Question

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An investment offers $7,300 per year for 15 years, with the first payment occurring one year from now. If the required return is 5.15 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever?

Answer 1

A=$7300

r=5.15%

For n=15

PV= A*(1-(1+r)^-n)/r

=7300*(1-(1+5.15%)^-15)/5.15%

=7300*(1-1.0515^-15)/0.0515

=7300*(1-0.4708)/0.0515

=7300*0.5292/0.0515

=$75009.07

For n=40

PV= A*(1-(1+r)^-n)/r

=7300*(1-(1+5.15%)^-40)/5.15%

=7300*(1-1.0515^-40)/0.0515

=7300*(1-0.1342)/0.0515

=7300*0.8758/0.0515

=$122730.46

For n=75

PV= A*(1-(1+r)^-n)/r

=7300*(1-(1+5.15%)^-75)/5.15%

=7300*(1-1.0515^-75)/0.0515

=7300*(1-0.0231)/0.0515

=7300*0.9769/0.0515

=$138467.98

For forever, PV=A/r=7300/5.15%=$141747.57