Chapter 3. The Optimal Capital Budget
Up this point, we have discussed some of the issues regarding a firm’s cost of capital and capital budgeting decisions. In the process, we have looked at some of the techniques a financial manager can use in identifying the cost of various forms of capital and choosing projects that are “profitable” to the firm. Based on our earlier discussions, we know there is a significant relationship between a firm’s cost of capital and capital budgeting decisions. In order to decide
whether a project is desirable, a financial manager uses the cost of capital the firm faces to determine the project’s net present value; or compare the project’s IRR with the cost of capital. In addition, we also know that the cost of capital a firm faces might not be constant (i.e. the firm’s
MCC schedule might experience several break points). In that case, how does a firm decide what is the appropriate cost of capital? And how does it decide the optimal budget it needs for project investments? In order to answer those questions, we need to first look at a firm’s investment opportunity schedule (IOS).
The Investment Opportunity Schedule (IOS)
The concept behind the IOS is very similar to that of the MCC schedule. The MCC schedule represents the cost of capital faced by the firm (ranking from the cheapest to the most expensive) while the IOS represents the projects that are available to the firm (ranking from the most desirable to the least desirable).
In order to construct the IOS, the firm needs to first estimate the IRR of each of the project it is considering. Once that is accomplished, the financial manager can plot the IOS, which is a chart of the IRRs of the firm’s projects arranged from the highest IRR to the lowest IRR.
Example: Microsoft is interested in five independent projects, and the financial information regarding those projects is presented in the following table.
Year Project 1 Project 2 Project 3 Project 4 Project 5
Initial Cost $250,000 $100,000 $100,000 $120,000 $200,000
IRR 34.54% 39.03% 33.87% 14.28% 16.41%
Payback 2.21 1.50 1.83 3.50 4.33
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Using the IRR information above, we can arrange the projects from the highest IRR to the lowest IRR as follows: Projects 2, 1, 3, 5 and 4. This information is used to plot the Microsoft’s IOS and
it is depicted below.
IRR
39.03%
34.54%
33.87%
16.41%
14.28%
New
Capital100 350 450 650 770
From the IOS above, we know that if Microsoft decides to undertake all five projects, it will need an investment budget of $770,000. However, Microsoft does not know if this is advisable because it does not know if all the projects will be able to generate a high enough return (i.e. IRR) to cover the cost of raising the new capital. In order to make the correct decisions, Microsoft needs to combine its IOS with its MCC schedule to determine which project it should undertake and which project it should reject.
Combining the MCC and IOS Schedules
A financial manager will continue to accept project as long as the marginal return generated by the project is higher than the marginal cost the firm needs to pay to finance it. The financial manager will stop accepting projects once the marginal return generated by the project is exactly offset by the marginal cost faced by the firm. This is the point where the IOS and MCC schedule of the firm intersects.
The intersection point indicates the marginal cost of capital faced by the firm. In other words, the cost the firm will have to pay if it decides to raise one additional dollar. This is usually the rate the firm uses to evaluate its average risk projects (i.e. finding the NPVs).
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The marginal cost of capital a firm faced depends on the availability of projects. If the firm has fewer available projects, the IOS will shift to the left and the firm will face a lower marginal cost. Whereas an increase in available projects will shift the IOS to the right, and this will raise the marginal cost.
The following graph shows the MCC schedule and IOS of a particular firm. The IOS indicates that the firm faces five potential projects, and its MCC schedule indicates the firm will experience a break point (most probably when it exhausts its retained earnings). From the graph below, we know from the intersection of the firm’s IOS and MCC schedule that the marginal cost of capital for the firm is 15.5%. The firm will use this marginal cost of capital to pick its projects. From our earlier discussion, we know a firm will pick a project only if its IRR is greater than its cost of capital. In this particular case, the firm will pick projects A, B and C (and rejects projects D and E). In addition, we know the optimal capital budget for the firm is $150 million.
WACC
A=18%
B=17%
C=16%
15.5%MCC
D=14%
E=13%
IOS
$150MAmount of Financing
Example: The financial manager of Surf the Net, Inc. (STN) is planning next year’s capital budget. STN expects its net income to be $2,700,000 next year, and its payout ratio is 30%. The
Dcompany’s earnings and dividends are growing at a constant rate of 8%; the last dividend, , was 0
$1.00; and the current equilibrium stock price is $16. STN can raise up to $1,800,000 of debt at 11% before-tax cost, the next $1,800,000 will cost 12%, and all debt after $3,600,000 will cost 13%. If STN issues new common stock, a 12% underwriting cost will be incurred. STN can sell the first $200,000 of new common stock at the current market price, but to sell any additional new stock, STN must lower the price to $14. STN is at its optimal capital structure, which is 60% debt Bus 441: Corporate Finance Chapter 3-3
and 40% equity, and the firm’s marginal federal-plus-state tax rate is 40%. STN has the following independent, indivisible, and equally risky investment opportunities:
Project Cost IRR (%)
A $3,200,000 13.0
B 1,300,000 10.7
C 1,750,000 12.0
D 450,000 11.2
What is STN’s optimal capital budget?
The first thing we need to determine is STN’s MCC schedule. In order to do that, we will follow the 3-step procedure. First, we will identify the different break points in the MCC schedule. In this
scenario, there will be 4 break points in the MCC schedule.
When the firm exhausts its retained earnings and issues new common Break Point 1:
stocks.
We will let T represents the total amount of capital STN can raise without 1
exhausting its retained earnings. We know that STN is expecting a net income
of $2,700,000 and it is planning on retaining 70% of it (since the payout ratio
is 30%). As a result, we know the following:
Retained earnings？0.7？2,700,000？$1,890,000
TSince we know 40% of comes from the retained earnings, it is true that: 1
1890000 0.4？T？1,890,000，T？？$4,725,000110.4
From the above calculation, we know STN can raise up to $4,725,000 in
capital without exhausting its retained earnings.
When STN has to go from issuing 11% debt to issuing 12% debt. Break Point 2:
TWe know STN can raise a total of $1,800,000 with 11% debt. We will let 2
be the total amount of capital STN can raise with the help of issuing 11% debt.
Since STN raises its capital with 60% debt, we know the following:
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1800000 0.6？T？1,800,000，T？？$3,000,000220.6
STN can raise up to $3,000,000 in capital with the help of issuing only 11% debt.
When STN has to go from issuing 12% debt to issuing 13% debt. Break Point 3:
We know STN can raise the first $1,800,000 with 11% debt and the next $1,800,000 with $12% debt. In other words, STN can raise a total of $3,600,000 using only 11% and 12% debt. We will let represents the T3
maximum amount of capital it can raise with the help of only 11% and 12% debt. We know the following is true:
3600000 0.6T？3,600,000，T？？$6,000,000330.6
From the above, we know that STN can raise up to $6,000,000 in capital with
the help of issuing only 11% and 12% debt.
When STN has to lower the price of its new stock from $16 to $14 per Break Point 4:
share.
It is important to remember that when a firm lowers its stock price, it represents a rise in its cost of new common stock because it is not getting as
much money from each share of new common stock as it can before.
We will let T be the maximum amount of capital STN can raise without 4
lowering its new stock price to $14 per share. STN can raise a total of
$200,000 and keep its new stock price at $16. However, it is important to
Tremember that the $16 stock is not the only equity used to help raise . STN 4
has already exhausted $1,890,000 of retained earnings before issuing new
Tcommon stocks. Hence the amount of equity in is $2,090,000 4
(=$1,890,000+$200,000). As a result, we know the following is true:
2090000 0.4？T？$2,090,000，T？？$5,225,000440.4
From the above calculation, we know that STN can raise up to $5,225,000 in capital with the help of using only retained earnings and $16 stocks.
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The break points we have discovered are not in the correct order. The following table summarizes the break points:
Events Leading to the Break Points Break Points
1. Exhausting all the retained earnings $4,725,000
2. Going from 12% debt to 14% debt 3,000,000
3. Going from 12% debt to 14% debt 6,000,000
4. Lowering price of new common stocks from $8.59 to $7.63 5,225,000
Using the table above as the guideline, we can break the MCC schedule into 5 intervals. It is important that we identify the types of capital use in each interval.
Interval Instruments Used Break Point
1 Retained earnings and 11% debt
2 Retained earnings and 12% debt $3,000,000
3 $16 common stocks and 12% debt 4,725,000
4 $14 common stocks and 12% debt 5,225,000
5 $14 common stocks and 13% debt 6,000,000
Before we proceed with plotting the MCC schedule, we need to first determine the cost of each type
of capital used. We are given the different costs of debt, so we need to solve only for the cost of
retained earnings and the cost of new common stock.
(1) Cost of retained earnings
D1？(1;0.08)1r？;g？;0.08？0.1475？14.75% reP160
(2) Cost of new common stock when the price is $16
D1？(1;0.08)1r？;g？;0.08？0.1567？15.67% sP(1；F)16(1；0.12)0
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(3) Cost of new common stock when the price is $14
D1？(1;0.08)1 r？;g？;0.08？0.1677？16.77% sP(1；F)14(1；0.12)0
Now we can determine the WACC for each of the interval, and the table below shows the results:
Interval WACC Break Point
1 9.86%
2 10.22% $3,000,000
3 10.58% 4,725,000
4 11.02% 5,225,000
5 11.39% 6,000,000
We can easily plot STN’s MCC schedule with the information we got. Now we need to plot the
IOS. It is important to remember to rank the projects according to their IRR. In this situation, the
ranking is projects A, C, D and B.
IRR, WACC (%)
A
13.0
C12.0
D11.3911.2
11.02B
10.710.58
10.22
9.86
New
Capital3,200,000 4,950,000 5,400,000 6,700,000
3,000,000 4,725,000 5,225,000 6,000,000
The graph above indicates that STN should invest only in projects A, C and D. In this case, we
know STN’s optimal budget is $5,400,000.
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There are two additional issues we need to discuss regarding a firm’s choice of investment projects: (i) choosing between mutually exclusive projects, (ii) evaluating marginal projects, and (iii) risk adjustment.
(i) Choosing between mutually exclusive projects
When a firm is faced with two mutually exclusive projects, it will have two IOS schedules. Similarly, three mutually exclusive projects will lead to three IOS schedules. When we plot the IOS schedules using the IRRs of the projects, we cannot simply pick the mutually exclusive project with the highest IRR. A firm is interested more in maximizing its value, and this can only be done by choosing the project with the highest NPV rather than the highest IRR. If you remember from our earlier discussion on capital budgeting decisions, a higher IRR does not always translate into higher NPV for a project.
In order to pick the right project, the firm needs to find the NPVs of the mutually exclusive projects. However, this cannot be done without knowing the marginal cost of capital. The firm needs the MCC schedule to determine the marginal cost of capital (for each IOS schedule). Once the marginal cost is determined, the firm can find the NPV for each mutually exclusive project. The one with the highest NPV will be chosen.
(ii) Evaluating marginal project
So far, we have encountered projects with IRR either above the MCC or below the MCC. In situations like this, it is very easy for the financial manager to make the decisions: accept projects that have IRRs above the marginal cost of capital and reject projects that have IRRs below the marginal cost of capital. This situation is depicted in Scenario 1 in the following graph. In this
particular situation, the firm will accept Projects A and B, and reject Projects C and D.
However, what should the financial manager do if “part” of the project has an IRR above the marginal cost of capital but the rest of it below the marginal cost? This situation is depicted in Scenario 2 in the following graph. In this particular situation, part of Project C has an IRR higher than the marginal cost of capital and part of it has an IRR below the marginal cost of capital. If Bus 441: Corporate Finance Chapter 3-8
Project C is divisible (i.e. the firm can invest in all or parts of the project), then the firm will invest only in the portion of Project C that has an IRR above the marginal cost of capital.
IRR, WACCIRR, WACC
AA
BB
CC
DD
NewNew
CapitalCapital
Scenario 1 Scenario 2
What if the project is not divisible? In that case, should it be rejected? The answer depends on the project’s average cost. We will illustrate that with an example.
Example: Suppose the marginal project considered by Microsoft has an IRR of 12%. We know that the project has an initial cost of $100,000. The first $60,000 of the project can be finance at a cost of 10%, and the last $40,000 at a cost of 14%. Should the project be accepted?
We need to determine the average cost for financing the marginal project.
6000040000！；！；Average cost？0.1？;0.14？？0.116？11.6% ，，，，100000100000(：(：
Since the average cost of the project is below that of the IRR, the project should be chosen.
(iii) Risk adjustment
So far, we have assumed that all the projects have the same level of risk. However, this is not true in the real world. In a later chapter, we will discuss the technique for adjusting for different risk level among the projects by adjusting the cost of capital. We can also adjust for the risk level by adjusting the IOS schedule (i.e. the IRR of the projects). Projects with above average risk will have a certain percentage points deducted from their IRRs while projects with below average risk will have a certain percentage point added to their IRRs.
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Capital Rationing
Our discussion so far has assumed that the firm invests in projects with IRR greater than its cost of capital. This implicitly assumes that the firm does not have an investment budget. In other words, it has an infinite amount of money to invest. However, in many situations, a firm will set a certain amount for its investment budget that is insufficient to undertake all the available profitable projects. This is known as capital rationing.
There are many reasons why there is capital rationing:
(1) A firm is unwilling to use external funding (i.e. debt and common stock) and rely solely on retained earnings. This is because the managers feel that using debt makes the firm riskier and using common stocks dilute their controlling power.
(2) A firm might have a shortage of resources such that additional projects would not be properly managed.
(3) A firm limits the investment budget to control the expansion rate so that it will not be over-extended.
There are two general types of capital rationing faced by a financial manager: soft capital rationing and hard capital rationing. Soft capital rationing is the type of capital rationing we have discussed earlier, i.e. the limit on the capital budget is adopted (or imposed) by the management for reasons cited above. On the other hand, hard capital rationing is a situation where the financial manager is unable to raise any capital for a project under any circumstances. This is a very unique situation, and financial manager usually faces hard capital rationing when the firm faces severe financial difficulties (possibly bankruptcy) or he/she is prohibited to do so due to some preexisting contractual agreements (such as those contained in a bond covenant).
How does a financial manager makes capital budgeting decisions facing a (soft) capital rationing? In our earlier discussions, we know that when a financial manager faces no capital rationing, his/her goal is to maximize the value of the firm. However, with capital rationing, the goal of the manager is to maximize the value of the firm within the investment budget constraint. In other words, he/she will try to invest in projects that will bring the highest overall NPV (as a group) the budget can support.
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