Question

A perpetuity costs $ 80 (price of perpetuity at ? = 0) and makes annual payments

at the end of the year. The perpetuity pays $1 at the end of year 2, $2 at the end of year 3,

……, and $ ? at the end of year (? + 1). After year (? + 1), the payments remain constant at

$ ?. The nominal interest rate is 10% convertible semiannually. Calculate $ ?.

Answer 1

The nominal interest is:

The present value after increasing annuity is:

Here, I represents the nominal interest and IR represents the interest rate.

The present value after paying perpetuity is:

From equations 1 and 2, the net present value is:

Take log both sides of the equation.