Lab for Lecture 24: Review Session
1 Problem 1: Equity Valuation of Aurora Robotics
1.1 Setup
Today is December 31, 2025. Aurora Robotics, Inc. (ARI) is a publicly traded robotics and AI firm whose shares currently trade at $90 per share. You have collected the following information about ARI’s most recent fiscal year (FY 2025) and a small group of close competitors.
Income statement and balance sheet data (FY 2025, in billions):
| Item | Value |
|---|---|
| EBITDA | $25 |
| Depreciation & Amortization | $5 |
| EBIT | $20 |
| Interest expense | $4 |
| Corporate tax rate | 25% |
| Net income | $12 |
| Capital expenditures (CapEx) | $10 |
| Increase in net working capital (\(\Delta\)NWC) | $2 |
| Long-term debt (end of FY 2025) | $50 |
| Long-term debt (end of FY 2024) | $40 |
| Cash and cash equivalents | $10 |
| Book value of equity | $60 |
| Shares outstanding | 2 |
| Annual dividend per share (just paid) | $2.40 |
Comparable firms’ valuation multiples:
| Comparable | Trailing P/E | P/B | EV/EBITDA |
|---|---|---|---|
| Comp A | 18 | 4 | 14 |
| Comp B | 22 | 5 | 16 |
| Comp C | 26 | 6 | 18 |
Capital market assumptions:
| Parameter | Value |
|---|---|
| ARI’s equity beta | 1.20 |
| Risk-free rate | 4.0% |
| Market risk premium | 6.0% |
| ARI’s pre-tax cost of debt | 5.0% |
Growth assumptions for forward-looking valuation:
- Dividends and free cash flows are both expected to grow at 12% per year for the next 5 years (FY 2026 through FY 2030).
- Beyond year 5, dividends and free cash flows are expected to grow at a constant 4% per year in perpetuity.
1.2 Questions
Multiples valuation. Using the average multiple from the three comparable firms in each case, estimate the intrinsic value per share of ARI based on:
- The trailing P/E ratio.
- The P/B ratio.
- The EV/EBITDA ratio.
Dividend Discount Model (DDM). Using a two-stage DDM with the growth assumptions above and CAPM to estimate the cost of equity, calculate the intrinsic value per share of ARI.
Discounted Cash Flow (FCFF approach). Using a two-stage FCFF model with the growth assumptions above:
- Compute ARI’s most recent free cash flow to the firm (FCFF).
- Compute ARI’s weighted average cost of capital (WACC). Use the current market value of equity (based on the current share price) and the book value of long-term debt as a proxy for its market value.
- Calculate ARI’s firm value by discounting projected FCFFs and the terminal value at the WACC.
- Calculate ARI’s intrinsic value per share by subtracting long-term debt from total firm value and dividing by shares outstanding.
2 Problem 2: A Call Option on SunPower Solar
2.1 Setup
Today is December 31, 2025. SunPower Solar (SPS) is a non-dividend-paying stock currently trading at $100 per share. You are analyzing the following European call option on SPS:
| Feature | Value |
|---|---|
| Underlying | SunPower Solar (SPS) |
| Type | European call |
| Strike price (\(X\)) | $100 |
| Time to expiration (\(T\)) | 3 months |
| Current market price (premium) | $7.00 per share |
| Continuously compounded risk-free rate (\(r\)) | 5.0% per year |
| Annualized volatility of SPS returns (\(\sigma\)) | 30% per year |
2.2 Questions
Long call payoffs and profits. Suppose you buy one call option at the $7.00 premium. For each of the following stock prices at expiration, calculate the per-share payoff and profit from the long call position: \(S_T = \$80\), \(\$100\), \(\$105\), \(\$110\), \(\$120\).
Long call breakeven. At what stock price (at expiration) does the long call position break even (zero profit)?
Covered call payoffs and profits. Suppose instead you already own a share of SPS (purchased today at $100) and simultaneously write one call option on that share, receiving the $7.00 premium. For each of the following stock prices at expiration, calculate the total dollar profit of the covered-call position: \(S_T = \$80\), \(\$100\), \(\$105\), \(\$110\), \(\$120\).
Covered call breakeven and maximum profit. For the covered-call position in part 3:
- At what stock price at expiration does the covered-call position break even (zero total dollar profit)?
- What is the maximum total dollar profit, and at what range of stock prices is it achieved?
Black-Scholes pricing. Using the Black-Scholes formula, the parameters above, and assuming SPS pays no dividends, calculate the fair value of the call option. Compare your result to the option’s market price of $7.00 — does the option appear to be trading rich or cheap relative to a 30% volatility assumption?
Implied volatility. Find the implied volatility of the SPS call option — i.e., the value of \(\sigma\) that, when plugged into the Black-Scholes formula, produces a model price equal to the market price of $7.00.