Question

What is the value of a building that is expected to generate fixed annual cash flows of 112,900 dollars every year for a certain amount of time if the first annual cash flow is expected in 5 years, the last annual cash flow is expected in 9 years, and the appropriate discount rate is 15.89 percent?

Answer 1

First we compute the present value of those cash flows at the beginning of year 5. The annual cash flows are a form of annuity. Present value of an annuity can be computed as -

where, A = annual cash flows, r = rate of interest, n = no. of years

This is amount is at the beginning of fifth year. Beginning because when computing the above value, we assume that cash flows are received at year end. So, the present value is at the beginning of the period, which is the fifth year. Beginning of fifth year can also be said as end of 4th year.

Now, we compute the present value of this single amount to present day.

Present value of a single amount is computed as -

PV = Amount / (1 + r)ⁿ

or, Value of building = $370,618.312094 / (1 + 0.1589)⁴ = $205,467.445882 or $205,467.45