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20181113002530ec516assign41.pdf

Assignment 4

Coverage Ratios and the Yields of 19th Century RR Bonds

It is common, nowadays, to calculate various financial ratios in conjunction with credit analysis. Among these are the coverage ratio, or times interest earned ratio, equal to Operating Income (or, EBIT) divided by Interest Expense.

In an accompanying Excel workbook, I have the Yield to Maturity and various coverage ratios (flipped over, equal to Interest Expense/Operating Income), and other information, pertaining to late 19th century U.S. Railroad bonds (see Appendix 2 for an example of such a railroad).

More specifically, for each month of 1890, I have the Yield to Maturity, the coverage ratios of up to five distinct classes of bonds, and the priority of claim for a sample of bonds generated as follows:

1.The bond had to be have at least 10 years remaining term to maturity.

2.The bond had to be traded in either the Baltimore, Boston, Cincinnati, New York or Philadelphia stock exchange, that month.

3.The bond had to be traded on that exchange in at least two of the prior twelve months.

4.The company issuing the bond was not in receivership in either 1889 or 1890.

5.The company had to have an overall average coverage ratio for 1889 and 1890 of no worse than 1.25 (remember, I’ve flipped over the coverage ratio, so smaller is more creditworthy).

6.The bond was a straight bond, i.e., neither an income bond nor a convertible bond.

7.If the bond was callable, it had to be trading for less than its call price.

8.If the bond was guaranteed, it had to be trading mostly based on its own creditworthiness, not much on the credit enhancement provided by the guarantee.

We can suppose that Yield is higher both as the “prior” and “own” coverage ratios are higher (see Appendix 2), and also that Yield is higher in the capital-‐poor regions of the country. These things suggest a multiple regression of the following form:

Y = α + β1X1 + β2X2 + β3X3

where Y is Yield, α is the risk-‐free rate, β1, β2 and β3 > 0, X1 is the coverage ratio pertaining to interest on senior securities above 30%, X2 is the coverage ratio pertaining to interest on senior and similar securities less the larger of X1 or 30%, and X3 is a dummy variable indicating bonds issued by railroads in the capital-‐poor regions of the country.

Your assignment is, for the month indicated in Grade (1 = January, 2 = February, etc.), to estimate the above equation and report your findings to me. Also, consider if one or at most two other X variables should be added to the above equation, from what I have provided in the dataset.

WARNING: Do not use coupon interest rate or other variables from which yield-‐to-‐maturity is calculated. While coupon interest rate is related to yield-‐to-‐maturity, the relationship is due to the definition or formula for yield-‐to-‐maturity, not because of a cause-‐and-‐effect relationship. To illustrate, height measured in inches is related to height measured in centimeters, but this is not because of a cause-‐and-‐effect relationship. Height measured in either inches or centimeters is caused by factors such as the height of one's parents and nutrition while young.

Appendix I

An Example of a 19th Railroad

My financial analysis of 19th Century Railroads focuses on identifying the priority of claim of the intricate pattern of securities issued by them. I have usually found that two or three tiers of bonds are adequate to describe a road’s priority of claim.

In an illustrative case involving three tiers, the first tier (or, best secured bonds) would be the first mortgage bonds on the main line and equipment trust bonds. After this would be the second tier which would include second mortgage bonds on the main line and first mortgage bonds on important branch lines. After this, the third tier (and, in this illustrative case, final tier) would include third mortgage (and inferior) bonds on the main line, second mortgage (and inferior) bonds on the important branch lines, first mortgage (and inferior) bonds on other branch lines, and debenture bonds.

In the following case, I treated the first 6s of 1908 (second line in the bond table on p. 4) as a first mortgage on the main line of the road (and, therefore, as part of the first tier), because of the relatively small amount outstanding of the Purchase Money 6s of 1898 (first line of the bond table on p. 4).

CHESAPEAKE & OHIO RAILWAY

1889

Old Point Comfort via Newport News VA to Big Sandy WV ........................................... 511 miles

Richmond via Lynchburg to Clifton Forge VA ................................................................. 230 miles

Total including other branch roads ................................................................................ 928 miles

The Chesapeake & Ohio Railway was formed by the consolidation of the Virginia Central RR and the Covington & Ohio RR in 1868. The Virginia Central RR was opened from Richmond to

Covington VA, at the base of the Alleghany range, in 1867, and included the Blue Ridge RR, an expensive tunnel built by the state of Virginia. The Covington & Ohio RR, designed to extend the road to the Ohio River, and whose construction was largely financed by the state of Virginia, was completed only in 1873 (following the Civil War). In that year, the company defaulted on interest, and a receiver was appointed. Following a foreclosure sale, it was reorganized in 1878. In 1888, the company was again reorganized, this time without a foreclosure sale.

Bonded Debt: Chesapeake & Ohio Ry, 1889 (Outstanding amounts in thousands).

Issued Outst. Security

C&O Purchase Money 6s 1898 1878 2,287 1st-‐-‐504 miles (main line)

C&O 1st 6s 1908 1878 2,000 2nd-‐-‐504 miles (main line)

C&O Peninsula Ext 6s 1911 1881 2,000 1st-‐-‐8 miles (main line)

C&O Terminal 6s 1922 1882 142 Terminal

C&O 1st R&D Div 4s 1989 1889 5,000 1st-‐-‐233 miles (branch line)

C&O 2nd R&D Div 4s 1989 1889 1,000 2nd-‐-‐233 miles (branch line)

C&O Elevator 4s 1939 1889 820 Elevator

C&O cons 5s 1939 1889 19,768 3rd—504 miles and 2nd–12 miles (main line)

C&O New River Br 6s 1898 1889 170 Bridge

equipment trusts NA 686 Equipment

Appendix 2

Coverage Ratios and Yield

If we can presume that absolute priority of claim holds, that financial markets extrapolate any change in earnings into the indefinite future, that all bonds are traded as perpetuities, that the subjective distribution of earnings is distributed as a uniform distribution on [A, B], and that investors are risk-‐neutral, then …

1.For bonds not junior to other bonds, the odds that earnings will fall below the amount C, where C is the required interest on these bonds, is

P(earnings being less than C) = (C – A) / (B – A)

This can be seen in the following chart:

IF earnings are less than C, then the expected loss will be

E(loss if earnings are less than C) = ½ (C – A)

This means that the probable loss = ½ (C – A) (C – A) / (B – A), and that Yield would have to be higher by this amount to be equivalent to the risk-‐free rate of return.

In terms of a regression equation, Y = α + βX, where Y is Yield, α is the risk-‐free rate, β is ½ (C – A), and X is (C – A) / (B – A).

2.For bonds that are junior to other bonds, the odds that earnings will fall below the amount D, where D is the required interest on the senior bonds, is

P(earnings being less than D) = (D – A) / (B – A)

And, the odds that earnings will fall above the amount D and below the amount C, is

P(earnings being between D and C) = ( C – D ) / (B – A)

These two things can be seen in the following chart:

IF earnings are less than D, the expected loss will be total (i.e., the junior bonds will be wiped-‐ out):

E(loss if earnings are less than D) = C

IF earnings are between D and C, the loss will be:

E(loss if earning are between D and C ) = ½ (C – D)

These things means that the probable loss will be C (D – A) / (B -‐ A) + ½ (C – D) (C – D) / (B – A) so that Yield would have to be higher by this amount to be equivalent to the risk-‐free rate of return.

In terms of a regression equation, Y = α + β1X1 + β2X2, where Y is Yield, α is the risk-‐free rate, β1 is C, β2 is ½ (C – D), X1 is (D – A) / (B – A) and X2 is (C -‐ D) / (B – A).