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// THE GROUNDWORK / THE NUMBER23 SUMS · ONE MINUTE EACH

THE IN-TRAY · THE GROUNDWORK

The Number

What is the figure?

The files on the second shelf that end in a number. Work it out, pick the figure, and the read shows the working — and which wrong figure each of the other options is.

// A · THE BORROWER · CAN THIS BUSINESS PAY?

THE NUMBER · EARNINGS · 1 OF 6

A distributor's reported EBITDA is US$5.1m. The CFO's bridge adds back three items.

Reported EBITDA
US$5.1m
Restructuring
US$0.9m · third year running
Legal settlement
US$0.3m · first in ten years
Owner's pay above market
US$0.2m

What EBITDA do you lend against?

THE NUMBER · CASH · 2 OF 6

A wholesaler asks to size its working capital line.

Debtor days
55
Stock days
70
Creditor days
40
Sales a day
US$100k

What is its cash conversion cycle?

THE NUMBER · CASH · 3 OF 6

A distributor's year, in four numbers:

Operating cash flow
US$4.0m
Maintenance capex
US$1.5m
Growth capex
US$2.0m
Dividends
US$1.0m

How much cash does it generate after keeping its assets in shape, before growth and dividends?

THE NUMBER · CASH · 4 OF 6

A supplier offers its customers 2% off for paying in 10 days instead of 40.

Roughly what annual rate is the supplier paying to be paid early?

THE NUMBER · BALANCE SHEET · 5 OF 6

A retailer's accounts keep its store leases off the balance sheet. Its banker restates them as if the leases were capitalised.

Net debt, as reported
US$6m
EBITDA, as reported
US$4m
Lease liability if capitalised
US$15m
Annual rent inside operating costs
US$3m

What is net debt to EBITDA with the leases on the balance sheet?

THE NUMBER · BUSINESS · 6 OF 6

A bakery sells 150,000 units a year at an average of US$10 each. Variable costs are US$6 a unit and fixed costs US$400k a year.

How far can its sales fall before it makes a loss?

6 FILES · PICK A CALL ON ANY OF THEM

THE WHOLE THE BORROWER TRAY →

// B · THE LOAN · ON WHAT TERMS?

THE NUMBER · CAPACITY · 1 OF 8

A company asks to refinance. Its year in four numbers:

EBITDA
US$6m
Capex + tax
US$2m
Interest
US$1m
Principal due
US$2m

What is its debt service cover, on cash available after capital spending and tax?

THE NUMBER · CAPACITY · 2 OF 8

A property investor collects US$2.4m of rent a year and spends US$0.4m running the building. Interest and principal on its loan come to US$1.6m a year.

What is its debt service cover?

THE NUMBER · CAPACITY · 3 OF 8

A US$2m machine is expected to save US$400k of cash a year. The borrower asks for a three-year loan to buy it.

How long does the machine take to pay for itself?

THE NUMBER · PROTECTION · 4 OF 8

A company fails. One lender is secured over the plant; the other is unsecured. The receiver's realisations, after costs, are below. There are no preferential claims.

Secured lender owed
US$10m
Unsecured lender owed
US$5m
Realised from the plant
US$9m
Realised from everything else
US$2m

What does the unsecured lender recover?

THE NUMBER · PRICE · 5 OF 8

A US$10m loan. The bank estimates a 2% chance the borrower defaults within a year, and expects to lose 40% of what is owed if it does.

What is the expected annual loss?

THE NUMBER · PRICE · 6 OF 8

A US$20m loan. The bank expects to lose 0.5% of it a year on average. It must hold capital equal to 10% of the loan, and its shareholders expect 12% a year on that capital. Funding and running costs are priced separately.

What margin covers expected loss and the return on capital?

THE NUMBER · PRICE · 7 OF 8

A company borrows at 8% a year. Its interest is deductible, and it pays tax at 25%.

What is its after-tax cost of this debt?

THE NUMBER · HEDGES · 8 OF 8

A borrower pays a floating rate on a five-year term loan: the base rate plus a margin. It enters a swap with the bank, paying a fixed rate and receiving the base rate.

Lending margin
2.50
Swap fixed rate
4.00
Base rate today
3.50

What does it pay all-in, and what if the base rate falls to 3.00?

8 FILES · PICK A CALL ON ANY OF THEM

THE WHOLE THE LOAN TRAY →

// C · THE BANK · CAN THE LENDER CARRY IT?

THE NUMBER · FUNDING AND LIQUIDITY · 1 OF 5

A bank holds US$3bn of assets it could sell within days at little loss. In a severe stress, it estimates US$2.4bn of its funding would leave within 30 days.

What is its liquidity coverage?

THE NUMBER · CAPITAL · 2 OF 5

A bank has US$10bn of loans: half to companies, half home mortgages. Suppose the capital rules weight company loans at 100% and these mortgages at 35%.

What are its risk-weighted assets?

THE NUMBER · CAPITAL · 3 OF 5

A bank holds US$900m of capital against US$10bn of risk-weighted assets, a ratio of 9%. A loan book goes bad and it writes off US$200m. Assume its risk-weighted assets are unchanged.

How much new capital takes it back to 9%?

THE NUMBER · ASSET QUALITY · 4 OF 5

A bank's annual report gives three figures for its loan book.

Gross loans
US$10bn
Non-performing loans
US$300m
Provisions held
US$180m

What is its provision coverage of non-performing loans?

THE NUMBER · RATE SENSITIVITY · 5 OF 5

A bank holds US$10bn of fixed-rate loans with an average duration of four years. Market rates rise by one percentage point.

Roughly how much value have the loans lost?

5 FILES · PICK A CALL ON ANY OF THEM

THE WHOLE THE BANK TRAY →

// D · THE ECONOMY · IN WHAT CONDITIONS?

THE NUMBER · RATES · 1 OF 4

A borrower's loan costs 7% a year. Inflation is running at 5%, and the borrower's selling prices rise with it.

Roughly what real rate is it paying?

THE NUMBER · CURRENCY AND TRADE · 2 OF 4

A company's costs are all in its home currency. It invoices an overseas customer in dollars, payable in 90 days. Between invoice and payment the dollar weakens.

Invoice
US$1.0m
Home currency per dollar, at invoice
1.50
Home currency per dollar, at payment
1.35

What did the move cost, in home currency?

THE NUMBER · COLLATERAL MARKETS · 3 OF 4

An office building earns US$1.0m a year of net operating income. Buyers price such buildings at a 5% yield, so it is valued at US$20m. The loan against it is US$12m.

If the yield buyers want rises to 6%, what is the loan-to-value?

THE NUMBER · COLLATERAL MARKETS · 4 OF 4

A bank lent 65% of the value of a factory valued at US$10m. If it has to sell, it expects a forced-sale discount of 30%, and selling costs of 5% of the sale price.

What does it recover against the US$6.5m loan?

4 FILES · PICK A CALL ON ANY OF THEM

THE WHOLE THE ECONOMY TRAY →

Each sum is one square of the map; the square holds the files around it that are not sums — the first question to ask, the signal to read, the call to make. The whole map → Thirty days, one a day →

The Groundwork's files are free to reuse under CC BY 4.0: copy a file into your notes, a tutorial or a slide, with a link back to the page it came from. The first shelf's files, on the chapters of How Bankers Think, are not under that licence.