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1. You are choosing between two investments. The first requires an initial inves

ID: 2657353 • Letter: 1

Question

1. You are choosing between two investments. The first requires an initial investment of $1000, and pays dividends of $250 starting at the end of the first year and continuing forever. The second requires an initial investment of $1500. It has an uncertain payout. With 25% probability it will pay $1500 every year forever. With 75% probability it will pay $100 every year forever. Assume that you are risk neutral and have a discount rate of 10%. Assume that you have to choose one of the investments now.
a. (10 points) Which investment should you make?

b. (10 points) What is the Expected Value of Perfect information on the payoff of the second investment?

Explanation / Answer

a. Investment 1:

Initial Investment = $1000

Dividends = $250 starting at the end of first year.

R = Discount Rate = 10%

This Perpetuity and PV = D1 / R

PV of Investment 1 = (250 / 0.1) = 2500

Net Present Value (NPV) = 2500 – 1000 = 1500

Investment 2:

Initial Investment = $1500

Payout 1, Probability 25%for $1500 forever and Probability 75%for $100 forever

Expected Value = 0.25 * (PV of $1500 payout) + 0.75 * (PV of $100 Payout)

= 0.25 * (1500 / 0.1) + 0.75 * (100 / 0.1)

= 3750 +750

= $4500

NPV of Investment 2 = 4500 – 1500

= $3000

Investment 2 is preferred because of higher Net Present Value.

b. EVPI = EVwI - EV

EVPI = Expected value of Perfect Information

EVwI = Expected value with Perfect Information

EV= Expected value = $4500 of investment 2

EVwI =

In investment 2 best payoffs will be $1500 with probability of 100%.

PV= 1500 / 0.1 = 15,000

Expected value Perfect Information = 15,000 – 4500

= $ 10,500