Valuation Methods

Question 1 (14 marks)

(a) WACC (weight each capital source by market value, tax-shield the debt)

Weights: $E/V = 600/800 = 0.75$; $D/V = 200/800 = 0.25$. After-tax cost of debt $= 7\% \times (1-0.25) = 5.25\%$.

$WACC = 0.75(12\%) + 0.25(5.25\%) = 9\% + 1.3125\% = 10.3125\%$

WACC = 10.3125% (≈ 0.1031). (1 weights, 1 after-tax kd, 2 formula/answer)

(b) Terminal value (Gordon Growth on year-4 FCF)

$FCF_4 = 52 \times 1.03 = 53.56$ $TV_3 = \frac{53.56}{0.103125 - 0.03} = \frac{53.56}{0.073125} = 732.44\text{m}$ (1 grow FCF, 1 formula, 1 answer ≈ $732.44m)

(c) Enterprise value (discount each flow at WACC = 10.3125%)

Discount factors: $1.103125^1=1.103125$, $^2=1.216885$, $^3=1.342122$.

• Yr1: $40/1.103125 = 36.26$
• Yr2: $46/1.216885 = 37.80$
• Yr3: $(52 + 732.44)/1.342122 = 784.44/1.342122 = 584.47$

$EV = 36.26 + 37.80 + 584.47 = 658.53\text{m}$ (1 each PV year, 1 include TV in yr3, 1 sum ≈ $658.5m)

(d) Equity value (EV − net debt; net debt = 200 − 30 = 170)

$Equity = 658.53 - 200 + 30 = 488.53\text{m}$ (2 marks)

Question 2 (12 marks)

(a) Two-stage DDM (explicit high-growth dividends + terminal Gordon value)

$D_1 = 2.00(1.10)=2.20$; $D_2=2.42$; $D_3=2.662$. $D_4 = 2.662(1.04)=2.76848$. Terminal value at yr3: $TV_3 = \dfrac{2.76848}{0.09-0.04} = \dfrac{2.76848}{0.05}=55.3696$.

Discount at 9%:

• $2.20/1.09 = 2.0183$
• $2.42/1.1881 = 2.0369$
• $(2.662+55.3696)/1.295029 = 58.0316/1.295029 = 44.8072$

$V_0 = 2.0183+2.0369+44.8072 = 48.86$ Intrinsic value ≈ $48.86. (2 growth dividends, 2 terminal, 3 discounting, 1 sum)

(b) Intrinsic $48.86 < market $52 → stock is overvalued (price exceeds intrinsic value); avoid/sell. (2)

(c) DDM requires dividends as the cash flow input; a non-dividend-paying firm gives a zero/undefined valuation, and forecasting when/if dividends begin for a high-growth tech firm is highly uncertain, so DCF on FCF is more appropriate. (2)

Question 3 (12 marks)

(a) Division values (multiply EBITDA by peer multiple)

• Logistics: $80 \times 6.0 = 480$m
• Software: $50 \times 12.0 = 600$m
• Operating EV $= 480 + 600 = 1080$m (4)

(b) Equity value (SOTP) (add non-operating stake, subtract net debt)

$Equity = 1080 + 150 - 220 = 1010\text{m}$ (4)

(c) Per share: 1010/40 = \25.25$ per share. (2)

(d) A single blended multiple ignores that the software division warrants a higher multiple; averaging drags it down toward the logistics multiple, understating the software value. SOTP captures each division's distinct growth/risk profile. (2)

Question 4 (12 marks)

(a) Margin of safety (discount of price to intrinsic value)

$MoS = \frac{80-60}{80} = 25\%$ (2)

(b) Need price ≤ 80% of intrinsic value (i.e. intrinsic ≥ 60/0.8 = $75). Purchase at 60 gives ≥20% MoS if intrinsic value ≥ $75.

(1.5 marks each correct verdict; alternatively compute MoS: 32%, 37.5%, 16.7%, 23.1%)

(c) In 3 of 4 scenarios a 20% margin holds; valuation is fairly robust but sensitive to the discount rate — the low-g/high-r corner fails, so the thesis depends on r staying near 9%. (2)

(d) Sensitivity analysis varies one input at a time to see the effect on value; scenario analysis changes several inputs simultaneously to reflect a coherent state of the world (e.g. recession). (2)

Question 5 (10 marks)

(a) Implied growth (rearrange perpetuity price = FCF₁/(r−g))

$45 = \frac{2.70}{0.10-g} \Rightarrow 0.10-g = \frac{2.70}{45}=0.06 \Rightarrow g = 0.04$ Implied g = 4% (0.0400). (4)

(b) The market prices in 4% perpetual growth, above the 3% GDP-linked achievable rate. This implies mildly optimistic expectations; sustaining above-GDP growth forever is unrealistic, so the stock may be somewhat overvalued unless a durable competitive edge justifies it. (3)

(c) A forward DCF assumes inputs (growth, r) to output a value. Reverse DCF fixes the observed market price and solves back for the growth (or return) the market is implying, so the analyst can judge whether that embedded expectation is achievable. (3)

[
  {"claim":"NovaTech WACC = 0.103125","code":"WACC=0.75*0.12+0.25*0.07*(1-0.25); result=(abs(WACC-0.103125)<1e-9)"},
  {"claim":"NovaTech TV3 approx 732.44m","code":"TV=(52*1.03)/(0.103125-0.03); result=(abs(TV-732.44)<0.5)"},
  {"claim":"NovaTech EV approx 658.5m","code":"w=0.103125; ev=40/(1+w)+46/(1+w)**2+(52+(52*1.03)/(w-0.03))/(1+w)**3; result=(abs(ev-658.5)<1.0)"},
  {"claim":"Meridian DDM intrinsic approx 48.86","code":"r=Rational(9,100); D=[2.2,2.42,2.662]; TV=(2.662*1.04)/(0.09-0.04); v=D[0]/1.09+D[1]/1.09**2+(D[2]+TV)/1.09**3; result=(abs(float(v)-48.86)<0.05)"},
  {"claim":"Apex per share = 25.25","code":"eq=80*6+50*12+150-220; result=(abs(eq/40-25.25)<1e-9)"},
  {"claim":"Reverse DCF implied g = 0.04","code":"g=symbols('g'); sol=solve(Eq(45,2.70/(0.10-g)),g); result=(abs(float(sol[0])-0.04)<1e-9)"}
]