You have an investment that in today's dollars returns 15% of your investment in Year 1, 12% in Year 2, 9% in Year 3 and the remainder in Year 4. What is the duration of this investment?

Question

Quizplus · Accepted Answer

To calculate the duration of the investment, we need to take the weighted average of the time it takes to receive each cash flow. The formula for duration is given by:

Duration = (CF1*1 + CF2*2 + CF3*3 + CF4*n) / (CF1 + CF2 + CF3 + CF4)

Where CF is the cash flow in the respective year and n is the number of years for the final cash flow.

Plugging in the given cash flows, we get:

Duration = (0.15*1 + 0.12*2 + 0.09*3 + x*4) / (0.15 + 0.12 + 0.09 + x)

Simplifying the equation, we get:

Duration = (0.54 + 4x) / (0.36 + x)

We know that the sum of the percentages must be 100%, so the remaining cash flow in Year 4 is:

100% - 15% - 12% - 9% = 64%

Therefore,

x = 0.64

Plugging x back into the duration equation, we get:

Duration = (0.54 + 4(0.64)) / (0.36 + 0.64) = 3.22 years

You Have an Investment That in Today's Dollars Returns 15