Calculating NPV, IRR, Payback, Stock Splits & Repurchases

Cornell Enterprises Project Evaluation

Use the following information for questions 1-4. Cornell Enterprises is considering a project with the following cash flow data, assuming an interest rate of 11%.

• Year 0: -$700 (Initial Investment)
• Year 1: $300
• Year 2: $350
• Year 3: $400

1. Calculate the Project’s NPV

To find the Net Present Value (NPV), we input the cash flows and the interest rate into a financial calculator or formula.

Inputs:

• CF0 (Initial Cash Flow): -$700
• C01 (Cash Flow Year 1): $300
• F01 (Frequency Year 1): 1
• C02 (Cash Flow Year 2): $350
• F02 (Frequency Year 2): 1
• C03 (Cash Flow Year 3): $400
• F03 (Frequency Year 3): 1
• I (Interest Rate): 11%

Result: The project's NPV is $146.81.

2. Calculate the Project’s IRR

Using the same cash flow data, we can compute the Internal Rate of Return (IRR).

Result: The project's IRR is 22.12%.

3. Calculate the Project’s Payback Period

The payback period is the time required to recover the initial investment.

Calculation Steps:

• Initial Investment: -$700
• After Year 1: -$700 + $300 = -$400 remaining
• After Year 2: -$400 + $350 = -$50 remaining
• Year 3 Recovery: The remaining $50 is recovered during Year 3. To find the fraction of the year, we calculate: $50 / $400 = 0.125.

Result: The payback period is 2 + 0.125 = 2.13 years.

4. Calculate the Project’s Discounted Payback Period

The discounted payback period considers the time value of money by using discounted cash flows.

Discounted Cash Flows at 11%:

• Year 1: $300 / (1.11)¹ = $270.27
• Year 2: $350 / (1.11)² = $284.07
• Year 3: $400 / (1.11)³ = $292.48

Calculation Steps:

• Initial Investment: -$700
• After Year 1: -$700 + $270.27 = -$429.73 remaining
• After Year 2: -$429.73 + $284.07 = -$145.66 remaining
• Year 3 Recovery: The remaining $145.66 is recovered during Year 3. The fraction of the year is: $145.66 / $292.48 = 0.5.

Result: The discounted payback period is 2 + 0.5 = 2.5 years.

Corporate Actions: Stock Splits & Repurchases

5. Troll Brothers' 2-for-1 Stock Split

You own 100 shares of Troll Brothers' stock, which currently sells for $120 a share. The company is about to declare a 2-for-1 stock split. How many shares will you own after the split?

Solution:

• New Stock Price: $120 * (1 / 2) = $60
• New Number of Shares: 100 * (2 / 1) = 200 shares

6. Mid-State BankCorp's 7-for-2 Stock Split

Mid-State BankCorp recently declared a 7-for-2 stock split. Before the split, the stock sold for $80 per share and had 10 million shares outstanding. What will the stock price be following the split, and how many shares will they now have outstanding?

Solution:

• New Stock Price: $80 * (2 / 7) = $22.86
• New Shares Outstanding: 10 million * (7 / 2) = 35 million shares

7. Beta Industries Stock Repurchase

Beta Industries' stock currently trades at $40 a share with 2,000,000 shares outstanding. They are considering a plan to use available cash to repurchase 15% of its shares. What will be Beta’s stock price following the stock repurchase?

Solution:

1. Calculate Market Value: 2,000,000 shares * $40/share = $80,000,000
2. Calculate Shares to Repurchase: 2,000,000 * 0.15 = 300,000 shares
3. Calculate Remaining Shares: 2,000,000 - 300,000 = 1,700,000 shares
4. Calculate New Stock Price: Since the market value of the firm does not change, the new price is $80,000,000 / 1,700,000 shares = $47.06.

8. Makeover Inc. Stock Repurchase

Makeover Inc. believes that at its current stock price of $20.00, the firm is undervalued. Makeover plans to repurchase 2 million of its 25 million shares outstanding. If management’s assumptions hold, what is the expected per-share market price after the repurchase?

Solution:

1. Calculate Market Value: 25,000,000 shares * $20/share = $500,000,000
2. Calculate Remaining Shares: 25,000,000 - 2,000,000 = 23,000,000 shares
3. Calculate New Stock Price: The market value of the firm remains the same. The new price is $500,000,000 / 23,000,000 shares = $21.74.