Question

An investment offers $7,952 per year for 24 years, with the first payment occurring 1 year from now. If the required return is 13 percent, what is the value of the investment?

An investment offers $3,751 per year for 18 years, with the first payment occurring 6 years from now. If the required return is 9 percent, what is the value of the investment? (HINT: Remember that when you calculate the PV of the annuity, the claculator gives you the present value of the annuity 1 period before the annuity starts. So if the annuity starts in year 7, that calculator will to give you the persent value of annuity in year 6. Now you have to bring this number to period 0 by inputting: N=6 (1 period before the annuity starts, in your case it would be a different number depending when your annuity starts) R=9 FV=Present value of annuity you found in step 1. And you solve for PV)

Answer 1

a.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=7,952[1-(1.13)^-24]/0.13

=7,952*7.28288303

=$57913.49(Approx)

b.Present value=Cash flows*Present value of discounting factor(rate%,time period)

=3,751/1.09^6+3,751/1.09^7+3,751/1.09^8+3,751/1.09^9+3,751/1.09^10+3,751/1.09^11+3,751/1.09^12+3,751/1.09^13+3,751/1.09^14+3,751/1.09^15+3,751/1.09^16+3,751/1.09^17+3,751/1.09^18+3,751/1.09^19+3,751/1.09^20+3,751/1.09^21+3,751/1.09^22+3,751/1.09^23

=$21345.27(Approx)