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One of the unsung heroes of Apple's (NASDAQ:AAPL) debt issuances has been a notable reduction in Apple's weighted average cost of capital, or WACC. Apple has issued bonds as a roundabout way to access foreign cash without actually accessing foreign cash. In the process, Apple added debt to its capital structure, which has a lower cost than equity.

What kind of a benefit are shareholders looking at? Fair warning: the following calculations are not for the faint of heart.

Cost of equity
First, investors need to calculate Apple's cost of equity. Last February, I estimated Apple's cost of equity at 10.47%. Here is the formula for cost of equity based on the capital asset pricing model:

Capm

I use the 10-year Treasury yield for the risk-free rate, which is currently 2.55%. Apple's beta has declined to 0.66 as its volatility has moderated. I'll still use Aswath Damodaran's estimate for the equity risk premium, which is currently 5.38%. This all translates into a cost of equity of 6.1%. The majority of that decline is from the substantial drop in beta.

Cost of debt
Here is where it gets tricky. Apple has issued $29 billion of debt thus far, which is comprised of both floating rate and fixed rate notes. Investors must calculate a weighted average to use in calculating WACC. Here are all of Apple's current outstanding bond tranches:

Tranche

Principal

Price

Market Value

2013 Offering

     

2016 Fixed

$1.5 billion

99.8

$1.497 billion

2016 Floating

$1 billion

99.8

$998 million

2018 Fixed

$4 billion

97.5

$3.9 billion

2018 Floating

$2 billion

100

$2 billion

2023 Fixed

$5.5 billion

94.3

$5.19 billion

2043 Fixed

$3 billion

89.4

$2.68 billion

2014 Offering

     

2017 Fixed

$1.5 billion

99.9

$1.49 billion

2017 Floating

$1 billion

100

$1 billion

2019 Fixed

$2 billion

100.2

$2.004 billion

2019 Floating

$1 billion

99.8

$998 million

2021 Fixed

$3 billion

100.9

$3.03 billion

2024 Fixed

$2.5 billion

101

$2.53 billion

2044 Fixed

$1 billion

100.6

$1.006 billion

Grand total

$29 billion

 

$28.32 billion

Source: SEC filings and Morningstar for prices.

Next, we must calculate a weighted average cost of debt. I'm using yield-to-maturity for the fixed rate tranches. Yield-to-maturity does not exist for floating rate notes though, since the cash flows are variable and the rates reset regularly. The cost of floating rate notes is very difficult to estimate because of this characteristic. Fortunately, Apple enters into interest rate swaps to effectively convert its floating rate notes into fixed rate notes. Apple then estimates effective interest rates, which is what I'll use for its floating rate tranches.

Apple's 2014 bond offering occurred during the June quarter, and therefore has not been detailed in a 10-Q. I'll assume that Apple similarly converts these floaters to fixed using swaps, and use an effective rate based on each respective LIBOR spread for each floating rate tranche.

Tranche

Effective Rate

2013 Offering

 

2016 Fixed

0.58%

2016 Floating

0.51%*

2018 Fixed

1.67%

2018 Floating

1.1%*

2023 Fixed

3.14%

2043 Fixed

4.51%

2014 Offering

 

2017 Fixed

1.1%

2017 Floating

0.3%**

2019 Fixed

2.07%

2019 Floating

0.53%**

2021 Fixed

2.7%

2024 Fixed

3.33%

2044 Fixed

4.41%

Weighted average cost of debt

2.33%

Source: SEC filings and Morningstar for yield-to-maturity. *Apple's estimate as of March. **Assumes converted to fixed rates using swaps and based on May LIBOR rates.

That 2.33% estimate is higher than the 1.85% that Apple's original 2013 offering was priced at, but rates have risen since then and Apple has conducted an additional offering.

Are we there yet?
With both cost of equity and cost of debt in hand, we can now proceed to calculating Apple's WACC. Here's the formula:

Wacc

The total market value of debt that we previously calculated will come in handy here. Apple's statutory corporate tax rate is 35%. Plugging all of the figures in, we arrive at an estimate of 5.88%. Before Apple took on any of this debt, I estimated Apple's WACC at 8.5% last April. That was an easier exercise since Apple had no debt at the time, in which case its WACC equaled its cost of equity.

That means that Apple has seen a total reduction of 2.62% in its WACC in just over a year, after issuing a total of $29 billion in bonds. Market conditions have also contributed to that decline, mostly in the form of reduced volatility for Apple shares. Still, taking on debt to fund capital returns has absolutely benefited shareholders.

Evan Niu, CFA owns shares of Apple. The Motley Fool recommends Apple. The Motley Fool owns shares of Apple. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.