Level 2 — RecallValuation Methods

Valuation Methods

⏱ 30 minutes50 marksprintable — key stays hidden on paper

Subject: Stock-Market | Chapter: Valuation Methods Level: 2 (Recall — definitions, standard problems, short derivations) Time limit: 30 minutes Total marks: 50

Section A — Definitions & Concepts (short answer)

Q1. Define intrinsic value and explain in one line how it differs from market price. (4 marks)

Q2. State the general Discounted Cash Flow (DCF) formula for the present value of a stream of future free cash flows $FCF_t$ over $n$ years using discount rate $r$ . (3 marks)

Q3. Write the formula for the Weighted Average Cost of Capital (WACC). Define each symbol. (5 marks)

Q4. State the margin of safety formula and briefly explain why value investors use it. (4 marks)

Q5. In one sentence each, define: (a) relative/comparable valuation, (b) sum-of-the-parts (SOTP) valuation, (c) reverse DCF. (6 marks)

Section B — Standard Problems

Q6. A stock is expected to pay a dividend of $D_1 = \$ 2.00 $next year. Dividends are expected to grow at a constant rate$ g = 4% $forever. The required return is$ r = 10%$. Using the Gordon Growth (constant-growth DDM) model, calculate the intrinsic value per share. (5 marks)

Q7. A firm's free cash flow in the final projection year is $FCF_5 = \$ 120 $million. Using a perpetuity-growth terminal value with$ g = 3% $and discount rate$ r = 9%$, calculate: (a) the terminal value at end of year 5, and (b) its present value today (discounted 5 years). (6 marks)

Q8. A company has:

Equity market value = $600m, Cost of equity = 12%
Debt market value = $400m, Cost of debt = 6%
Tax rate = 25%

Calculate the WACC. (6 marks)

Q9. A DCF gives an intrinsic value of $80 per share. The stock trades at $60. Calculate the margin of safety as a percentage of intrinsic value. (3 marks)

Q10. A comparable company trades at a P/E ratio of 15. Your target company has earnings per share of $4. Estimate the target's fair value per share using relative valuation, and state one limitation of this method. (3 marks)

Answer keyMark scheme & solutions

Q1. (4 marks)

Intrinsic value = the estimated "true" worth of an asset based on its fundamentals (expected future cash flows, growth, risk), independent of its current trading price. (2)
Market price = the price at which the stock currently trades in the market, driven by supply/demand and sentiment. Intrinsic value may be above or below market price; gaps signal over/undervaluation. (2)

Q2. (3 marks) $PV = \sum_{t=1}^{n} \frac{FCF_t}{(1+r)^t}$

Correct summation form (2), correct discount factor $(1+r)^t$ (1).

Q3. (5 marks) $WACC = \frac{E}{V}\,r_e + \frac{D}{V}\,r_d(1-T)$

Formula (2). Definitions: $E$ = market value of equity, $D$ = market value of debt, $V = E+D$ , $r_e$ = cost of equity, $r_d$ = cost of debt, $T$ = tax rate. (3, ½ each — round up)

Q4. (4 marks) $\text{Margin of Safety} = \frac{\text{Intrinsic Value} - \text{Market Price}}{\text{Intrinsic Value}}$ Formula (2). Explanation: it provides a buffer against errors in estimation and adverse events, reducing downside risk when buying below intrinsic value. (2)

Q5. (6 marks — 2 each)

(a) Relative valuation: valuing a company by comparing its multiples (P/E, EV/EBITDA, etc.) to those of similar peer companies. (2)
(b) SOTP: valuing each business segment/division separately and summing them (adjusting for net debt) to get total enterprise/equity value. (2)
(c) Reverse DCF: starting from the current market price and solving for the growth/assumptions the market is implicitly pricing in. (2)

Q6. (5 marks) Gordon Growth: $P_0 = \dfrac{D_1}{r-g} = \dfrac{2.00}{0.10-0.04} = \dfrac{2.00}{0.06} = \$ 33.33$

Correct formula (2), substitution (1), denominator = 0.06 (1), answer ≈ $33.33 (1).

Q7. (6 marks) (a) $TV_5 = \dfrac{FCF_5(1+g)}{r-g} = \dfrac{120 \times 1.03}{0.09-0.03} = \dfrac{123.6}{0.06} = \$ 2060 $m. **(3)** (b)$ PV = \dfrac{2060}{(1.09)^5} = \dfrac{2060}{1.53862} \approx $1338.9$ m. (3)

(a) numerator, denominator, TV = 2060 (1 each). (b) discount factor $1.09^5≈1.5386$ (2), PV ≈ $1338.9m (1).

Q8. (6 marks) $V = 600 + 400 = 1000$ . $WACC = \frac{600}{1000}(0.12) + \frac{400}{1000}(0.06)(1-0.25)$ $= 0.6\times0.12 + 0.4\times0.06\times0.75$ $= 0.072 + 0.018 = 0.090 = 9.0\%$

Weights (2), equity term 0.072 (1), after-tax debt term 0.018 (2), total 9% (1).

Q9. (3 marks) $MoS = \dfrac{80-60}{80} = \dfrac{20}{80} = 0.25 = 25\%$ .

Formula (1), computation (1), answer 25% (1).

Q10. (3 marks) Fair value = P/E × EPS = $15 \times 4 = \$ 60$ per share. (2) Limitation (any one): relies on peers being truly comparable; multiples can be distorted by market sentiment/accounting differences; ignores company-specific growth/risk. (1)

[
  {"claim":"Q6 Gordon Growth value = 33.33","code":"D1=2.00; r=Rational(10,100); g=Rational(4,100); P0=D1/(r-g); result=abs(float(P0)-33.3333333)<0.01"},
  {"claim":"Q7a Terminal value = 2060","code":"FCF=120; g=Rational(3,100); r=Rational(9,100); TV=FCF*(1+g)/(r-g); result=abs(float(TV)-2060)<0.001"},
  {"claim":"Q7b PV of TV approx 1338.9","code":"TV=2060; PV=TV/(1.09**5); result=abs(PV-1338.9)<1.0"},
  {"claim":"Q8 WACC = 9%","code":"E=600; D=400; V=E+D; re=Rational(12,100); rd=Rational(6,100); T=Rational(25,100); w=(E/V)*re+(D/V)*rd*(1-T); result=abs(float(w)-0.09)<1e-9"},
  {"claim":"Q9 Margin of safety = 25%","code":"iv=80; mp=60; mos=(iv-mp)/iv; result=abs(mos-0.25)<1e-9"},
  {"claim":"Q10 relative value = 60","code":"pe=15; eps=4; val=pe*eps; result=val==60"}
]