FM: Business valuations

Answer: D. Business valuations are needed when ownership stakes change hands or must be priced — for example in mergers and acquisitions, when an unquoted company is sold, when a company seeks a market listing, for tax purposes, or when buying out a shareholder. Recording a routine credit sale (option D) is ordinary bookkeeping and needs no business valuation. Options A, B and C are all classic occasions for a valuation.

Answer: A. Net asset value = total assets − total liabilities = £5m − £2m = £3m, which is the book value of the equity. Per share = £3,000,000 ÷ 1,000,000 = £3.00. Option B uses total assets without deducting liabilities, option C uses the liabilities figure, and option D adds assets and liabilities together. The asset-based method gives a 'floor' value but ignores intangibles and future earnings, so it often understates a going concern.

Answer: B. Under the P/E method, value per share = earnings per share × P/E ratio = 30p × 12 = £3.60. The P/E ratio of a comparable quoted company is applied to the target's earnings. In practice the quoted P/E is usually reduced (a 'haircut') before applying it to an unquoted company, to reflect the lower marketability of its shares. Option A divides instead of multiplying, while options C and D misplace the decimal or misapply the ratio.

Answer: C. Under the earnings yield method, value per share = earnings per share ÷ earnings yield = 30p ÷ 0.10 = £3.00. The earnings yield is the reciprocal of the P/E ratio, so this is the P/E method seen from the other direction (a 10% earnings yield equals a P/E of 10). Option A simply restates the EPS, and options B and D misplace the decimal point. The method values the share by capitalising its earnings at the market's required yield.

Answer: D. The dividend growth model gives P0 = D1 ÷ (Ke − g) = 21p ÷ (0.12 − 0.05) = 21p ÷ 0.07 = £3.00. The model values the share as a growing perpetuity of dividends discounted at the required return less the growth rate. Option C divides by the growth rate alone, while options A and B use the wrong numerator or denominator. The valuation is sensitive to the growth and required-return assumptions because they appear as a small difference in the denominator.

Answer: C. The dividend growth model assumes dividends grow at a single constant rate forever, which is unrealistic, and because the growth rate and required return appear as a small difference in the denominator, the valuation is very sensitive to small changes in those estimates. It also struggles with companies that pay no dividends. Option A and option B are untrue (the model is widely used and is built on dividends), and option D is incorrect, since different methods typically give different values.

Answer: A. With no growth, share value = dividend ÷ required return = 40p ÷ 0.10 = £4.00. The general dividend valuation model, D ÷ (r − g), reduces to D ÷ r when growth is zero, treating the share as a perpetuity paying a constant dividend. Option B is just the dividend itself, option C adds the dividend to the value, and option D inverts part of the calculation. The required return is the rate that capitalises the dividend stream.

Answer: B. An irredeemable (undated) bond is a perpetuity, so its market value = annual interest ÷ required return = £7 ÷ 0.10 = £70 per £100 nominal. Because the required return (10%) exceeds the coupon (7%), the bond trades below par. Option A is the nominal value, option C inverts the calculation (100 ÷ 0.70), and option D applies the interest to an incorrect base. It is the investors' required return, not the coupon, that sets the price.

Answer: C. Market value = present value of the interest stream + present value of the redemption amount. Interest: £6 × 2.577 (the three-year annuity factor) = £15.46. Redemption: £100 × 0.794 (the year-3 factor) = £79.40. Total = £15.46 + £79.40 = £94.86. The bond trades below par because the 8% required return exceeds the 6% coupon. Option A is par, option B adds one year's interest to par, and option D omits part of the interest stream.

Answer: D. The conversion value = number of shares × expected share price = 20 × £6.00 = £120. A rational holder compares this with the £100 cash redemption value and takes the higher amount, so they convert and realise £120. Option A ignores the financial comparison, option B uses the wrong figure for the conversion value, and option C mislabels the £120 as a redemption amount. The bond's market value today would discount this £120 (plus any interim interest) back to the present.

Answer: A. A preference share pays a fixed dividend in perpetuity, so its value = dividend ÷ required return = 5p ÷ 0.08 = 62.5p (the 5% dividend on £1 nominal is 5p). There is no tax adjustment, because preference dividends are not tax-deductible. Option B is the nominal value, while options C and D misapply the figures. As with irredeemable debt, the value is a perpetuity capitalised at the investors' required return.

Answer: B. The market value of debt is the present value of the cash flows the holder expects to receive — future interest plus any redemption amount — discounted at the return investors currently require on that debt. This is why bond prices move inversely to required returns. Option A holds only by coincidence, when the coupon equals the required return; options C and D describe historical or accounting figures, which usually differ from current market value.

Answer: C. The semi-strong form holds that prices reflect all publicly available information — past prices plus all published data such as results announcements — so neither technical analysis nor fundamental analysis of public information can consistently beat the market. The weak form (option A) covers only past prices, and the strong form (option B) covers all information, including private and insider data. Option D describes an inefficient market. Most developed stock markets are believed to be at least semi-strong efficient.

Answer: D. In a semi-strong efficient market, prices already reflect all public information, so the share price is a fair value: managers cannot fool the market with cosmetic accounting changes, and there is little point trying to time share issues to catch a mispricing. Option A and option C contradict efficiency — the market sees through cosmetic changes and past prices are already impounded — and option B assumes a reliable mispricing that efficiency rules out.

Answer: A. In a semi-strong efficient market, new public information is rapidly and accurately built into the share price, so prices adjust almost immediately to announcements. Option B describes a slow, inefficient reaction; options C and D imply that publicly available information or past prices could be used to earn consistent excess returns, which efficiency rules out. Empirical evidence broadly supports the semi-strong form in developed markets.

Answer: B. The net asset method values a business at the worth of its separable net assets, but it ignores the company's earning power and the intangible value — brands, know-how, internally generated goodwill — that often makes a business worth more than its balance sheet suggests. It also depends heavily on whether assets are stated at book, replacement or realisable values. It can certainly be calculated (option A), it usually gives a lower figure than earnings methods (option C), and it is not restricted to NFPs (option D).

Answer: D. A high P/E ratio means investors are paying more for each pound of current earnings, which usually reflects expectations of strong future earnings growth and/or a perception of lower risk. Option A would tend to depress, not raise, the P/E; option B is too absolute, since a high P/E may be fully justified by prospects; and option C is the opposite of what a high P/E normally signals. P/E ratios are most useful when comparing similar companies within the same sector.

Answer: A. An unquoted company has no observable market price, so a value must be estimated using methods such as net assets, an adjusted P/E multiple or discounted cash flow. The shares are also less marketable and harder to sell, and information about the company is typically more limited — all of which add uncertainty, often leading to a discount being applied. Options B, C and D are simply untrue.