Question

Grandpa Joe decides to purchase a trust fund for his grandson Danny. The fund will start making payments 6 months from now, and will make semiannual payments forever. Grandpa Joe would like the payments to be of the form X,2X,X,2X,X,2X,…, but it would cost him 11300 dollars for such a fund. Since he doesn't want to spend that much money, he instead decides to purchase a trust fund where the first 30 payments will be for 45 dollars each, and then the remaining payments will be of the form X,2X,X,2X,X,2X,…. If the interest rate is 6.4 percent convertible semiannually, what is the price that Grandpa Joe pays for this trust fund?

Answer 1

In the first instance Joe pays 11300 for a X,2x,x,2x,x outflow trust. in the new structure Grandpoe joe effectively delays this outlfow by 30 semi-annual periods i.e. 15 years. Hence, the PV of the second half of the new trust (which is paying x,2x,x,2x) will still be 11,300 but after 15 years.

Hence the new trust value will be the same present value of 45 dollars every 6 months for 15 years and 11,300 at the end of 15 years.

Hence NPV = present value of annuity of 45 for 30 periods at 3.2% + preent value of 11,300 @6.4%

NPV = $45 [1-(1+3.2%)^-30]/3.2% + 11,300/(1.064^15)

Value of Trust = 5,315.8