Weighted Marginal Cost of Capital (WMCC) and Investment Opportunities Schedule

By finding all break points, we can construct the weighted marginal cost of capital – WMCC – schedule. (WMCC) schedules show the relationship between the level of total new financing and a company’s weighted average cost of capital.

Thereafter, we can construct the investment opportunities schedule (IOS), which is a graph where the business’s investment opportunities are ranked based on their returns and financing required, arranged from the highest returns and all the way to the lowest returns. It is the decreasing function of the level of total financing.

If we combine the weighted marginal cost of capital (WMCC) schedule and investment opportunities schedule (IOS), we can use it to make investment decisions. The rule is to invest in projects up to the point on the graph where marginal return from investment equals its WMCC (where IOS=WMCC).

All projects on the left of the point where IOS=WMCC will maximize shareholders wealth and all points on the right of the point where IOS=WMCC will decrease shareholders’ wealth.

It is important to note that the majority of firms stop investing before the marginal return from investment equals its weighted marginal cost of capital (WMCC). Therefore, the majority of businesses prefer a capital rationing position (the position below the optimal investment budget, which is also called the optimal capital budget).

Test yourself


ABC Company has to make an investment of $1,000,000. The long-term debt weight in the capital structure is 35%. ABC has $700,000 of retained earnings but 50% of it must be paid to common stock shareholders in the form of dividends. Preferred stock is currently not used as a source of finance by ABC.

What are the weights that ABC will have for each source of capital?

SOLUTION:

Firstly, we need to find out how much of retained earnings ABC has left after payment of dividends to shareholders: $700,000*0.5=$350,000.

Therefore, the weight of retained earnings is 35% ($350,000 out of $1,000,000).

$1,000,000-$350,000 (35%, funds available from long-term debt source) – $350,000 (35%, funds available from retained earnings) = $300,000 (30%)

Therefore, the weights are as follows:

Long-term debt – 40%

Retained earnings – 35%

Common stock – 30%

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The cost of capital

What is the cost of capital? It is the required rate of return a business must earn on its investments (capital budgeting projects) to maintain the market value of the firm’s shares and to attract funds.

It is a measure used to determine whether or not certain project will decrease or increase the firm’s value in the market place and, consequently, whether or not it should be recommended.

If NPV is more than zero and IRR is greater than the cost of total capital, then a proposed project will increase the market value of the firm and it should be recommended.

If, however, NPV is less than zero and IRR is lower than the cost of all capital, then a proposed project will decrease the market value of the firm and it should not be recommended.

Therefore, if a firm’s risk is assumed to be constant, than any projects with the rate of return higher than the cost of all capital will increase the market value of the firm and any projects with the rate of return below the cost of capital of the enterprise will decrease market value of the firm.

In the discussions that follow we assume that the cost of all capital is measured on the after-tax basis and that a firm’s acceptance of the project does not affect FINANCIAL and BUSINESS RISKS.

FINANCIAL RISK is the chance that a firm will not be able to meet its financial obligations, which can result in bankruptcy. Financial risk is directly affected by a firm’s capital structure (its mix of debt and equity financing). The more debt the firm uses in its capital structure mix, the higher the financial risk.

BUSINESS RISK is the chance that a firm will not be able to cover its operating costs. There are three factors that affect business risk. These are increases in operating leverage, revenue instability and cost instability.

1 – Increase in operating leverage refers to higher use of fixed operating costs.

2 – Increase in revenue instability (or decrease in revenue stability) refers to deterioration of stability of sales of the firm.

3 – Lastly, increase in cost instability (decrease in cost stability) refers to how predictable are costs of the firm, such as labour and raw materials’ costs.

Business risk must be taken as is and the capital structure mix the firm chooses does not influence it.

Firms usually try to maintain an optimal mix of financing (debt and equity) referred to as the target capital structure. Firms have various sources of capital and the cost of capital may be different for each source of financing. When determining the cost of capital, it is helpful to determine an average cost of all sources of capital, which is called the weighted average cost of capital (WACC).

 

Risk Adjusted Discount Rate: Dealing with Risk in Capital Budgeting

Breakeven cash inflow analyses, risk adjusted discount rate (RADR) and scenario analyses are tools that facilitate better insight into managing risk in capital budgeting.

Risk in capital budgeting especially refers to variability of the returns (variability of cash inflows), because the initial investment is more or less known with some level of confidence. Therefore, we need to ensure that present value (PV) of cash inflows will be large enough to ensure that project is acceptable.

To adjust the present value of future cash inflows for risk embodied in particular project, we can either adjust cash inflow directly or we can adjust the discount rate. Because adjusting cash inflow is highly subjective, we will rather adjust discount rate. This is when risk adjusted discount rate technique comes into play.

RADR is a discount rate that must be earned to compensate an investor for the risk undertaken. Under RADR the value of the firm must be at least maintained or must increase. Risk adjusted discount rate is the most popular risk adjustment technique that utilize NPV.

The higher is the risk of specific project, the higher RADR will be.

The deployment of RADR is best illustrated by the use of an example:

EXAMPLE

Amanda can invest in two shares, A and B. Both shares presently cost $50 and Amanda wants to hold shares for 4 years. Annual dividends from share A expected to be $7. Annual dividends from share B are expected to be $12. However, shares B are more risky. In 4 years time Amanda expects to be able to sale shares A for $55 each and shares B for $70 each. Amanda’s required return is 8%. However, for shares B she adjusts her return so that her risk adjusted discount rate becomes 12%. Calculate risk adjusted net present values (NPVs) of shares A and B and recommend which shares should Amanda purchase.

Solution:

We will use financial calculator to find risk adjusted net present values (NPVs) of shares A and B.

Risk adjusted NPV of shares A:

Clear calculator: second function, C ALL

CFo: -50

CF1: 7

CF2: 7

CF3: 7

CF4: 62 (7+55)

I: 8

Second function, NPV: $15.38

Risk adjusted NPV of shares B:

Clear calculator: second function, C ALL

CFo: -50

CF1: 12

CF2: 12

CF3: 12

CF4: 82 (12+70)

I: 12

Second function, NPV: $30.94

Since investment in shares B offers higher risk adjusted NPV, Amanda should choose to invest in shares B.

The main difficulty in using risk adjusted discount rate (RADR) technique is in determining level of risk and approximating an appropriate risk adjusted discount rate (RADR). There is currently no systematic way to adjust required return to risk adjusted discount rate (RADR). Management usually determines risk adjusted discount rate (RADR) subjectively.

Sometimes risk index is determined which reflects risk adjusted discount rate (RADR) for every subsequent level of risk. For example, risk can be categorized into below average, average, above average and very high. Past experience and CAPM can be used to subjectively determine the risk adjusted discount rate (RADR) appropriate for each subsequent level (category) of risk.

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Risk Scenario Analysis: Dealing with Risk in Capital Budgeting

Another way to evaluate risk of the project is to undertake scenario analysis.

Scenario analysis focus on developing few alternative scenarios and evaluating variability between returns, which can be measured by net present value (NPV).

For example, we can generate 3 scenarios (optimistic, most likely and pessimistic) and than find NPVs for each of the scenarios. When we know net present values for each scenario, we can find the range.

The range here is found by taking NPV of optimistic outcome less NPV of pessimistic outcome, as shown below:

range (1) = NPV of optimistic outcome – NPV of pessimistic outcome

Alternatively, the range is found by taking annual cash inflow from optimistic outcome and subtracting annual cash inflow from pessimistic outcome, as shown below:

range (2) = annual cash inflow from optimistic outcome – annual cash inflow from pessimistic outcome

Range shows us variability between returns.

Risk in Capital Budgeting

When it comes to capital budgeting, risk refers to probability that project will proof to be unacceptable with net present value (NPV) less than zero or internal rate of return (IRR) less than cost of capital. Particularly, it refers to variability of the returns.

To find the minimum cash inflow level acceptable, we need to calculate breakeven cash inflow.

Breakeven cash inflow refers to the minimum cash inflow that it required for the project to be acceptable. It is calculated as follows:

PV – Initial investment

N – number of periods over which cash inflow is received

I – required cost of capital

Find PMT – breakeven cash inflow

Test yourself:

ABC Corporation have an option to invest in project A which requires investment of $120,000. The duration of the project is 5 years and ABC’s cost of capital is 9%. What is the breakeven cash inflow?

Solution:

We can find breakeven cash inflow of project A with the help of financial calculator.

PV: -120,000

N: 5

I: 10

Find PMT: $31,448.94

The above calculation helps us to determine that the minimum annual cash inflow that will be acceptable for project A is $31,448.94.

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Net Present Value Method

Sophisticated capital budgeting techniques include Net present value method (NPV), Internal Rate of Return method (IRR), Profitability index (PI) and Equivalent Annual Annuity (EAA). NPV is discussed below.

NPV is a sophisticated capital budgeting technique. Theoretically, Net Present Value (NPV) is the best technique out of sophisticated capital budgeting techniques but it is difficult to use it in practice. Sometimes Net Present Value method is referred to as the “gold standard” for investment decisions.

It is very easy to use Net Present Value with the help of a financial calculator if all necessary data is available. However, it is important to firstly understand the logic behind this calculation. NPV is determined by finding present value of cash inflows and then subtracting an initial investment.

NPV=Present value of cash inflows – initial investment

Now, after we understand the logic behind usage of Net Present Value method, we can calculate NPV using a financial calculator. We will always use a HP 10bll financial calculator throughout the website. Other calculators are similar but may have some small differences.

Before you make any calculations, make sure that you:

1 – Clear the calculator – by pressing the second function followed by “C All”

2 – Ensure that it is set for end if cash flows occur at the end of the period and that it is set for beginning if cash flows occur at the beginning of the period.

To set for end/beginning – press second function followed by beg/end. If it is set for the beginning than word “begin” will be displayed. If it is set for the end than no word will be displayed.

Majority of calculations will be with the “end” setting (used when cash flows occur at the end of the period). Therefore, it is important to acquire a habit of re-setting your calculator to the “end” setting after every calculation with the “begin” setting. Otherwise, you are running a risk of forgetting to re-set the calculator and obtaining an incorrect result from future calculations.

NPV FOR ANNUITY IS CALCULATED AS FOLLOWS:

Initial investment: amount, minus sign, CFi

Annual cash inflow: amount, CFi1

Number of periods: number of periods, second function, Ni

Cost of capital: number, i

Find NPV: second function, NPV

NPV FOR A MIXED STREAM IS CALCULATED AS FOLLOWS:

Initial investment: amount, minus sign, CFi

Put in amount for each cash inflow separately following with CFi1, CFi2 etc

Cost of capital: number, i

Find NPV: second function, NPV

If NPV is higher than zero than we know that this project will earn returns higher than the business’s cost of capital. Further, the owner’s wealth will increase by the amount equal to NPV.

Test yourself


ABC Corporation has an option to invest in projects A. Project A has aninitial investment of $15,000, and operating cash inflows of $3,000 over the economic life of the project, which is 8 years. The cost of capital (also called discount rate or rate of return) is 8%.

Find the net present value (NPV) of project A?

SOLUTION:

With the use of a financial calculator, we can find the net present value (NPV) as follows:

Clear the calculator by pressing second function followed by “C ALL”.

Make sure calculator is set to the “end”. This setting is used because in this problem cash flows occur at the end of each period. It is commonly accepted that if problem does not state when cash flows occur, you need to assume that cash flows occur at the end of the period, not at the beginning of the period.

WE KNOW THAT NPV FOR AN ANNUITY IS CALCULATED AS FOLLOWS:

Initial investment: amount, minus sign, CFi

Annual cash inflow: amount, CFi1

Number of periods: number of periods, second function, Ni

Cost of capital: number, i

Find NPV: second function, NPV

NOW YOU NEED TO PLUG IN THE NUMBERS:

NPV for annuity:

Initial investment: 15000, minus sign, CFi

Annual cash inflow: 3000, CFi1

Number of periods: 8, second function, Ni

Cost of capital: 8, i

Find NPV: second function, NPV

= $2,239.92

The above calculation makes it clear that project A is an acceptable project for ABC because the NPV is higher than zero ($2,239.92).

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Unsophisticated capital budgeting techniques

Simple (unsophisticated) capital budgeting techniques include average rate of return (ARR) and the payback method (also called PB or payback period).

Average Rate of Return


Average Rate of Return (ARR) is an unsophisticated budgeting technique and generally considered to be ineffective. Average Rate of Return (ARR) evaluates relative profitability of the investment. In other words, it evaluates how project affects accounting profits. Average Rate of Return (ARR) is calculated as follows:

ARR = Average income / Average investment

Average income refers to annual average net profits after tax (refer to income statement to see how net profits after tax are determined). Annual average net profits after tax is found by taking total net profits after tax over the useful life of the project and dividing it by number of years over useful life of the project. Average investment refers to average investment over the economic life of the project. The ARR capital budgeting technique does not consider the time value of money. It also considers net profits rather than cash inflows. Consequently, the technique overlooks the possibility of reinvestment of returns.

The positive side of this technique, as compared to payback period discussed below, is that it considers returns on investment over entire useful life of the project. However, this technique is generally not recommended.

Payback method


Payback period (PB), also called a payback method, is another unsophisticated budgeting technique. It determines how long it takes to recover the initial investment by taking into account cash inflows from the investment. If we deal with an annuity (an equal periodic cash flow over a specific period) than all we need to do is to divide initial investment by an annuity.

However, if we deal with a mixed stream of cash inflows (unequal cash flows during specific period with no precise pattern) than we need to add up cash flows until the initial investment is recovered.

Management needs to subjectively determine the maximum payback period and then projects are evaluated according to this. If the project’s payback period is below maximum than the project is acceptable and vice versa.

The payback period budgeting technique measures business’s risk exposure because the project’s risk level depends on how long it takes to recover the initial investment. However, it does not explicitly consider the time value of money.

Moreover, this budgeting technique is weak because it is subjective in nature since the minimum payback period is subjectively determined. Furthermore, it does not take into account the cash flows that occur after the payback period.

A variation of payback period capital budgeting technique allows to account for time value of money and risk (due to usage of discount rate which incorporates risk). Such variation is called discounted payback period technique. This technique determines how long it takes for discounted cash flows to recover the investment. However, this variation still does not consider cash flows after the payback period.

Test Yourself


ABC Corp has a proposed project A, which has expected cash inflows of $4,000 over 10 years period. The initial investment is $30,000. Find the payback period.

SOLUTION:

Payback period = 30,000/4,000 = 7.5 years

This means that it will take 7.5 years for ABC to recover its investment in project A.

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International Capital Budgeting Decisions

International capital budgeting decisions are similar to domestic capital decisions but are more demanding due to additional considerations that must be taken into account. Such additional considerations may include foreign currency considerations, transfer pricing and political (country) risk.

Exchange rate risk is one of the additional considerations that has to be taken into account. Exchange rate risk refers to the risk that arises due to fluctuations in the exchange rate between foreign and domestic currency. To counteract this risk, at least partly, organization may use various techniques. Particular cash flows can be hedged in the short-term. Further, an organization can borrow in the foreign market in the foreign currency to counteract long-term exchange rate risk.

Transfer Prices


Transfer prices is another consideration to be taken into account and refer to internal prices (which are different from market prices) on goods which are moving from one subsidiary to another within multinational corporation (MNE). It arises due to the tendency of multinational corporations (MNEs) to price products exchanged between subsidiaries at prices which are not aligned with the market prices to minimize the overall tax that the organization (MNE) has to pay.

Transfer prices have distorting and misleading effects on the capital budgeting decisions. In other words, due to transfer prices, the value of the cash flows and that of the project is likely to be distorted. This occurs because value of costs and incremental cash flows are distorted and therefore incorrect data is used in the capital budgeting analysis.

To counteract distorting and misleading effects of transfer prices on capital budgeting decisions, MNEs need to make few adjustments. Firstly, MNEs need to use market prices in capital budgeting decisions. Secondly, any fees and royalties paid from one subsidiary to another or to parent as well as appropriate fixed costs must be added back to the cash inflows.

Political (Country) Risk


Political (country) risk is another consideration that must be taken into account and refers to risks associated with doing business in particular country. Political risks may include difficulties with transferring returns on investment (repatriating profits) from the foreign country to domestic due to foreign government’s actions or even expropriation.

Political risk can be partly counteracted by sharing risks via partnerships with local businesses that will have a better understanding of how to most efficiently and safely conduct business in that specific country. Discount rates (cost of capital) should reflect the level of political risk.

Other country risks include domestics uprisings such as the May 2010 demonstrations in Bangkok, Thailand which effectively shutdown the commercial hub of the country. Such an upheaval would have impact the both domestic (delays in building hotels etc) and international decisions (changes in forex, country risk profiles, international insurance rates etc).

Overall, international capital budgeting decisions incorporate all the issues that must be considered when operating domestically. However, there are also few additional considerations that must be taken into account. The adjusted present value technique is often used to incorporate such additional risks into calculations.

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Capital Budgeting Techniques

The Capital budgeting techniques discussed here focus on financial considerations, although, there are financial and non-financial considerations that should be taken into account when selecting a project for capital expenditure.

There are unsophisticated (simple) and sophisticated (advanced) techniques.

1 – Unsophisticated techniques include payback period (PB, also called payback method) and average rate of return(ARR).

2 – Sophisticated techniques include net present value (NPV), internal rate of return (IRR), equivalent annual annuity (AEE) and profitability index (PI).

Out of this range of techniques, payback period is the most popular unsophisticated technique. From the sophisticated techniques, the most popular methods are net present value (NPV) and internal rate of return (IRR).

Capital budgeting techniques used to select most profitable projects for capital expenditure, which is aligned with enterprise’s objective of maximizing shareholder’s wealth. Sophisticated techniques are considered to be the most effective means of selecting the most appropriate projects for capital expenditures. Such techniques take into account risk, the time value of money and focus on cash flows rather than on accounting profits.

The result of educated usage of capital budgeting techniques knowledge generated on which projects and in which order should be accepted based on the available funds for investment.