Introduction to Bond Math: Bond Pricing
Let’s say we have $100 in debt with 15% in PIK. How does this flow through the three statements? Let’s assume a 20% tax rate.
PIK accounting questions are very common in RX interviews because so many of the out-of-court restructurings done will involve some PIK.
Note: Why is this the case? The obvious answer is because the company likely doesnt have much cash on hand (negative FCF, limited liquidity) so PIK allows them to avoid imminent cash crunches. The less obvious answer, perhaps, is that PIK allows the company to offer a much higher interest rate (in this case 15%), which current holders who may be exchanging bonds into will find enticing.
So lets go through it. On the income statement (IS) you will have $15 in new interest expense in the form of newly issued debt. This creates a tax shield (another reason why you can have higher interest rate) of $3 ($15*20%). Therefore, net income is down by $12.
Moving to the top of the cash flow statement (CFS) you have $12, you then add back the $15 as its a non-cash expense (thats the primary reason to do PIK!), so you have cash flow from operations up by $3.
On the balance sheet (BS) you have assets (cash) up by $3, on the liabilities side you have debt up by $15, and within shareholders equity (retained earnings) you have a $12 decrease from net income. So both sides of the equation are up by $3.
How to Prepare for a Fixed-Income Interview
Most people immediately think of government, corporate, or municipal bonds when they hear the words “fixed income.” However, fixed-income securities can include mortgage loans and a variety of financial derivatives of interest rate, corporate, and credit products.
Typically, many fixed-income traders further specialize in handling specific types of fixed-income investments, such as government or corporate bonds. Fixed-income traders must be skilled at evaluating specific investment opportunities and be able to analyze and assess the current market and economic conditions and trends to be successful.
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Back of envelope approach:
$dP simeq frac{partial P}{partial y} times Delta y$
You know that when $y=3%$, $P=100$. So you can write
$P-100 simeq frac{partial P}{partial y} times (c-y)$
Price $simeq$ 100 + Duration x (3%-9%).
Guess a duration of around 7.0 for a 10 year bond (they would assume that you would have a feel for this number).
So I get 100 – 7 x 6 = 100 – 42 = $58.
If I do this carefully assuming annual compounding then I get $61.5 which is in the same ball park. You can refine this using a second order correction but this would be an acceptable first guess that you can do without calculators.
It might be more impressive to demonstrate that you have the tools and can use them. Go to the interview with a handheld calculator. The answer is a few keystrokes away.
consider your bond initially was at par (cpn=3%~=yld_0) and now answer the question what is the price change given new yld_1=9%. for a very dirty estimate use relationship between price change vs yield change and duration (~=10).for a less dirty estimate youll need some educated guess on the level of convexity. have a look at closed formula of convexity of par bond. hope this helps.
Use Taylor Expansion to approx price changes for some variations in Yield. Guess the Duration to be less than Full maturity since its Paying coupons and go from there. First price it at Par.
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