Investment Banking puzzles, solved step by step
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013A company issues Rs 100 crore of new shares and uses all of it to repay debt. What happens to enterprise value, equity value and EV/EBITDA?Bulge bracket IBElite boutique IB
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What happens to enterprise value?
Show the worked solution
Enterprise value is unchanged, equity value rises by Rs 100 crore and EV/EBITDA stays the same. Equity value rises because Rs 100 crore of new shares now exist, and debt falls by the same Rs 100 crore. Enterprise value is equity plus net debt, so the two moves cancel. EBITDA sits above the interest line and is untouched, so the multiple cannot change either.
Why does enterprise value not move?
Think of a house worth Rs 1 crore with a Rs 40 lakh mortgage. If you pay down Rs 10 lakh of the loan with your savings, your stake rises to Rs 70 lakh and the loan falls to Rs 30 lakh, but the house is worth exactly what it was. Enterprise value measures the business, and swapping one kind of claim for another changes how that value is split, not how big it is. At first order, issuing shares to repay debt is exactly that swap.
Before the deal, equity of Rs 600 crore and debt of Rs 400 crore make an enterprise value of Rs 1,000 crore; afterwards equity of Rs 700 crore and debt of Rs 300 crore make the same Rs 1,000 crore, so EV/EBITDA stays at 10.0x while P/E falls to 18.7x. Then what does change?
Everything below the interest line. Take EBITDA of Rs 100 crore, D&A of Rs 20 crore, Rs 400 crore of debt at 10% and a 25% tax rate, with 60 crore shares at Rs 10. Interest falls from Rs 40 crore to Rs 30 crore, so net income rises from Rs 30 crore to Rs 37.5 crore, and with equity now worth Rs 700 crore, P/E falls from 20.0x to 18.7x. Equity multiples such as P/E move with capital structure; enterprise multiples such as EV/EBITDA do not, which is why bankers compare companies on enterprise multiples.
EPS also rises, from Rs 0.50 to Rs 0.54. The reason is a comparison of two costs: the new shares were sold at an earnings yieldNet income divided by equity value, the inverse of the P/E. It is what each rupee of equity earns. of 5%, and the debt they retired cost 7.5% after tax. Replacing a 7.5% cost with a 5% cost lifts earnings per share.
Rs crore Before After Enterprise value 1,000 1,000 EV / EBITDA 10.0x 10.0x Equity value 600 700 Debt 400 300 Net income 30.0 37.5 P/E 20.0x 18.7x EPS, Rs 0.50 0.54 Illustrative company: EBITDA Rs 100 crore, D&A Rs 20 crore, debt at 10%, tax at 25%, shares issued at the Rs 10 market price. What could make enterprise value move after all?
Three second-order effects, worth one sentence each. Fees on the share issue leak value out to advisers. Less debt means a smaller interest tax shield, which in Modigliani and Miller's analysis with taxes lowers value slightly. Against that, lower leverage reduces the risk and cost of financial distress. In an interview, give the first-order answer, unchanged, and then name the effects that could nudge it.
Where candidates lose it
The common slip is to say enterprise value rises because the company raised money. The cash went straight out to lenders, so nothing is left behind; and even if the cash had stayed on the balance sheet, net debt would still have fallen by 100 and enterprise value would still be flat.
The second slip is saying the share price must fall because of dilution. If the shares are sold at the market price, each holder's slice is smaller but the pie is bigger by exactly the cash paid in, so the price does not move at the moment of issue.
What the interviewer asks next
- What if the company keeps the Rs 100 crore as cash instead?
- What if it uses the Rs 100 crore to buy back shares instead of repaying debt?
- When would issuing shares to repay debt dilute EPS?
091A company has a Rs 500 crore convertible bond with a conversion price of Rs 100, and its shares trade at Rs 120. In the enterprise value bridge, do you count the bond as debt or as shares? What changes if the share price falls to Rs 80?Bulge bracket IBElite boutique IB
Try it first
At a share price of Rs 120, how should the bond enter the bridge?
Show the worked solution
At Rs 120, count it as 5 crore extra shares and not as debt; at Rs 80, count it as Rs 500 crore of debt and no new shares. Rs 500 crore at a Rs 100 conversion price is 5 crore shares. At Rs 120 those shares are worth Rs 600 crore, so the holder will convert. At Rs 80 they are worth Rs 400 crore, so the holder takes the Rs 500 crore back. Treat the bond as whichever it is most likely to become, never as both.
Why does the share price decide whether a bond is debt?
Suppose a friend lends you Rs 5 lakh and you agree they can take either the money back or a share of your shop. If the shop is booming, they will take the share; if it is struggling, they will take the cash. You plan around what they will choose. A convertible gives the holder a choice between repayment and shares, and the valuation should assume the choice a rational holder makes at today's price. The comparison is simple: conversion value, shares received times share price, against face value.
At Rs 120, converting gives 5 crore shares worth Rs 600 crore, more than the Rs 500 crore face value. The holder converts, so add 5 crore shares to the diluted count and remove the bond from debt. With, say, 50 crore existing shares, diluted equity value becomes 55 crore x 120 = Rs 6,600 crore. At Rs 80, converting gives shares worth only Rs 400 crore, so the bond stays as Rs 500 crore of debt and the share count stays at 50 crore.
At Rs 120 the 5 crore conversion shares are worth Rs 600 crore against Rs 500 crore of repayment, so the bond counts as shares, while at Rs 80 they are worth Rs 400 crore and it counts as Rs 500 crore of debt; counting it both ways double counts it. What goes wrong if you count it the other way?
Counting it as debt at Rs 120 puts Rs 500 crore into the bridge when the holder will in fact take Rs 600 crore of value in shares, understating the claim by Rs 100 crore. The serious error is counting it twice, as debt and as diluted shares, which overstates enterprise value by the full Rs 500 crore. That happens when the share count comes from one source that already includes the conversion and the debt figure from a balance sheet that still shows the bond.
The relationshipface the bond's face value, Rs 500 crore conversion price Rs 100 per share share price today's price, Rs 120 What it says in wordsIf the shares a holder would receive are worth more than the repayment, assume conversion.Say the limitation. Near the conversion price the choice is close and the bond carries option value either way, so some banks value it at fair value rather than flipping between debt and shares. Settlement terms also matter: some convertibles repay the face value in cash and deliver only the excess in shares, which needs a different share count.
Where candidates lose it
The common mistake is treating the convertible as debt because it is called a bond, whatever the share price. At Rs 120 the holder is not waiting to be repaid; they are holding shares in all but name.
The quieter loss is double counting when pulling numbers from different sources. Say out loud that the bond is in one place only, and which.
What the interviewer asks next
- At what share price does the treatment switch?
- How would you treat a convertible that settles the face value in cash and only the excess in shares?
- How does a convertible change the accretion or dilution of a deal paid for in stock?