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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