Homemade Leverage

Homemade leverage is the use of borrowing or lending to alter financial leverage of the company the investor is exposed to (Bhatnagar, 2009). The MM proposition demonstrates that if investors prefer an alternative capital structure different to the chosen leverage of the firm, investors may achieve same results by homemade leverage (Wilkinson, 2003).

We will now illustrate that a firm’s capital structure choice becomes irrelevant as any investor who favours the proposed capital structure can simply create it using homemade leverage model (Berk, 2011:455-458). For example, an investor who prefers to hold levered equity as opposed to the wholly equity firm can do so by adding leverage onto his portfolio i.e. buying stock on margin.

	Recession	Initial cost	Expansion
Unlevered equity	$900	$1000	$1400
Margin loan	(£525)	($500)	($525)
Levered equity	$375	$500	$875

While the cash flows of the unlevered equity serve as a security for the margin loan, the loan becomes risk free and investors may borrow at 5% risk free rate. The investor is able to replicate the payoffs to the levered equity using homemade leverage as illustrated in the table above for a cost of $500. Thus, by the Law of One Price, the levered equity must be valued at $500.

Supposing that the entrepreneur of the unlevered firm introduces debt, but the investor prefers to hold unlevered equity. The investor can replicate the payoffs of the unlevered equity by purchasing both of the firm’s debt and equity. Combining the cash flows of both stocks produces cash flows identical to unlevered equity ($1000) as illustrated below.

	Recession	Initial cost	Expansion
Debt	$525	$500	$525
Levered equity	$375	$500	$875
Unlevered equity	$900	$1000	$1400

In this scenario, a firm’s capital structure choice becomes irrelevant in respect of homemade leverage. However, under perfect market assumptions, different choices of capital structure offer no advantage to investors as they do not affect the firm’s value.

Net Present Value (NPV) or Internal Rate of Return (IRR)?

Although the popularity of NPV is growing in recent years, internal rate of return and payback period methods are commonly used in practice. A survey study conducted by John Graham and Campbell Harvey in 2001 shows that 75% of firms surveyed use the NPV for making investment decisions. This contrasts with a similar study done by LJ. Gitman and JR. Forrester, who argued that only 10% of firms use NPV (Berk, 2011:158-159) and Cohen & Yagil claims that IRR is more popular than NPV (Atrill, 2012)

F. Alkaraan and D. Northcott’s study agrees with Graham and Campbell (Atrill, 2012:155-157). They surveyed 83 senior financial managers from large manufacturing corporations and concluded that NPV is seen the most popular, followed by IRR and payback method. However, as capital budgeting decisions often involve major undertakings, therefore risk and rewards had to be carefully weighed, Alkaraan and Northcott also found out that 98% of the managers do not rely on just one investment appraisal technique and 88% have used more than three methods.

In my view, each appraisal method has its advantages and shortcomings as discussed in previous postings, its beneficial to include a combination of alternative methods in evaluating an investment opportunity and using own business judgement as well. Sometimes using alternative rules may give the same answer as NPV, but other times they may differ. In the case the rules conflict, following the alternative rule means undertaking a negative NPV project, thus leading to bad decisions that reduces wealth.

Systematic and Unsystematic Risk

While investing in a stock market, one must take into account the risk that affects the stock return i.e. systematic risk and unsystematic risk. This can be differentiated as below:

Systematic Risk

Systematic risk refers to risk that cannot be diversified away (non-diversifiable risk). It is uncontrollable by an organisation and is macro in nature e.g. interest rate risk, inflations, war. Investors have to face the systematic risks, regardless. For instance, a global recession affects the whole share market and not just one single share. Similarly, interest rates increase affects every stock in the market. For example, Black Monday in 1987, stock markets crashed and almost all stock dropped in significant value in that single day (Colombo, 2012).

Unsystematic Risk

Unsystematic risk is unique to an industry which affects the variability in stock or security return. It is also known as “unique risk” as it is due to influence of internal factors prevailing within a company. From an organisation’s point of view, this is controllable. i.e. business risk, financial risk and operational risk. For example, the long running row over cost cutting caused staff at British Airways to go on strike in 2010, causing a loss of £142m in revenues, subsequently causing it share value to suffer (R.Massey, 2010).

Investors may mitigate this risk by diversifying their portfolio.  Following an increase of securities in a portfolio, the portfolio’s standard deviation of the rate of return reduces. It is said that unsystematic risk can be fully diversified by holding 15–20 asset portfolio (Wiley, 2004).

CAPM calculation

According to CAPM (Shapiro, 2003), if an asset is correctly priced, it should be positioned on the SML. However, in reality, the expected returns may differ from what it should be according to CAPM. Using the information given, the required returns are calculated using the formula below:

Required returns = Risk free rate + (Share’s beta x market Risk premium)

Stock A: CAPM = 4% + 1.5 (6%) = 13%

Stock B: CAPM = 4% + 0.5 (6%) = 7%

On the basis of the above calculations, investors would require a return of 13% to justify buying Stock A and 7% for Stock B. Using the derived CAPM, this is plotted on to the SML chart to analyse if the expected returns given reflect the correct price.

Shares should be bought if the security is plotted above the SML as it is undervalued and investors can expect greater takings. Vice versa, the stock should be sold if it is plotted below the line as it means it is overvalued and the returns are not enough to compensate for the risk.

Applying the above calculations and information given, Stock A is undervalued (required return is 13% against 19%), while Stock B is also undervalued (7% against 8%), therefore both stock should be bought.

CAPM is an equilibrium model. This then pushes the market to move towards equilibrium, meaning that all assets would be correctly priced and the expected and required return would be equal. The market is efficient when no investor can recognise any mispriced assets (Zivot, 2006).

Security Market Line (SML) and Capital Market Line (CML)

Security Market Line (SML)

According to Brearley (2012), the SML represents the CAPM equation and implies a linear connection between the expected return and systematic risk (beta). The SML intercept on the Y-axis (expected returns) represents the risk free rate when beta equals to 0. CAPM states that the market portfolio is efficient, thus all stocks should lie on the SML (Berk, 2011). Shares should be bought if the security is plotted above the SML as it is undervalued and investors can expect greater takings. Vice versa, the stock should be sold if it is plotted below the line as it means it is overvalued and the returns are not enough to compensate for the risk. This will push back the market to equilibrium.

Capital Market Line (CML)

The CML represents the best possible group of portfolio assets that makes the most out of the expected level of returns at a  given level of risk (as defined by volatility/ standard deviation). Thus, investors should choose a portfolio with a combination of both risk free investments and market portfolio (RiskLearn, 2012). It is noted that when investors have identical expectations the market portfolio and efficient frontier coincides (JM Samuels, 1995:258-262). This is known as the tangency portfolio.

Beta

Beta is a measure of the stock’s volatility and is used to evaluate the expected rate of return i.e. the amount of return that investors required to compensate for the risk (KSigman, 2005). Generally, representative index e.g. S&P 500 for US stocks can be used to obtain beta. With the given information, this can be applied to the above CAPM equation to obtain the stock’s beta.

E(r) = Rf + B(Rm – Rf)

8% = 2% + B (8%)

B = 0.75

The beta obtained shows that it is less volatile than the market as a whole and a beta less than 1.0 implies stocks from a utility company(Little, 2013). So during a bear market, when the market moves down by 10%, the stock price will tend to fall by 7.5%. Vice versa, during a bull market, it may not give the highest returns.

In general, a mix of high and low beta stocks aids as an adequate diversification. Like most financial prediction tools, the beta only measures the volatility of the stock in the past using historical data. Beta fluctuates all the time, thus it may not be an accurate measure to predict its current volatility.

CAPM

The CAPM model (Berk, 2011:357) explains the relationship between risk and expected returns. The following assumptions are applied:

·         Investors can borrow and lend at risk free rates

·         All investors are rational and risk adverse

·         All investors receives the same information and that information are costless

·         The markets are perfect, thus no tax, inflations or transaction cost are taken into account

·         Investors have same expectations regarding risk and expected returns of security

With the given information and assumptions, the expected returns can be derived using the CAPM formula as below:

E(r) = Rf + B(Rm – Rf)

Where:

E(r) = 3% + (1.2) (12% – 3%) = 3% + (1.2 x 9%) = 13.8%

Based on the calculations above, investors can expect a rate of return of 13.8% to compensate for the stock’s individual risk, stock market’s risk and the risk free rate interest. From the beta given, it denotes volatility greater than 1 and implies that the stock probably represents stock from a technology company.

A limitation to note is that the expected return derived is based on historical data and may not guarantee the returns as expected. (Investors Chronicle, 2001)

Internal Rate of Return (IRR)

The Internal rate of return is the discount rate which yields a zero net present value (P.Atrill, 2012:157). The higher the IRR, the more desirable to undertake the project. Thus, projects can be ranked accordingly and the highest will be selected. An attribute of the IRR is that it takes into account the power of compounding interest and assumes that all cash flows are reinvested at the IRR.

To obtain the IRR, the trial and error approach is applied. At 3% interest rate, we obtained the following:

Now: Present value (PV) = -$1350k

Year 1: PV = $700k / 1.03 = $679.63k

Year 2: PV = $750k / 1.03² = $706.95k

Adding those up gets NPV = -$1350k + $679.63k + $706.95k = $36.58k

The results shows a positive NPV, thus a larger interest rate is needed to derive a negative NPV in order to calculate the IRR. For this purpose, a 10% interest rate is selected.

Now: PV = -$1350k

Year 1: PV = $700k / 1.10 = $636.37k

Year 2: PV = $750k / 1.10² = $619.8k

Adding those up gets NPV = -$1350k + $636.37k + $619.8k = -$93.83k

Using the figures obtained, this can be tabulated into the table below:

Year	Cash Flow ($’000)	DF@3%	DF@10%	PV@3%	PV@10%
0	(1350)	1	1	(1350)	(1350)
1	700	0.9709	0.9091	679.63	636.37
2	750	0.9426	0.8264	706.95	619.8
				36.58	(93.83)

Using the above calculations, we could easily derive the IRR using the following formula and plot it into a graph.

IRR = NPV1 + (DR2-DR1) x NPV1 / (NPV1 – NPV2)

IRR = 3% + (10% - 3%) x 36.58/ 130.41

       = 3% + 1.96% = 4.96% = 5%

According to Berk (2011), the company should undertake the project since its IRR (5%) exceeds the cost of capital (3%).

Ranking projects by IRR

Year	Project A	Project B	Discount Factor @ 18%	Present Value - A	Present Value - B
0	-500	-500	1	-500.00	-500.00
1	167	200	0.8475	141.53	169.50
2	180	250	0.7182	129.28	179.55
3	160	170	0.6086	97.38	103.46
4	100	25	0.5158	51.58	12.90
5	100	30	0.4371	43.71	13.11
				-36.53	-21.48

Internal rate of return  = small % + (large % - small %) [positive NPV/(positive NPV - negative NPV)]

IRR - A = 12% + (18% - 12%) [26.79/ 26.79+36.53]
            = 12% + (6%) (26.79/63.32)
            = 0.1454

IRR - B = 12% + (18% - 12%) [31.80/ 31.80 + 21.48]
            = 12% + (6%) [31.80/ 53.28]
            = 0.1566

Project B will be preferred as it has a higher IRR compared to Project A.
However, both projects are desirable as they both have IRR higher than the cost of capital of 12%.

Calculating ARR and Payback period

Your firm is considering two projects with the following cashflow:

Year	Project A	Project B
0	-500	-500
1	167	200
2	180	250
3	160	170
4	100	25
5	100	30

Assumption: Straight line depreciation is used = (Initial Investment - residual value) / n = (500 - 0)/5 = 100

				Project A	Project B
Nominator
Average profits before depreciation				(167+180+160+100+100)/5 = 707/5 = 141.4	(200+250+170+25+30)/5 = 675/5 = 135
Average annual profit after depreciation				141.4 - 100 = 41.4	135 - 100 = 35
Denominator
Average Investment				500/2 = 250	500/2 = 250
Annual Rate of Return (ARR)				41.4 / 250 * 100 = 16.56%	35/250 *100 = 14%

If the company's ARR target was set at 20%, then both projects will be rejected.
If the company's ARR target was set at 15%, then project A will be accepted and project B will be rejected.
If the company's ARR target was set at 10%, then the project with the highest ARR will be selected, thus project A will be selected.

Year	Project A	Cumulative CF	Project B	Cumulative CF
0	-500	-500	-500	-500
1	167	-333	200	-300
2	180	-153	250	-50
3	160	7	170	120	<------ Break even point
4	100	107	25	145
5	100	207	30	175

Payback period / Break even point
Project A	2 years	11.475	months
Project B	2 years	3.53	months

If the company's payback target was 2 years, then both projects will be rejected.
If the company's payback target was 2.5 years, Project B will be selected and Project A will be rejected.
If the company's payback target was 3 years, the project with the shortest payback period will be selected, thus Project B will be selected.