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Bonds, Bond Valuation, and Interest Rates

CHAPTER 5

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Topics in Chapter

Key features of bonds

Bond valuation

Measuring yield

Assessing risk

Determinants of Intrinsic Value: The Cost of Debt

Key Features of a Bond (1 of 2)

Par value: Face amount; paid at maturity. Assume $1,000.

Coupon interest rate: Stated interest rate. Multiply by par value to get dollars of interest. Generally fixed.

Key Features of a Bond (2 of 2)

Maturity: Years until bond must be repaid. Declines.

Issue date: Date when bond was issued.

Default risk: Risk that issuer will not make interest or principal payments.

Call Provision

Issuer can refund if rates decline. That helps the issuer but hurts the investor.

Therefore, borrowers are willing to pay more, and lenders require more, on callable bonds.

Most bonds have a deferred call and a declining call premium.

What’s a sinking fund?

Provision to pay off a loan over its life rather than all at maturity.

Similar to amortization on a term loan.

Reduces risk to investor, shortens average maturity.

But not good for investors if rates decline after issuance.

Sinking funds are generally handled in 2 ways

Call x% at par per year for sinking fund purposes.

Call if rd is below the coupon rate and bond sells at a premium.

Buy bonds on open market.

Use open market purchase if rd is above coupon rate and bond sells at a discount.

Value of a 10-year, 10% coupon bond if rd = 10%

The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10:

PV annuity	= $614.46
PV maturity value	= 385.54
Value of bond	= $1,000.00

What would happen if expected inflation rose by 3%, causing r = 13%?

When rd rises, above the coupon rate, the bond’s value falls below par, so it sells at a discount.

What would happen if inflation fell, and rd declined to 7%?

If coupon rate > rd, price rises above par, and bond sells at a premium.

Bond Value ($) vs. Years remaining to Maturity (1 of 2)

Suppose the bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if the required rate of return remained at 10%, or at 13%, or at 7%?

See next slide.

Bond Value ($) vs. Years remaining to Maturity (2 of 2)

Bond Value ($) vs. Years remaining to Maturity (2 of 3)

At maturity, the value of any bond must equal its par value.

The value of a premium bond would decrease to $1,000.

The value of a discount bond would increase to $1,000.

A par bond stays at $1,000 if rd remains constant.

What’s “yield to maturity”?

YTM is the rate of return earned on a bond held to maturity. Also called “promised yield.”

It assumes the bond will not default.

YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $887

Find rd

If coupon rate < rd, bond sells at a discount.

If coupon rate = rd, bond sells at its par value.

If coupon rate > rd, bond sells at a premium.

If rd rises, price falls.

Price = par at maturity.

Find YTM if price were $1,134.20.

Sells at a premium. Because coupon = 9% > rd = 7.08%, bond’s value > par.

Definitions

9% coupon, 10-year bond, P = $887, and YTM = 10.91%

YTM = Current yield + Capital gains yield.

Could also find values in Years 1 and 2,

get difference, and divide by value in

Year 1. Same answer.

Semiannual Bonds

1. Multiply years by 2 to get periods = 2N.

2. Divide nominal rate by 2 to get periodic rate = rd/2.

3. Divide annual INT by 2 to get PMT = INT/2.

Value of 10-year, 10% coupon, semiannual bond if rd = 13%.

Spreadsheet Functions for Bond Valuation

See Ch04 Mini Case.xls for details.

PRICE

YIELD

Callable Bonds and Yield to Call

A 10-year, 10% semiannual coupon, $1,000 par value bond is selling for $1,135.90 with an 8% yield to maturity. It can be called after 5 years at $1,050.

Nominal Yield to Call (YTC)

If you bought bonds, would you be more likely to earn YTM or YTC?

Coupon rate = 10% vs. YTC = rd = 7.53%. Could raise money by selling new bonds which pay 7.53%.

Could thus replace bonds which pay $100/year with bonds that pay only $75.30/year.

Investors should expect a call, hence YTC = 7.5%, not YTM = 8%.

In general, if a bond sells at a premium, then coupon > rd, so a call is likely.

So, expect to earn:

YTC on premium bonds.

YTM on par & discount bonds.

rd = r* + IP + MRP + DRP + LP.

What is the real risk-free rate (r*)?

Rate that a hypothetical riskless security pays each moment if zero inflation were expected.

r* changes over time depending on economic conditions.

r* can be approximated by rate on short-term Treasury Inflation-Protected Securities (TIPS).

What is the nominal risk-free rate (rRF)?

The rate on a U.S. Treasury security

Short-term security: T-bill

Long-term security: T-bond

Estimating IP

Treasury Inflation-Protected Securities (TIPS) are indexed to inflation.

The IP for a particular length maturity can be approximated as the difference between the yield on a non-indexed Treasury security of that maturity minus the yield on a TIPS of that maturity.

Bond Spreads, the DRP, and the LP

A “bond spread” is often calculated as the difference between a corporate bond’s yield and a Treasury security’s yield of the same maturity. Therefore:

Spread = DRP + LP.

Bond’s of large, strong companies often have very small LPs. Bond’s of small companies often have LPs as high as 2%.

Bond Ratings

Bond Ratings			% defaulting within:
S&P and Fitch	Moody’s	1 yr.	5 yrs.
Investment grade bonds:
AAA	Aaa	0.13	0.68
AA	Aa	0.00	0.00
A	A	0.09	0.96
BBB	Baa	0.07	1.72
Junk bonds:
BB	Ba	0.62	6.35
B	B	2.06	11.68
CCC	Caa	21.36	35.38

Bond Ratings and Bond Spreads (October 2016)

Long-term Bonds	Yield (%)	Spread (%)
10-Year T-bond	1.72
AAA	2.21	0.49
AA	2.27	0.55
A	2.42	0.70
BBB	3.46	1.74
BB	5.16	3.44
B	6.58	4.86
CCC	8.37	6.65

What factors affect default risk and bond ratings?

Financial ratios

Debt ratio

Coverage ratios, such as interest coverage ratio or EBITDA coverage ratio

Profitability ratios

Current ratios

Bond Ratings Median Ratios (S&P)

	Return on capital	Debt to capital
AAA	27.6%	12.4%
AA	27.0%	28.3%
A	17.5%	37.5%
BBB	13.4%	42.5%
BB	11.3%	53.7%
B	8.7%	75.9%
CCC	3.2%	113.5%

Other Factors that Affect Bond Ratings (1 of 2)

Provisions in the bond contract

Secured versus unsecured debt

Senior versus subordinated debt

Guarantee provisions

Sinking fund provisions

Debt maturity

Other Factors that Affect Bond Ratings (2 of 2)

Other factors

Earnings stability

Regulatory environment

Potential product liability

Accounting policies

Interest rate (or price) risk for 1-year and 10-year 10% bonds

Interest rate risk:

Rising rd causes bond prices to fall

	1-Year	1-Year	10-Year	10-Year
rd	Price	Change	Price	Change
5.0%	$1,048		$1,386
		4.8%		38.6%
10.0%	$1,000		$1,000
		4.5%		33.5%
15.0%	$957		$749

Value

What is reinvestment rate risk? (1 of 2)

The risk that CFs will have to be reinvested in the future at lower rates, reducing income.

Illustration: Suppose you just won $500,000 playing the lottery. You’ll invest the money and live off the interest. You buy a 1-year bond with a YTM of 10%.

What is reinvestment rate risk? (2 of 2)

Year 1 income = $50,000. At year-end get back $500,000 to reinvest.

If rates fall to 3%, income will drop from $50,000 to $15,000. Had you bought 30-year bonds, income would have remained constant.

The Maturity Risk Premium

Long-term bonds: High interest rate risk, low reinvestment rate risk.

Short-term bonds: Low interest rate risk, high reinvestment rate risk.

Nothing is riskless!

Yields on longer term bonds usually are greater than on shorter term bonds, so the MRP is more affected by interest rate risk than by reinvestment rate risk.

Term Structure Yield Curve

Term structure of interest rates: the relationship between interest rates (or yields) and maturities.

A graph of the term structure is called the yield curve.

Hypothetical Treasury Yield Curve

Bankruptcy (1 of 4)

Two main chapters of Federal Bankruptcy Act:

Chapter 11, Reorganization

Chapter 7, Liquidation

Typically, company wants Chapter 11, creditors may prefer Chapter 7.

Bankruptcy (2 of 4)

If company can’t meet its obligations, it files under Chapter 11. That stops creditors from foreclosing, taking assets, and shutting down the business.

Company has 120 days to file a reorganization plan.

Court appoints a “trustee” to supervise reorganization.

Management usually stays in control.

Bankruptcy (3 of 4)

Company must demonstrate in its reorganization plan that it is “worth more alive than dead.”

Otherwise, judge will order liquidation under Chapter 7.

If the company is liquidated, here’s the payment priority:

Past due property taxes

Secured creditors from sales of secured assets.

Trustee’s costs

Expenses incurred after bankruptcy filing

Wages and unpaid benefit contributions, subject to limits

Unsecured customer deposits, subject to limits

Taxes

Unfunded pension liabilities

Unsecured creditors

Preferred stock

Common stock

Bankruptcy (4 of 4)

In a liquidation, unsecured creditors generally get zero. This makes them more willing to participate in reorganization even though their claims are greatly scaled back.

Various groups of creditors vote on the reorganization plan. If both the majority of the creditors and the judge approve, company “emerges” from bankruptcy with lower debts, reduced interest charges, and a chance for success.

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1NN

ddd

$100$100$1,000

V...

1r1r1r

$90.91...$38.55$385.54

$1,000.

=+++

+++

=+++

(

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(

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(

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(

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(

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(

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1NN

ddd

1NN

ddd

INTINTM

V...

1r1r1r

90901,000

887...

1r1r1r

=+++

+++

=+++

+++

Annual coupon pmt

Current yield

Current price

Change in price

Capital gains yield

Beginning price

Exp totalreturn= YTM ExpCurr yldExp cap

gains yld

$90

Current yield

$887

0.101510.15%.

Cap gains yieldYTMCurrent yield

10.91%10.15%

0.76%.

Here:

rd Required rate of return on a debt se

curity.

r* Real riskfree rate.

IP Inflation premium.

MRP Maturity risk premium.

DRP Default risk premium.

LP Liquidity premium.