Question

5. Suppose that Ed Scahill owns a farm in a small town. In exchange for allowing a road to pass through his farmland, the town has agreed to pay Ed and the future owners of the land $135 per year in perpetuity. Now, however, the town has offered, and he has accepted, a one-time payment of $1,125 in exchange for his giving up the right to receive the annual $135 payment. What implicit interest rate have Ed and the township used in arriving at this settlement?

Answer 1

Answer)

Calculation of Implicit rate of interest

The implicit rate of interest in the given case will the rate at with the present value of annual case inflows (i.e. $ 135) will be equal to the amount of one-time payment proposed to be received in lieu thereof (i.e. $ 1,125). The said rate can be calculated by using the following formula:

Present value of cash inflows in perpetuity = Annual cash inflows/ Implicit rate of interest

$ 1,125 = $ 135/ Implicit rate of interest

Implicit rate of interest = $ 135/ $ 1,125

                                           = 0.12 or 12%

Therefore the implicit rate of interest in the given case is 12% per annum.