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1. You possess a small manufacturing facility making

\$ 2

million annually. D...

May 7, 2024

a Solution

Expected Revenue Calculation: If the government contract is not awarded, the revenue decreases by 25%. The new revenue is calculated as

2 million \times (1 - 0.25)

Operating Profit Calculation: Subtract the additional costs from the new revenue to find the operating profit. Operating profit = New Revenue - Additional Costs

Present Value of Perpetuity Formula: The value of the plant is the present value of the perpetuity of the operating profit. Use the formula

PV = \frac{C}{r}

, where

C

is the operating profit and

r

is the cost of capital

a Answer

The value of the plant if the government contract is not awarded is $2 million.

Key Concept

Present Value of Perpetuity

Explanation

The value of the plant is calculated as the present value of the expected stream of operating profits, which is a perpetuity since the plant can operate indefinitely.

b Solution

Calculation of Expected Revenue with Option: The expected revenue is the average of the two scenarios, increase by 20% and decrease by 25%. Expected Revenue = \frac{($2 million \times 1.2) + ($2 million \times 0.75)}{2}

Calculation of Expected Operating Profit: Expected Operating Profit = Expected Revenue - Additional Costs

Calculation of Plant Value with Option to Sell: The value of the plant is the higher of the present value of the expected operating profit perpetuity and the option to sell at $5 million

b Answer

The value of the plant, given the embedded option to sell, is $5 million.

Key Concept

Explanation

c Solution

Calculation of Operating Profit in Worst Case: If the plant operates at a loss, the option to abandon production can be exercised. The worst-case operating profit is when revenue decreases by 25%

Value of Abandonment Option: The value of the option to abandon is the present value of avoiding future losses. If operating at a loss, the value is $0 since the plant can be shut down at no cost

c Answer

The value of the option to abandon production is $0.

Key Concept

Explanation

a Solution

Calculation of Combined EPS: To find the EPS following the merger without any premium, we combine the earnings of both companies and divide by the new total number of shares

a Answer

New EPS = \frac{Alpha's Earnings + Gamma's Earnings}{Total Shares Post-Merger} = \frac{(2 \times 10,000,000) + (1.25 \times 4,000,000)}{10,000,000 + 4,000,000} = \frac{20,000,000 + 5,000,000}{14,000,000} = \frac{25,000,000}{14,000,000} = \$1.7857 (rounded to four decimal places)

Key Concept

Earnings Per Share (EPS) Post-Merger

Explanation

The EPS after the merger is calculated by dividing the total earnings of the combined company by the total number of shares outstanding after the merger.

b Solution

Calculation of Exchange Ratio and Per-Share Price Post-Merger: To calculate the per-share price of the combined company post-merger with a 20% premium, we first determine the exchange ratio and then the new share price

b Answer

Exchange Ratio = \frac{Gamma's Share Price \times (1 + Premium)}{Alpha's Share Price} = \frac{15 \times (1 + 0.20)}{20} = \frac{15 \times 1.20}{20} = 0.9 New Share Price = \frac{Total Earnings}{Total Shares Post-Merger} = \frac{Alpha's Earnings + Gamma's Earnings}{Alpha's Shares + (Gamma's Shares \times Exchange Ratio)} = \frac{20,000,000 + 5,000,000}{10,000,000 + (4,000,000 \times 0.9)} = \frac{25,000,000}{13,600,000} = \$1.8382 (rounded to four decimal places)

Key Concept

Per-Share Price Post-Merger with Premium

Explanation

The per-share price post-merger is calculated by dividing the total earnings by the total number of shares after considering the exchange ratio, which includes the premium paid for the acquisition.

c Solution

Calculation of Exact Premium Paid: To determine the exact premium Alpha pays for the transaction, we compare the offer price per share to Gamma's current share price

c Answer

Offer Price Per Share = Alpha's Share Price \times Exchange Ratio = 20 \times 0.9 = \$18 Premium Paid = Offer Price Per Share - Gamma's Current Share Price = 18 - 15 = \$3 Percentage Premium = \frac{Premium Paid}{Gamma's Current Share Price} \times 100\% = \frac{3}{15} \times 100\% = 20\%

Key Concept

Exact Premium Paid for Acquisition

Explanation

The exact premium paid is the difference between the offer price per share and the current share price of the company being acquired, expressed as a percentage of the current share price.