Sum-of-the-Parts Valuation

Sum-of-the-Parts Valuation

Sum-of-the-Parts Valuation: How It Works

What it does

Many companies are several businesses under one roof, and the businesses can differ in growth, risk and profitability. One multiple for the whole company hides those differences. A sum-of-the-parts valuation values each business (each segment) on its own, adds the values, takes off what is owed to others, and divides by the number of shares. The page does this at a low and at a high multiple for every segment, so that the answer is a range, and prints every step as formula, numbers put in, answer. When a share price is typed, it states the gap between the price and the middle of the range in percent. That gap is arithmetic on the multiples entered; the page makes no judgement about the price.

The method

Symbols. Money is in millions of one currency and shares are in millions, so a value per share is in the currency itself. For segment k, M_k is its metric, a yearly figure such as EBITDA (earnings before interest, taxes, depreciation and amortization) or revenue; x_Lk and x_Hk are the low and the high multiple, the number of times its metric the segment is taken to be worth.

Segment values. V_Lk = M_k x_Lk and V_Hk = M_k x_Hk. The mid value is their average, which is the metric times the middle multiple (x_Lk + x_Hk) / 2.

Enterprise value. EV = Σ V_k, in the low, mid and high case. Enterprise value is the value of the businesses to lenders and shareholders together.

Bridge to equity. Value of the shares Q = EV − N_D + A_net. N_D is the net debt (debt less cash; negative for net cash). A_net is the sum of the other adjustments, each with its sign: minority interests (the part of a subsidiary that belongs to other owners) and a pension deficit are subtracted; investments and stakes held at their value are added.

Value per share. v = Q / N_sh, with N_sh the number of shares.

Share of the mid value. Segment k carries V_Mk / Σ V_Mk of the total of the segment mid values.

Implied whole-company multiple. x_W = EV / Σ M_k: the single multiple that would give the same enterprise value. It is the average of the segment multiples weighted by the metrics.

Price against the mid value. d_c = (P_mkt − v_M) / v_M · 100, with P_mkt the typed price and v_M the mid value per share. A negative result is called an implied conglomerate discount, a positive one an implied conglomerate premium.

Advanced. Unallocated corporate costs C_c a year are capitalised at a multiple x_c and subtracted: EV = Σ V_k − C_c x_c, and the implied multiple becomes EV / (Σ M_k − C_c). A holding-company discount d_h in percent multiplies the value of the shares by (1 − d_h / 100). A segment can be valued by a price-to-earnings multiple on its net income (usual for a financial arm, whose debt is part of its business) or by a value entered directly (a stake); both are values to shareholders, so they are left out of the enterprise value and added in the bridge, Q = EV − N_D + O + A_net. The sensitivity table recomputes the mid value per share with the multiples of two chosen segments moved two steps down and two steps up.

What it assumes

• Each segment could be valued as if it stood alone, at the multiple of comparable stand-alone companies.
• The segment metrics add up to the company: costs, debt, tax and cash not assigned to a segment are captured by the net debt, the adjustments and (Advanced) the corporate costs, or not at all.
• The multiples are yours. The page takes them as given and does not look anything up.
• The mid case is the midpoint of each segment's multiples. It is a convention, not a most likely value.

When it misleads

• The answer is the multiples. Nothing in the arithmetic tests them. A discount or premium to the sum can mean the price is off, or that the multiples are; the page cannot tell which.
• Segment figures are the company's own cut. In U.S. filings they follow the way management runs the business. Shared costs may be allocated by a rule of the company's choosing, and the measure of segment profit is often not EBITDA, so segment metrics may not be comparable with those of stand-alone companies.
• Costs of the centre. Leaving out head-office costs overstates the sum. Separating the businesses would also cost money and tax, which the sum ignores.
• Double counting. A stake entered as a segment and again as an adjustment, or a financial arm's debt left in net debt while the arm is valued by P/E, is counted twice.
• Mixed metrics. The implied whole-company multiple has no meaning when one segment's metric is EBITDA and another's is revenue.
• Leverage. Debt and adjustments are fixed amounts, so a small change in multiples moves the value per share by a larger percentage, and with high debt the low case can be negative.

Worked example

The default case is illustrative, not a real company. Four segments with EBITDA of 800, 500, 300 and 150 million are valued at 9 to 11, 11 to 13, 7 to 9 and 14 to 18 times.

Low values: 800 · 9 = 7,200; 500 · 11 = 5,500; 300 · 7 = 2,100; 150 · 14 = 2,100; enterprise value 16,900. High values: 8,800 + 6,500 + 2,700 + 2,700 = 20,700. Mid: (16,900 + 20,700) / 2 = 18,800.

Implied whole-company multiple, mid: 18,800 / (800 + 500 + 300 + 150) = 18,800 / 1,750 = 10.743.

Bridge, mid: net debt 3,500; minority interests −400, pension deficit −300, investments +600, together −100. Value of the shares = 18,800 − 3,500 − 100 = 15,200. With 400 million shares, 15,200 / 400 = 38.00 per share. Low: (16,900 − 3,600) / 400 = 33.25. High: (20,700 − 3,600) / 400 = 42.75.

Shares of the mid value: 8,000 / 18,800 = 42.6 %, 6,000 / 18,800 = 31.9 %, and 2,400 / 18,800 = 12.8 % for each of the last two.

Typed price 32.00: (32.00 − 38.00) / 38.00 · 100 = −15.79, an implied conglomerate discount of 15.79 % on these multiples.

A calculator for education and analysis, not investment advice.