Your firm is considering an expansion into a new investment project. The investm
ID: 2779031 • Letter: Y
Question
Your firm is considering an expansion into a new investment project. The investment would cost $1,000K and there are two states of the world that will determine the values of your existing assets and new investment project today. As the manager, assume your objective is to maximize the value to current shareholders.
The following table provides you with financial information for your firm in each state of the world (all values are in thousands of $):
State G State B
Probability of State 50% 50%
Value of Existing Assets 8,000 4,000
Cost of New Investment 1,000 1,000
Value of New Investment 2,500 1,500
NPV of New Investment 1,500 500
Value with Investment (no frictions) 10,500 5,500
The manager announces that he will invest in the new project. The public does not know the true state of the world, but knows that the manager knows the true state of the world. Suppose first that the manager will raise the $1,000K by issuing equity.
a) What percentage of the firm will these new shareholders demand in exchange for $1,000K?
b) What is the APV of the new investment project (NPV of the new investment plus the NPV of financing) if the manager knows that the true state of the world is State G?
c) What is the APV of the new investment project (NPV of the new investment plus the NPV of financing) if the manager knows that the true state of the world is State B?
Suppose that the manager could also raise the $1,000K from bondholders in the form of perpetual parvalued debt. Assume that these bondholders know nothing about the firm and that the bonds are fairly priced. Assume a tax rate of 20 percent for determining the tax shield benefit from issuing this debt. There are no bankruptcy costs.
d) What is the APV of the new investment project if the manager raises the $1,000K via debt markets and knows that the true state of the world is State G? What is the APV in State B?
e) Will the manager issue debt or equity to finance the project in State G? What about State B?
f) Investors can now infer the true state of the world based on the manager’s decision to invest and whether he issues debt or equity to pay for the new project. Given this, what percentage of the firm will these new shareholders demand in exchange for $1,000K if the manager announces he will pay for this new project by issuing equity?
Explanation / Answer
a)Value of New Investment after considering both the states=Probability of State G*Value of New Investment in state G + Probability of State B*Value of New Investment in state B
Value of New Investment after considering both the states=.50*2500 + .50*1500=1250+750=2000
Value of Existing Assets after considering both the states=Probability of State G*Value of Existing Assets in state G + Probability of State B*Value of Existing Assets in state B
Value of Existing Assets after considering both the states.50*8,000+ .50*4000=4000+2000=6000
Total Value of firms assets=Value of Existing Assets+Value of New Investment=2000+6000=8000
percentage of the firm will these new shareholders demand in exchange for $1,000 = Value of New Investment/Total Value of firms assets= 2000/8000= =.25=25%
b) if the manager knows that the true state of the world is State G,
APV of the new investment project =NPV of the new investment in state G + the NPV of financing=1,500+(0)=1500
There are no benefits of financing,thus for equity issue NPV of financing=0.
c) if the manager knows that the true state of the world is State B,
APV of the new investment project =NPV of the new investment in state B + the NPV of financing=500+(0)=500
d) After tax cost of Debt=Cost of New Investment=1000*(1-taxRate)=1000*.80=800, Thus tax shield/benefit provided is 200 is the NPV of financing.What is the cost of debt % is info i think is missing.
If the true state of the world is State G,
APV of the new investment project =NPV of the new investment in state G + the NPV of financing =1,500+200=1700
If the true state of the world is State B,
APV of the new investment project =NPV of the new investment in state B + the NPV of financing =500+(200)=700
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