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An investment of I = \$2, 000 dollars now results in the cash flow Fn = \$50,
n = 0, 1, . . . ....∞
Assume that the inflation-free interest rate is currently i = 2.5%. The
inflation-free interest rate will change at the end of the first year. There is a 0.5 probability that it will increase to 3%, and a 0.5 probability that it will decrease to 2%. It will then remain at this new level.

1. What is the expected net present value of the project if you invest at time zero? Would
you invest in this project if you had to make the decision at time zero?

2. Suppose that you decide to wait a year until the interest rate uncertainty is resolved.
Would you invest if the interest rate goes up? Would you invest if the interest rate goes
down?

3. Find the expected net present value, ENPVw that results from waiting and investing
only if it is to your advantage. Is it better to wait?

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An investment of I = \$2, 000 dollars now results in the cash flow Fn = \$50,
n = 0, 1, . . . ....∞
Assume that the inflation-free interest rate is currently i = 2.5%. The
inflation-free interest rate will change at the end of the first year. There is a 0.5 probability that it will increase to 3%, and a 0.5 probability that it will decrease to 2%. It will then remain at this new level.

Present Worth for Cash Flows which are till infinity is given by:

P = A/i

1. What is the expected net present value of the project if you invest at time zero? Would
you invest in this project if you had to make the decision at time zero?

Expected NPV at time 0: Expected Interest Rate = .5*2 + .5*3 = 2.5%

P = 50/.0025 = \$2000 ( which is exactly equal to our investment). I would still not invest in the project because it is only an expected value . ( what if the interest rate goes up to 3%?).

2. Suppose that you decide to wait a year until the interest rate uncertainty is resolved.
Would you invest if the interest rate goes up? Would you invest if the interest rate goes
down?

If the interest rate goes up , P = 50/.03 = \$1666.67 ( since it 1667<2000 , don't invest)

If the interest rate goes down , P = 50/.02 = \$2500 ( since it 2500>2000 , invest)

3. Find the expected net present value, ENPVw that results from waiting and investing
only if it is to your advantage. Is it better to wait?

ENPV = 50/1.025 +( 2500*.5 +1666.7*.5)
= \$2132.

Note: 50/1.025 is to account for first year when interest rate is 2.5%
If interest rate goes down , NPV is 2500 ( calculated above) , but the chances of it happening is only.5
If interest goes up , NPV is 1667 and chances of it happening is .5. So expected NPV is given by : 50/1.025 +( 2500*.5 +1666.7*.5)

Yes it is advantageous to wait.

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