A new product has two major potential markets. The product will succeed in both

Question

A new product has two major potential markets. The product will succeed in both or fail in both, with equal probability. The markets are otherwise independent. You may enter the markets sequentially or simultaneously either now, one year from now, or two years from now. Later entry is not feasible. Market A requires an initial investment of $100 regardless of when it is entered. If the product is successful, market A will have a present value of $150 one year after entry. If the product fails Market A will be worth $90 one year after entry. Market B requires an initial investment of $55 regardless of when it is entered. One year after entry, B will have a present value of $130 or $20 for success and failure, respectively. For simplicity, perform all discounting in the problem at 5%.

c. Can you state a general capital budgeting rule for selecting the optial strategy in this and similar problems?

d. Suppose there are three potential markets, A, B, C, where A and B are as above and C requres an investment of $30 regardless of when entered, and promises a return of $50 or $30 one year later. Does the decision rule you formulated in part (c.) aboev produce the optimal decision for this revised problem? Why or why not?

Explanation / Answer

C) Let us take market A first.

Initial Investment = $100

Present Value after 1 year if successful (PVs)= $150

Present Value after 1 year if it fails(PVf)= $90

Probability of failure, P(f) = Probability of succes, P(s) = 0.5

So, expected present value = P(s) * PVs + P(f) * PVf = 0.5 * 150 + 0.5 * 90 = 75 + 45 = $120

NPV of market A = Present Value after year 1 / (1 + 5%) - Inital Investment

                           = 120/1.05 - 100 = 114.29 - 100 = $14.29

Thus, market A should be entered since it has a positive NPV. However, it can only be enter maximum till 2 years from now. Beyond that, it is not feasible.

Thus, for this a general capital budgeting rule is

1) Multilpy the present value of success and failure with their respective probabilities.

2) Discount them to year 0.

3) Subtract Initial investment from it to get the net present value.

4) If the net present value is positive, enter the market.

Similarly for market B

Initial Investment = $55

Present Value after 1 year if successful (PVs)= $130

Present Value after 1 year if it fails(PVf)= $20

Probability of failure, P(f) = Probability of succes, P(s) = 0.5

So, expected present value = P(s) * PVs + P(f) * PVf = 0.5 * 130 + 0.5 * 20 = 65 + 10 = $75

NPV of market A = Present Value after year 1 / (1 + 5%) - Inital Investment

                           = 75/1.05 - 55 = 71.43 - 55 = $16.43

Thus, both the markets A and B should be entered as both have positive NPV. However, since later entry is not feasible, market A and market B can only be entered today 1 year from now or 2 years from now.

d) Similarly, we can apply this strategy to C (Assuming it can also be entered simultaneously or sequentially)

Initial Investment = $30

Present Value after 1 year if successful (PVs)= $50

Present Value after 1 year if it fails(PVf)= $30

Probability of failure, P(f) = Probability of succes, P(s) = 0.5

So, expected present value = P(s) * PVs + P(f) * PVf = 0.5 * 50 + 0.5 * 30 = 25 + 15 = $40

NPV of market A = Present Value after year 1 / (1 + 5%) - Inital Investment

                           = 40/1.05 - 30 = 38.10 - 30 = $8.10

Again, since the NPV is positive, market C should be entered.

Thus, decision rule you formulated in part (c.) above produces the optimal decision for the problem as NPV is positive.

Since, all the the markets can be entered simultaneously, all the markets shoud be entered as they all have positive NPVs.

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