Suppose the opportunity cost of capital is 10 percent and you have just won a $1 million lottery that entitles you to $100,000 at the end of each of the next ten years. Alternatively, you can accept an immediate cash payment of $600,000. Ignoring the tax implications, which option is better and by how much?

It is more convenient to accept the first offer. It has a higher present value than accepting $600,000 now. Exactly $14,456.712

Explanation:

Giving the following information:

Discount rate = 10%

Offer:

Cash flow = $100,000

Years = 10

Or:

You can accept an immediate cash payment of $600,000.

First, we need to calculate the present value of the first offer. We will determine the final value, and then, the present value.

FV = {A*[ (1+i) ^n-1]}/i

A = annual cash flow

FV = {100,000*[ (1.10^10) - 1]} / 0.10

FV = 1,593,742.46

Now, the present value:

PV = FV / (1+i) ^n

PV = 1,593,742.56 / (1.10^10)

PV = $614,456.712

It is more convenient to accept the first offer. It has a higher present value than accepting $600,000 now. Exactly $14,456.712