Question

Consider a firm financed with an initial investment of $100 million in February 2006. In exactly one year it must decide whether to go ahead with a project that requires an additional $100 million investment. The present values (as of February 2007) of the firm's payoffs from taking or not taking the additional investment in the three future states of the economy are given as follows This problem is from the book by Grinblatt and Titman, Financial Markets and Corporate Strategy, p. 641. Medium Good Bad Value with investment S125 $250 $50 Value without investment $50 $50 What is the NPV of the project in each of the states as of February 2007? a) b) When financing the investment in February 2006, the original entrepreneurs believe that the manager they hire will want to fund the new investment in February 2007 even if it has a negative NPV. Why might they be concerned about this? c) Is there a way that the initial entrepreneurs can finance the original investment in February 2006 to ensure that the firm can raise sufficient funds only when the additional investment has a positive NPV at the end of year 1?

Answer 1

Answer a)

NPV = Present value of cash inflows ‐ Present value of cash outflow

When an investment is made in feb 2007

Good state

PV of cash inflow = $250 and initial investment =$100

NPV = $250‐$100 = $150

When no investment is made

NPV = $50

Net gain in NPV=$150 ‐$50 = $100

MEDIUM STATE

In the same way at medium state when investment is made NPV = $175‐$100 =$75

When no investment is made NPV = $50

Net gain in NPV = $75‐$50 = $25

BAD STATE

In the bad state when investment is made NPV = $125‐$100=$25

When investment is not made NPV = $50

Net Loss in NPV = $25‐$50 = ‐$25

Summary

In the good state NET NPV = $100 million

In the medium state Net NPV = $25 million

In the bad state Net NPV = ‐$25 million

Answer b)

Since there can be three NPV in the future state of economy it means there will be three multiple investment choices in the hand of the chosen manager. Among such three options if the highest NPV come positive and other two NPV becomes positive and negative then for one negative NPV i.e. ‐$25 million the manager will not bother for further investment as the highest NPV of the multiple investment choices is positive. He will undertake further investment option.

Answer c)

Assuming that there exists no unforeseen costs in the future projected cash flows. There are three factors to be assessed in the NPV.

• Investment costs
• discount rate
• projected returns

Investment cost refers investment related costs like fees to the appropriate person during the time of investment or other associated cost for undertaking such investment.

Discount rate generally refers cost of capital also known as opportunity cost of capital that an owner misses out for not investing the amount to other investment. It means for losing such opportunity the owner must earn at least the opportunity cost to justify his investment.

Projected returns mean the series of cash flow to be received in the future for investing in the project.

It is assumed in NPV that any investment is valid when it has positive NPV.

When NPV is positive a project should be accepted otherwise, it should be rejected. Therefore, emphasis to be given upon positive NPV which is comprised of three factors initial investment; discount rate and projected cash flows.

If the entrepreneurs get sure by making an analysis to the projected cash flow that an additional investment will create NPV › 0 they can be ensured that such positive NPV will bring sufficient funds in the future.