Question

Meals for the Homeless plans to lease some new equipment. The lease calls for payments of $1,000 per year and is based on eight annual payments and a 9% interest rate. As an accommodation to the not-for-profit organization, the bank has agreed to lease payments at the end of each year rather than the beginning, which is more common. What is the present value of the obligation? How much did the bank lose by allowing payments at the end of each year rather than at the beginning?

Answer 1

a) Present value of obligation =Value of Annuity= (C/r) * (1- (1/(1+r)^n))

where C is cash flow per year and r is rate of return, n is time period

= (1000/0.09)* (1- (1/(1+0.09)^8))

Present value of obligation=$5534.82

b) Payment at the starting of the year= Value of annuity due =(1+r )*(C/r) * (1- (1/(1+r)^n))

= 1.09 *(1000/0.09)* (1- (1/(1+0.09)^8))

=$6032.95

Banks loss = $6032.95 -$5534.82 = $498.13

Note: Incase of any doubt, please do comment. I will get back to you. Thanks!!