept the project if NPV

0.
NPV = PV(Benefits) – PV(Costs). (8.1)
2

C.
Calculating NPV using a financial calculator is not difficult once the cash flows have been entered correctly.
1.
Very Important NPV/IRR Point I : To deal with the frequency of non-annual payments (in both your financial calculator and EXCEL) the actual cash flows are used. THE DISCOUNT RATE IS THE FACTOR
THAT IS ADJUSTED, i.e., it needs to be r%/m to find
NPV. Further, once the IRR has been found using the function it will also be r%/m, so it must be multiplied by m to annualise it as the last step.
2.
Very Important NPV Point IIa : In using the Excel
NPV function, the Initial Cash (Out)flow MUST be entered as a separate part of the formula, i.e., assuming it appears in the spreadsheet as a negative number it needs to added to the NPV function.
3.
Very Important IRR Point IIb : Conversely, in using the Excel IRR function the initial cash flow is part of the array in the function. These three points are demonstrated in Ex. 8.1a) and b) below.
D.
Internal Rate of Return: As if you need to be reminded, the IRR is THE discount rate which makes the
NPV of an investment project equal to zero.
E.
The IRR decision rule is that a given project is acceptable if the IRR equals or exceeds the project’s required return or hurdle rate.
F.
Calculating Coupon Bond values (PV and NPV) and returns (IRR) may be viewed as an investment project
(which it surely is, especially if you purchase a bond, or several, for your investment portfolio). Thus, calculation
3

of NPV and IRR for the two bonds previously analysed
( Example 7.3
) will be utilised to illustrate this point.
G.
The difference here is that rather than using the Time
Value functions utilised in the previous sub-section, the
NPV and IRR functions (for EXCEL) will be employed.
Ex. 8.1
The following condensed information is repeated from the
Example 7.3
in LN #7 . As the relevant cash flow calculations have been previously illustrated they will not be repeated. Rather the cash flows are shown as part of the answer.
Bond Center
OVERVIEW FORD MOTOR CREDIT WACHOVIA CORP
Price:
Coupon (%):
Maturity Date:
? (108.00)
7.500
1-Aug-2012
Yield to Mat (%): 3.327
Current Yield (%): 6.944
Fitch Ratings: BB
Cpn Pmt Freq: Semi-Annual
First Cpn Date: 1-Feb-2010
Type: Corporate
Callable: No
109.05
5.250
1-Aug-2014
? (2.839)
4.814
A
Semi-Annual
1-Feb-2005
Corporate
Yes
Employ the LN #7 , Spreadsheet 5 for both parts. a) Use the Excel NPV function to determine the Net
Present Value (round to nearest cent, based on a quote of
100) of purchasing the Ford Motor Credit LLC.
bond assuming that it will mature in two years. b) Calculate the Internal Rate of Return on the Wachovia
Corp.
bond assuming that it will mature in four years using the Excel IRR function.
4

A8.1a) The cash flows on the Ford Motor Credit bond are as follows and are shown as a spreadsheet excerpt.
C D E F G
22 Ford Motor Credit Coupon Bonds as a Net Present Value Problem
23
24 Inputs Year Cash Flow
25
26
27
Face Value
Cpn Rate
YTM
$1,000.00
7.5000%
3.3270%
0
1/2
1
-$1,080.101
$37.500
$37.500
28 m
29 #Yrs to Mat
2
2
1 1/2
2
$37.500
$1,037.500
30 Mkt Price -$1,080.10 NPV $0.000000
General Excel Function: = NPV(rate,value1, [value2], [value3], …)
SS Solution: =(NPV($D$27/$D$28,$G$26:$G$29))+$D$30
A8.1b): The cash flows on the Wachovia Corp. bond are as follows and are shown as a spreadsheet excerpt.
C
38 Wachovia Corp.
39
40 Inputs
41 Face Value
42 Cpn Rate
43 Cur Yld
44 m
45 #Yrs to Mat
46 Mkt Price
47
48
49
50
D E
$1,000.00
5.2500%
4.8143%
2
4
-$1,090.50
F
1
1 ½
2
2 ½
G
Year Cash Flow
0
½
-$1,090.500
$26.250
$26.250
$26.250
$26.250
$26.250
3
3 ½
$26.250
$26.250
4 $1,026.250
IRR 2.84052%
General Excel Function: = IRR(values, [guess])
SS Solution: =IRR($G$41:$G$49,0.08)*$D$44
5

IV.
Modified Internal Rate of Return
A.
Modified Internal Rate of Return
1.
MIRR is the discount rate which forces the PV of the
Terminal Value (TV) to equal the present value of the costs.
2.
Overcomes the problems inherent with IRR’s implicit assumption of reinvestment at the IRR (instead of the firm’s discount rate).
3.
In this formulation the Terminal Value is found by converting all interim cash inflows (outflows) into their future (present) value at the end of the project.
4.
Then the Modified IRR is found exactly the same way as the implicit rate of return between single payments.
PV(Costs) = PV(Terminal Value)

PV(Costs) =



TV
(1

MIRR) n



;



 n
 t

0 (
COFt
1
 k ) t



=





 t

MIRR =



TV
PV(Cost)



1 n

1 . (8.2)
MIRR Excel Function: n


CIFt
0
* (1
 k) n
(1

MIRR) n
 t






;
Syntax
6

MIRR ( values , finance_rate,reinvest_rate )
Returns the modified internal rate of return for a series of periodic cash flows. MIRR considers both the cost of the investment and the interest received on reinvestment of cash.
Values are an array or a reference to cells that contain numbers. These numbers represent a series of payments (negative values) and income (positive values) occurring at regular intervals.
 Values must contain at least one positive value and one negative value to calculate the modified internal rate of return.
Finance_rate is the interest rate you pay on the money used in the cash flows.
Reinvest_rate is the interest rate you receive on the cash flows as you reinvest them.
Remarks
 MIRR uses the order of values to interpret the order of cash flows. Be sure to enter your payment and income values in the sequence you want and with the correct signs (positive values for cash received, negative values for cash paid).
Ex. 8.2
In Spreadsheet #6 and below you will find data on the after-tax cash flows for two mutually-exclusive investment projects that the Browning Firearms Co.
is evaluating.
Row
9
10
11
12
13
14
15
16
17
18
5
6
7
1
2
3
4
B
Columns
C D
Expected net cash flows
Time Project A Project B
0 ($950) ($1,100)
($150)
$200
$400
$600
$700
$800
($200)
$375
$375
$375
$375
$375
$375
$0 a) Use the Excel NPV function to determine the Net
Present Value of the two projects using both a discount of 12% and 16%. Put the results in cells
7

B25:E26 as indicated. Note: Even though the Year
7 cash flow is zero, do not exclude it in using this and the following functions. b) Construct and graph NPV profiles for both projects using varying discount rates from 5% to 16% (in
1% increments) and from 18% to 24% (in 2% increments). Put the NPV results in cells B37:C52. c) Use the Excel IRR function to determine each project’s Internal Rate of Return and place the results in B57:B58. d) Use the Excel MIRR function to calculate each project’s Modified Internal Rate of Return at both a reinvestment (and financing) rate of both 12% and 16%. Place the results in cells C65:F66. e) Use the difference in cash flows and the IRR function to determine the crossover rate between the two projects—which is the discount rate at which the two projects have the same NPV. Put the crossover rate in cell F75. Use the NPV function to verify that at this discount rate both projects have the same NPVs. Put the results in cells I79:I80.
A8.2a) The answers to the NPV-function calculations are shown below. Interestingly, at a discount rate of
12%, Project A is preferred. Whereas at the 16% discount rate, Project B is preferable. This tells us that the crossover rate (question 8.2e) ) will be somewhere between the two discount rates.
A B
23 @ a 12% cost of capital
24 WACC = 12%
C D E
@ a 16% cost of capital
WACC = 16%
25 NPV A =
26 NPV B =
$453.57
$441.78
NPV A =
NPV B =
$247.83
$281.78
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Excel Function B25: =NPV($B$24,C12:C18)+C11
A8.2b) The NPV Profile results and graph are shown below. That these results are correct can be verified by comparing the NPVs for both projects at the 12% and 16% rates to those found in part
A8.2a) .
46
47
48
49
50
51
52
39
40
41
42
35
36
37
38
43
44
45
A
@ 12%
5.0%
6.0%
7.0%
8.0%
9.0%
10.0%
11.0%
12.0%
13.0%
14.0%
15.0%
16.0%
18.0%
20.0%
22.0%
24.0%
B
Project A
$453.57
$931.01
$851.63
$776.37
$704.98
$637.21
$572.85
$511.70
$453.57
$398.27
$345.65
$295.55
$247.83
$158.98
$78.14
$4.45
($62.84)
C
Project B
$441.78
$803.38
$744.00
$687.45
$633.58
$582.22
$533.22
$486.45
$441.78
$399.08
$358.25
$319.18
$281.78
$211.60
$147.07
$87.59
$32.68
NPV Proje ct Profile s
Project A
Project B
$1,000.00
$800.00
$600.00
$400.00
$200.00
$0.00
($200.00)
5% 7% 9% 11% 13% 15% 17% 19% 21% 23% 25%
Discount Rate
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A8.2c) The IRR results suggest that Project B is preferred.
A
57 IRR
A
=
58 IRR
B
=
59
60
61
62
63
64
B
22.13%
C D E F
Note in the graph above that the X-axis
G
25.27%
@ a 12% cost of capital
MIRR
A
= 17.35% intercepts would equal the two projects' IRRs.
@ a 16% cost of capital
MIRR
A
= 19.28%
MIRR
B
= 17.53% MIRR
B
= 19.84%
Excel Function B57: =IRR(C11:C18)
A8.2d) The MIRR results also suggest that Project B is preferred at both assumed reinvestment/finance rates. On the following page, the equation approach is used to verify the MIRR for Project B at a 12% reinvestment/finance rate.
Excel Function C65: =MIRR(C11:C18,$B$24,$B$24)
A8.2e) The Crossover Rate is the discount rate at which both projects have the same NPV and is 12.93% in this comparison. This equality is verified in cells
I79:I80.
A B C
71 Cash flow
72 Time differential
73
74
75
76
77
78
79
80
0
1
2
3
4
5
6
7
$150
($525)
($175) Crossover rate =
$25
$425
($200)
D E F
12.93%
G values are equal at the crossover cost of capital.
H
$225 The crossover rate represents the cost of capital at which the two projects
$325 have the same net present value. In this example, verify that net present
Project A:
Project B:
I
$401.85
$401.85
Excel Function F75: =IRR(B73:B80)
Excel Function I79: =NPV(F75,C12:C18)+C11
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A8.2.
Time-Line Calculation of Browning’s (Plan B) Terminal Value @ 12%.
0 1 2 3 4 5 6
($1,100.00) $375.00 $375.00 $375.00 $375.00 $375.00 $375.00
Terminal
7 FVIF Value
$0.00
Factor @ YR 7
* (1+.12) 6
* (1+.12)
* (1+.12)
* (1+.12)
* (1+.12)
* (1+.12)
* (1+.12)
5
4
3
2
1
0
= $ 420.00
= $ 470.40
= $ 526.85
= $ 590.07
= $ 660.88
= $ 740.18
= $ 0.00
Total FV = $ 3,408.38
Use (8.2) to find MIRR:
MIRR =


$ 3
$ 1 ,
, 408 .
38
100 .
00


1 / 7
-1 = 17.53%.
11