Question

The Smiths have bought an investment which will pay them $1,000 per year for five years. Ajax Brokers has just offered to buy the annuity from the Smiths for $4,200. If the Smiths require a rate of return of 7% per year, should they sell?

    A. Yes, because the offer exceeds the present value of $4,100.

    B. Yes, because the offer exceeds the PV of $3,740.

    C. No, because the offer is less than the PV of $4,329.

    D. No, because the IRR for Ajax is less than 5%.

    E. No, because the tax effects are undetermined.

Please show work, Thanks!

Answer 1

A. Yes, because the offer exceeds the present value of $4,100.

present value of annuity = A*[1-(1+r)^(-n)]/r

here,

A = 1000

r =7%

=>0.07.

n = 5.

1000*[1- (1.07)^(-5)]/0.07

=>1000*4.10019714

=>$4,100.

since the present value of all the payments is only $4100, the offer can be accepted since it is for $4,200.