17Valuation and Financial Statements

Answer to Question 17.1.

Net income falls by 7.5. Operating cash flow and cash rise by 2.5. Fixed assets fall by 10, and retained earnings fall by 7.5.

Depreciation is an expense, so pre-tax profit falls by 10, and tax falls by 2.5, which leaves net income down 7.5. On the cash flow statement you start from net income and add back the extra depreciation, because it is not cash, so $-7.5 + 10 = +2.5$: the only real cash effect is the tax saved. On the balance sheet, assets change by $+2.5 - 10 = -7.5$, and equity changes by $-7.5$ through retained earnings. So it balances.

Answer to Question 17.2.

Net income is 30, and operating cash flow is $-10$. Profit is positive while cash falls.

Pre-tax profit is $100 - 60 = 40$, tax is 10, and net income is 30. For cash flow, start at 30. Receivables rise by 100, which you subtract. Inventory rises and falls by 60, so it nets to zero. Payables rise by 60, which you add. So $30 - 100 + 60 = -10$, which is the tax paid. Sales and purchases have moved no cash.

Assets are receivables of 100 and cash of $-10$, so 90. Liabilities are payables of 60, and equity is retained earnings of 30. And $90 = 60 + 30$.

Answer to Question 17.3.

Enterprise value is $1000 + 300 - 100 + 50 + 30 = 1{,}280$, and the multiple is 8.0 times. None of the three transactions changes the enterprise value.

Enterprise value is the value of the operations to everyone who has a claim on them. It adds the other claims to equity and takes off the cash, which the operations do not need. It matches EBITDA, a number before any payment to capital providers.

If it borrows 100, then debt and cash both rise by 100. If it pays a dividend of 50, market capitalisation and cash both fall by 50. If it buys back 100 of shares, market capitalisation and cash fall by 100. In each case operations have not changed, and that is the point of the measure. In the last two cases the market capitalisation falls because value has left the company. It does not fall because of bad news.

Answer to Question 17.4.

Free cash flow to the firm is 100. Free cash flow to equity is 95. You discount the first at the weighted average cost of capital, because it belongs to all the capital providers.

To the firm: tax operating profit as if there were no debt, $200 \times 0.75 = 150$, add back the non-cash 40, and take off the 70 of investment and the 20 of working capital. That gives 100.

To equity: take off the interest after its tax shield, $20 \times 0.75 = 15$, and add the 10 of new borrowing, which gives 95. A check from the top: net income is $(200 - 20) \times 0.75 = 135$, and $135 + 40 - 70 - 20 + 10 = 95$.

Answer to Question 17.5.

It is worth $100/(0.09 - 0.03) \approx 1{,}667$. With 4% growth, or with an 8% cost of capital, it is worth 2,000, which is 20% more. If 100 is this year’s flow, next year’s is 103, and the value is about 1,717.

This is the Gordon growth formula: value is next year’s flow divided by the spread between the discount rate and growth. The spread here is 6 points, so moving it by one point is a large change. A 2% growth rate gives $100/0.07 \approx 1{,}429$, a fall of 14%. That is smaller than the 20% rise from 4% growth, because the value is convex in the spread.

Answer to Question 17.6.

There are 118 diluted shares, and the diluted equity value is 2,950. Because the convertible is treated as shares, you take its 200 out of debt in the bridge to enterprise value.

Options, by the treasury stock method: if exercised, they bring in $10 \times 10 = 100$, which buys back 4 shares at 25, for a net addition of 6. Restricted shares add 2 in full, as there is nothing to pay. The convertible is in the money, because 25 is above 20, so it becomes $200/20 = 10$ shares. So $100 + 6 + 2 + 10 = 118$, and at 25 that is 2,950, against 2,500 undiluted.

Answer to Question 17.7.

Operating profit rises by 40%, from 20 to 28. Pre-tax profit rises by 80%, from 10 to 18. Operating profit reaches zero at revenue of 75, and pre-tax profit at revenue of 87.5.

Each extra unit of revenue adds 0.8 of profit, so 10 of extra revenue adds 8. The base of 20 is small, because fixed costs take most of the contribution. Operating leverage is the ratio of contribution to operating profit, $80/20 = 4$. Financial leverage is $20/10 = 2$. Together they multiply to 8, so a 10% rise in revenue gives 80%.

For break-even, $0.8R = 60$ gives $R = 75$, and $0.8R = 70$ gives $R = 87.5$. Revenue only has to fall 12.5% to wipe out the pre-tax profit.

Answer to Question 17.8.

The cost of equity is 10%, and the weighted average cost of capital is 8.75%. With equal debt and equity, the equity beta is about 1.77, the cost of equity is about 12.84%, and the weighted average cost of capital is about 8.67%.

By the capital asset pricing model, the cost of equity is $4\% + 1.2 \times 5\% = 10\%$. After tax, debt costs $5\% \times 0.75 = 3.75\%$. The weights are 80% and 20%, so $8\% + 0.75\% = 8.75\%$.

To remove the leverage, $\beta_u = \beta / \left(1 + (1 - t)D/E\right) = 1.2/(1 + 0.75 \times 0.25) \approx 1.01$. To restore it at $D/E = 1$, multiply by $1 + 0.75 = 1.75$, which gives about 1.77. The cost of equity is $4\% + 1.77 \times 5\%$, about 12.84%. The new weighted average cost of capital is $0.5 \times 12.84\% + 0.5 \times 6\% \times 0.75 \approx 8.67\%$.

Answer to Question 17.9.

The company is worth 1,125, its equity 625, its cost of equity 13%, and its weighted average cost of capital about 8.89%. It is not about 7% because equity gets more expensive as debt rises.

With no debt the company is worth $100/10\% = 1{,}000$. Interest gives a tax saving of $25\% \times 5\% \times 500$ every year forever. Discounted at the debt’s own 5%, that is $tD = 125$. This is the tax shield, and the value is $1{,}000 + 125$, as Modigliani and Miller showed with taxes. Equity is $1{,}125 - 500 = 625$.

Equity holders get $100 - 500 \times 5\% \times 0.75 = 81.25$, so their return is $81.25/625 = 13\%$. Then $\tfrac{625}{1125} \times 13\% + \tfrac{500}{1125} \times 3.75\% \approx 8.89\%$. And $100/8.89\% = 1{,}125$, which closes the loop.

Answer to Question 17.10.

It is worth about 2,101, and the terminal value makes up about 78%. At 4% terminal growth it is worth about 2,446. If cash arrives in mid-year, the value rises by a factor of $1.09^{1/2} \approx 1.044$, to about 2,193.

The five years give about 467. The terminal value at year 5 is $146.41 \times 1.03/(0.09 - 0.03) \approx 2{,}513$. Discounted by $1.09^5 \approx 1.539$, it is about 1,634.

Those present values are nearly equal because 10% growth almost cancels 9% discounting. So a quick sum is about $5 \times 93$.

Answer to Question 17.11.

A multiple of 10 implies growth of about 3.32%. Growth of 2% implies about 8.0 times. A multiple of 18 requires about 5.8%, which is too high to last forever.

The terminal value is $\mathrm{FCF}(1 + g)/(r - g)$. Setting it equal to $TV$ and solving gives

At $g = 2\%$, the terminal value is $55 \times 1.02/0.07 \approx 801$, about 8.0 times EBITDA. At 1,800, the same formula gives $(162 - 55)/1855 \approx 5.8\%$.

A company that grows at 5.8% forever would eventually outgrow any economy. So that growth is what you say: 18 times assumes a rate above long-run nominal growth, unless margins or capital needs change too.

Answer to Question 17.12.

It is worth 0 at a 5% return, 1,000 at 10%, and 1,500 at 20%. With no growth, it is worth 1,000. Growth adds value only when the return on new investment is above the cost of capital.

To grow at $g$ you must reinvest a fraction $g/\mathrm{ROIC}$ of profit, because new profit equals investment times the return. So free cash flow is $\mathrm{NOPAT}(1 - g/\mathrm{ROIC})$, and

With a return of 20%, you reinvest 25 out of 100, which adds $25 \times 20\% = 5$ of profit, or 5% growth. The cash flow is 75, and $75/5\% = 1{,}500$. With a return of 10%, the cash flow is 50, and $50/5\% = 1{,}000$, the same as no growth. So growth at the cost of capital is worth nothing. With a return of 5%, all the profit is reinvested, and no cash ever comes out.

Answer to Question 17.13.

EV to EBITDA is 10 times for both. The price to earnings multiple is 16 for $A$ and about 11.4 for $B$. It differs because the two have different leverage. With debt at 12%, $B$’s multiple is about 28.6.

EBITDA is 120 for both, and $1200/120 = 10$. Company $A$ has net income of $100 \times 0.75 = 75$ and equity of 1,200, so 16 times. Company $B$ pays interest of 30, so its net income is 52.5, and its equity is 600, which is about 11.4 times.

The rule compares the unlevered earnings yield with the after-tax cost of debt. $A$’s earnings yield is $75/1200 = 6.25\%$, and debt after tax costs 3.75%. Replacing expensive equity by cheaper debt raises earnings per unit of equity, so the multiple falls. At 12%, debt costs 9% after tax, which is above 6.25%. Net income is $(100 - 72) \times 0.75 = 21$, and the multiple rises.

Answer to Question 17.14.

Free cash flow is 100 either way. Expensing gives EBITDA, operating profit and operating cash flow of 100, and investing cash flow of 0. Capitalising gives EBITDA of 200, operating profit of 180, operating cash flow of 200 and investing cash flow of $-100$. In a steady state operating profit is equal again. With spending growing 20% a year, it stays above, by about 70 in year 6.

Capitalising moves 100 from an operating cost to an investment, so EBITDA and operating cash flow both improve by the whole 100. Operating profit bears one fifth of it, 20, and improves by 80. Nothing about the cash has changed.

With 100 every year, after five years the amortisation is $5 \times 20 = 100$, the same as expensing, although EBITDA stays 100 higher. With growth of 20%, year 6 spending is about 248.8 and amortisation is about 178.6, the average of the last five years’ spending, and the gap is about 70. A growing capitaliser keeps reporting more than a company that expenses.

Under IFRS, research is expensed, and development is capitalised when it meets specified criteria, so two companies can really differ.

Answer to Question 17.15.

The cash conversion cycle is 75 days, and net working capital is about 172.6. Growth of 20% absorbs about 34.5, and cutting 15 days of inventory releases about 24.7.

Receivables are $1000 \times 45/365 \approx 123.3$. Inventory is $600 \times 60/365 \approx 98.6$. Payables are $600 \times 30/365 \approx 49.3$. So net working capital is $123.3 + 98.6 - 49.3 = 172.6$. The cycle is $45 + 60 - 30 = 75$.

With days unchanged, working capital scales with sales, so growth of 20% needs 20% more, which is 34.5 of cash. Fifteen days of inventory are $600 \times 15/365 \approx 24.7$.

Answer to Question 17.16.

Management quotes a yield of 5%. Treating share-based pay as a cost, it is about 3.33%. Keeping the share count flat takes about 1.67 shares a year. At 20 times, the two valuations are 3,000 and 2,000, so the higher is 50% above the lower.

Market capitalisation is $100 \times 30 = 3{,}000$. The reported yield is $150/3000$, and the adjusted one is $100/3000$. New shares of 50 at 30 are about 1.67 shares, or about 1.67% dilution a year. Buying them back would cost the 50 in cash, which makes the true free cash flow 100.

IFRS requires share-based pay to be recognised as an expense in the accounts. It is added back in cash flow because no cash leaves. But employees have still been paid, and the holders have paid them, through dilution.

Answer to Question 17.17.

With shares, earnings per share are $120/115 \approx 1.043$, up 4.3%. With debt, they are $106.5/100 = 1.065$, up 6.5%. At a price of 450 in shares, it falls to about 0.98. A deal that adds to earnings per share does not by that fact create value.

Company $A$ earns 1 per share, at a price to earnings multiple of 20. In shares, it issues $300/20 = 15$ shares. In debt, interest is $300 \times 6\% = 18$, which is 13.5 after tax, so net income is $120 - 13.5 = 106.5$.

The rule for shares is to compare multiples: a target bought at 15 times is accretive for a buyer at 20 times. At 450, the price is 22.5 times, above 20, and so it dilutes. The rule for debt is to compare yields: $B$’s earnings yield at this price is $20/300 \approx 6.67\%$, above the after-tax cost of debt of 4.5%.

Answer to Question 17.18.

Equity at exit is about 976, a multiple of 2.44 on 400, and an annual return of about 19.5%. At 9 times, equity is about 849, a multiple of 2.12, and the return is about 16.2%.

EBITDA grows to $100 \times 1.05^5 \approx 127.6$. At 10 times, the enterprise value is about 1,276. Debt has fallen to 300, so equity is about 976. The return is $2.44^{1/5} - 1$. A quick check: at 15% money doubles in about five years, and 2.44 is a bit more than one doubling, so the return is a bit above 15%.

The total gain of 576 comes from two places: 276 from EBITDA growth at a constant multiple, and 300 from paying off debt. None comes from a change in the multiple. The debt is why the 28% rise in enterprise value turns into a 144% rise in equity.

Answer to Question 17.19.

The lease liability and the asset are both about 421.2. In year 1, depreciation is about 84.2 and interest about 25.3, EBITDA rises by 100, and pre-tax profit falls by about 9.5. Enterprise value including the lease is about 1,421, and EBITDA is 250, which gives about 5.68 times, down from 6.67. Cash does not change. Total expense over 5 years stays at 500.

The present value of five payments of 100 at 6% is 421.24. The asset is depreciated evenly over 5 years, $421.24/5 = 84.25$. Interest in year 1 is $6\% \times 421.24 = 25.27$. Together they come to 109.52, against rent of 100. Interest falls as the liability falls, to 346.51 after year 1 and on to zero, so the expense is higher early and lower late: from 109.52 in year 1 to 89.91 in year 5.

EBITDA gains the whole rent, because rent has left operating costs. Operating profit gains only $100 - 84.25 = 15.75$. The cash payment of 100 is the same, but of it, $100 - 25.27 = 74.73$ now counts as repaying a debt.

This is IFRS 16. Under the US model, such a lease goes on the balance sheet too, but the expense typically stays a straight-line operating cost.

Answer to Question 17.20.

Net income is 30 every year. The rest changes by year:

At 8%, paying later instead of evenly is worth about 2.3.

In the accounts, pre-tax profit is $60 - 20 = 40$, tax expense is 10, and net income is 30. For tax in years 1 and 2, the deduction is 50, so taxable profit is 10 and cash tax is 2.5. In years 3 to 5, there is no deduction, so cash tax is 15. The expense of 10 exceeds the cash tax by 7.5 in the first two years, and that builds a liability, the deferred tax balance. It reverses by 5 a year afterwards. Under IAS 12, a company recognises this for temporary differences between the carrying amount of an asset and its tax base.

Total tax paid is 50 either way, the same as $25\% \times 200$. So the gain is only one of timing: $10$ a year discounted, less the actual path, comes to about 2.3.

Answer to Question 17.21.

Goodwill is 225. The write-up lowers net income by 7.5 a year. An impairment of 100 lowers net income by 100, with no effect on cash or on tax.

Goodwill is what is left after assets are marked to fair value. The target’s net assets at fair value are book equity of 200, plus the write-up of 100, less a deferred tax liability of $25\% \times 100 = 25$. So they come to 275, and $500 - 275 = 225$. Check: the buyer’s assets change by $+200 + 100 + 225 - 500 = +25$, which equals the new liability of 25.

Extra depreciation of 10 a year lowers pre-tax profit by 10. Since it is not deductible, cash tax does not change. Reported tax falls by 2.5 as the deferred tax unwinds, so net income falls by 7.5.

IFRS 3 allocates the price to identifiable assets and liabilities at fair value, and the rest goes to goodwill. IAS 36 tests goodwill for impairment every year, and a loss on goodwill is never reversed. Under both IFRS and US rules for listed companies, goodwill is not amortised.

Answer to Question 17.22.

The price implies constant growth of about 5.88% forever. With 3% growth after 10 years, it implies about 14.3% a year for the 10 years. At 3% growth from today, the company is worth about 1,236.

For constant growth, solve $3000 = 60(1 + g)/(0.08 - g)$, which gives $g = 180/3060 = 1/17 \approx 5.88\%$. At a growth rate of 3%, the value is $61.8/0.05 = 1{,}236$.

The two-stage version has no closed form that helps, so you solve numerically. At 14.3% for 10 years, cash flow grows by a factor of about 3.8, to about 228. The discounted terminal value then makes up about 72% of the price.

This is a reverse DCF. You do not ask what the company is worth. You ask what you must believe to pay this price. The 1,236 says that about 59% of the price is paying for growth above 3%. Then compare 14.3% with what comparable companies have done, and what the reinvestment would have to earn.

Answer to Question 17.23.

Revenue is 213, and operating profit is 20.15, up about 11.9% from 18. One point of same-store sales moves profit by 0.6, about 3.0% of 20.15. With flat same-store sales, operating profit is 18.35, up about 1.9%.

Base year: revenue of 200, store profit of 30, central costs of 12, so operating profit of 18.

Next year: existing stores sell $200 \times 1.03 = 206$, and the extra 6 of revenue adds $6 \times 30\% = 1.8$ of store profit. New stores sell at an annual rate of $2 \times 0.7 = 1.4$ each, for half a year, so $10 \times 1.4 \times \tfrac12 = 7$, and at 5% that earns 0.35. Store profit is $30 + 1.8 + 0.35 = 32.15$. Less 12, that is 20.15.

Each point of same-store sales is 2 of revenue, and at 30% flow-through that is 0.6. With flat sales, existing stores earn their old 30, the new stores add 0.35, and operating profit is 18.35. If the new stores did not open either, it would be last year’s 18 exactly, as it must be. So of the 2.15 of growth, 1.8 comes from same-store sales, about 84%, and the new stores add little in their first year.

Answer to Question 17.24.

Earnings rose 30%, but cash fell and every working-capital line moved the wrong way. Free cash flow went from $+50$ to $-50$. With development spending at Year 1’s share of revenue, net income would have been about 95.5, down from 100 instead of up 30%.

The checks, with 365 days:

The accruals of 70 are about 6.2% of average assets, which is large. Had receivables grown with sales, they would be 144, so 66 of them, or 5.5% of revenue, are excess. That points to revenue booked early, or to customers who are not paying. Inventory is 50 above its old ratio to cost of goods sold, which points to weak sales or goods building up.

Deferred revenue fell by 20. Billings, meaning revenue plus the change in deferred revenue, are 1,180, below revenue of 1,200. So part of this year’s revenue is drawn from the old balance and is not being replaced.

Capitalised development is 5.8% of revenue against 2%. At 2%, it would be 24, so 46 more would have been expensed, about 34.5 after tax. I ignore amortisation, which would be small here.

Innocent explanations to test. A large sale near year end would explain receivables, and the January cash receipts would settle it. A new product launch could justify both inventory and development. A big customer on longer terms is a real change, but it is a cost, not growth.

Questions for management. What share of Q4 sales came in the last month? How have terms changed? What is being capitalised and why now? What has been collected since year end?

Answer to Question 17.25.

The old price implied 33% recovery, and the new price implies about 18.6%. You need about 32.1% for a 15% expected return. At 35%, your expected return is about 18.3%. A fresh position sized by the 1% rule would be about 4.8% of capital, against about 3% originally. You have lost 0.9% of capital so far. My recommendation is to hold or add only if you can say why the guidance cut does not break the recovery case, and to cut otherwise.

Each price is a probability-weighted average of its two cases, so $p = (P - \text{bear})/(\text{bull} - \text{bear})$. So $(90 - 60)/90 = 1/3$, and $(63 - 50)/70 \approx 18.6\%$. Then a 15% return requires $(63 \times 1.15 - 50)/70 \approx 32.1\%$. At 35%, the value is $0.35 \times 120 + 0.65 \times 50 = 74.5$, and $74.5/63 - 1 \approx 18.3\%$.

Originally, the downside was $30/90 = 33.3\%$, so a 1% loss limit meant $1\%/33.3\% = 3\%$ of capital. It has lost $3\% \times 27/90 = 0.9\%$. Now the downside is $13/63 \approx 20.6\%$, so the same rule allows about 4.8%, and the upside is about 90.5%.

The arithmetic says buy more, but it depends on your 35%. You were wrong about one thing already, and your new bear case is only your estimate. Before adding, ask what the cut says about the recovery, whether your bear case is now really the floor, and whether you would buy it today with no history. To hold your nerve for the sake of it is not an argument.