Question & Answer

To value XYZ Corporation using the Discounted Cash Flow (DCF) analysis, follow these steps:

1. Calculate the Present Value (PV) of Free Cash Flows (FCFs) for the Next Five Years

The formula for calculating the present value of each year's FCF is:

​

PV=FCF/(1+WACC)t

Where:

• $\mathrm{<br>}\mathrm{<span\; style="color:\; var(--text-secondary);\; font-size:\; 1.125rem;\; background-color:\; var(--main-surface-primary);\; font-family:\; "Helvetica\; Neue",\; Helvetica,\; Arial,\; sans-serif;">F<span\; class="katex"\; style="color:\; var(--text-secondary);\; font-size:\; 1.125rem;\; background-color:\; var(--main-surface-primary);"><span\; class="katex-html"\; aria-hidden="true"><span\; class="base"><span\; class="mord\; mathnormal">CF</span></span></span></span><span\; style="color:\; var(--text-secondary);\; font-size:\; 1.125rem;\; background-color:\; var(--main-surface-primary);">\; is\; the\; Free\; Cash\; Flow\; in\; a\; given\; year</span></span>}$
• $WACC$ is the Weighted Average Cost of Capital
• $t$ is the year number

• Given data:

  • WACC = 10% or 0.10
  • FCF for Year 1 = $5 million
  • FCF for Year 2 = $6 million
  • FCF for Year 3 = $7 million
  • FCF for Year 4 = $8 million
  • FCF for Year 5 = $9 million
  • Calculate the PV for each year:
  • Year 1: $PV_{1} = \frac{5}{(1 + 0.10)^1} = \frac{5}{1.10} = 4.545 \text{ million}$

Year 2: $PV_{2} = \frac{6}{(1 + 0.10)^2} = \frac{6}{1.21} = 4.959 \text{ million}$

2. Calculate the Terminal Value (TV) at the End of Year 5

The Terminal Value is calculated using the perpetuity growth model:

TV=FCF 5 ​×(1+g)/W ACC-g​

​Where:

• $FCF_{5}$ is the Free Cash Flow in Year 5 ($9 million)
• $\mathrm{<br><span\; class="katex"\; style="color:\; var(--text-secondary);\; font-size:\; 1.125rem;\; background-color:\; var(--main-surface-primary);\; font-family:\; "Helvetica\; Neue",\; Helvetica,\; Arial,\; sans-serif;"></span><span\; style="color:\; var(--text-secondary);\; font-size:\; 1.125rem;\; background-color:\; var(--main-surface-primary);\; font-family:\; "Helvetica\; Neue",\; Helvetica,\; Arial,\; sans-serif;">g\; is \; the\; perpetual\; growth\; rate\; (3\%\; or\; 0.03)</span>}$
• $WACC$ is the Weighted Average Cost of Capital (10% or 0.10)
• TV=0.10−0.039×(1+0.03)​=0.079×1.03​=0.079.27​=132.857 million 

• 3. Calculate the Present Value of Terminal Value

  Discount the terminal value back to the present value:

  PV TV​=(1+WACC)5TV​=(1+0.10)5132.857​=1.61051132.857​=82.45 million

  4. Calculate the Total Enterprise Value

  Add the present value of the FCFs and the present value of the terminal value:

  $\text{Total Enterprise Value} = PV_{1} + PV_{2} + PV_{3} + PV_{4} + PV_{5} + PV_{TV}$

  $$
  

  $\text{Total Enterprise Value} = 4.545 + 4.959 + 5.263 + 5.471 + 5.594 + 82.45 = 107.282 \text{ million}$

  
  

  Summary

  • Present Value of Free Cash Flows for the Next Five Years: $25.832 million
  • Terminal Value: $132.857 million
  • Present Value of Terminal Value: $82.45 million
  • Total Enterprise Value: $107.282 million.

• Enterprise Value Calculation

  To determine the enterprise value of XYZ Corporation, follow these steps:

  1. Calculate the Present Value (PV) of Free Cash Flows (FCFs)

  As previously calculated:

  • Year 1: $4.545 million
  • Year 2: $4.959 million
  • Year 3: $5.263 million
  • Year 4: $5.471 million
  • Year 5: $5.594 million

  Total PV of FCFs for the next five years

  4.545+4.959+5.263+5.471+5.594=25.832 million

  2. Calculate Terminal Value (TV)

  Using the perpetuity growth model: $TV = \frac{FCF_{5} \times (1 + g)}{WACC - g}$ $TV = \frac{9 \times (1 + 0.03)}{0.10 - 0.03} = \frac{9 \times 1.03}{0.07} = \frac{9.27}{0.07} = 132.857 \text{ million}$

  3. Discount Terminal Value to Present Value

  PVTV​=(1+WACC)5TV​=(1+0.10)5132.857​=1.61051132.857​=82.45 million

  4. Calculate Total Enterprise Value

  $\text{Total Enterprise Value} = PV_{\text{FCFs}} + PV_{\text{TV}}$

  $\text{Total Enterprise Value}=25.832+82.45=108.282\text{ million}$

  Sensitivity Analysis

  To understand how sensitive the enterprise value is to changes in WACC and the perpetual growth rate, calculate the enterprise value under various scenarios.

  Sensitivity to WACC (±1%)

  • WACC = 9% $TV = \frac{9 \times (1 + 0.03)}{0.09 - 0.03} = \frac{9.27}{0.06} = 154.5 \text{ million}$ $PV_{TV} = \frac{154.5}{(1 + 0.09)^5} = \frac{154.5}{1.53862} = 100.63 \text{ million}$ $\text{Total Enterprise Value} = 25.832 + 100.63 = 126.462 \text{ million}$

  WACC = 11% $TV = \frac{9 \times (1 + 0.03)}{0.11 - 0.03} = \frac{9.27}{0.08} = 115.875 \text{ million}$ $PV_{TV} = \frac{115.875}{(1 + 0.11)^5} = \frac{115.875}{1.68506} = 68.7 \text{ million}$ $\text{Total Enterprise Value} = 25.832 + 68.7 = 94.532 \text{ million}$
  

  Sensitivity to Growth Rate (±0.5%)

  • Growth Rate = 2.5% $TV=\frac{9\times (1+0.025)}{0.10-0.025}=\frac{9.225}{0.075}=$ $PV_{TV} = \frac{123}{(1 + 0.10)^5} = \frac{123}{1.61051} = 76.36 \text{ million}$
    

  • $\text{Total Enterprise Value}=25.832+76.36=102.192\text{ million}$

    Growth Rate = 3.5%

  • $\mathrm{TV}=\frac{9\times (1+0.035)}{0.10-0.035}=\frac{9.315}{0.065}=143.615\text{ million<span style="color: var(--text-secondary); font-size: 1.125rem; background-color: var(--main-surface-primary); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;"></span>}$$P{V}_{TV}=\frac{143.615}{(1+0.10{)}^5}=\frac{143.615}{1.61051}=89.10\text{ million}$

    • $\text{Total Enterprise Value}=25.832+89.10=114.932\text{ million}$

    Discussion

    Assumptions Behind the DCF Model:

    Future Cash Flows: Assumes that future cash flows can be accurately estimated and will grow at a constant rate beyond the forecast period.

    Discount Rate (WACC): Assumes that the WACC appropriately reflects the risk of the cash flows and remains constant over time.

    Perpetuity Growth Rate: Assumes a constant growth rate in perpetuity, which might not reflect future uncertainties or market conditions.

    Impact of Key Inputs:

    • WACC: A higher WACC decreases the present value of future cash flows and terminal value, leading to a lower enterprise value. Conversely, a lower WACC increases the present value.
    • Growth Rate: A higher growth rate increases the terminal value, thus increasing the enterprise value. A lower growth rate has the opposite effect.
    • Small changes in  small changes in WACC or growth rate can significantly impact the enterprise value, highlighting the sensitivity of the DCF model to its assumptions. This underscores the importance of accurate and realistic input assumptions to ensure reliable valuation results.