How much would you pay to participate in a real estate proje

How much would you pay to participate in a real estate project that pays nothing for the first 10 years and $2,500 for the following 10 years if you can earn 13% return on other investments of similar risk? How much would you pay to participate in a real estate project that pays nothing for the first 10 years and $2,500 for the following 10 years if you can earn 13% return on other investments of similar risk?

Solution

Project will not pay anything from t=0 to t=10 and will pay $2500 from t=11 to t=20.

Hence Present Value is given as-

PV_(t=0) = (PV of annuity of 10 years at t=10) discounted back to 10 years

PV_(t=0) = (PV of annuity of 10 years at t=10) / (1+r)¹⁰ ...(1)

Annuity formula: PMT = [r * PV_annuity]/[1-(1+r)^-n] ...(2)

where PMT is payment, r=rate, n=number of periods, PV=present value of annuity

Rearranging (2) we get, PV_annuity = PMT * [1-(1+r)^-n] / r ...(3)

Thus PV_{annuity(n=10, r=13%, PMT=2500)} = PMT * [1-(1+r)^-n] / r = 2500 * (1 - 1.13^-10)/0.13 = 13565.60869 ...(4)

{Note above result of (4) can also be solved in financial calculator with N=10, PMT=2500, I/Y=13, FV=0 and computing (CPT) PV}

Substituing result of (4) in (1),

PV_(t=0) = (PV of annuity of 10 years at t=10) / (1+r)¹⁰ = 13565.60869  / 1.13¹⁰ = 3996.27 (rounded)

Hence $ 3996.27 should be paid today at t=0 to receive $2500 from t=11 to t=20 when required rate of return = 13%.