Question

Company has machinery that cost $150,000. It is to be leased for 15 years with rent received at the begining of each year. Compony wants a return of 10%. compute the amount of the annual rent.

Answer 1

Formula for PV of annuity due can be used for computation of cash flow.

PV = P + P x [1-(1+r)^-(n-1)/r]      

PV = $ 150,000

P = Cash flow per period

r = Rate of interest per period = 10 % or 0.1 p.a.

n = Numbers of periods = 15

Putting the values in above formula, we get P as:

$ 150,000 = P + P x [1-(1+0.1)^-(15-1)/0.1]

$ 150,000 = P + P x [1-(1.1)^-(15-1)/0.1]

$ 150,000 = P + P x [1-(1.1)^-14/0.1]

$ 150,000 = P + P x [1 - 0.263331/0.1]

$ 150,000 = P + P x [(1 - 0.263331)/0.1]

$ 150,000 = P + P x (0.736669/0.1)

$ 150,000 = P + P x 7.366687

P x (1+7.366687) = $ 150,000

P x 8.366687 = $ 150,000

P = $ 150,000/8.366687 = $ 17,928.24

Amount of the annual rent should be $ 17,928.24.