Question

A project requires a start up cost of $105000 today and 10 annual cost of $3500 starting in one year. Starting at the end of the 11th year, the project returns 20 annual payments of $X. Determine X so that the project yields an annual effective rate of 6% over the 30 years.

PLEASE show by hand and NOT excel!!!

Answer 1

Solution:-

For the project to yield 6%, the present value o cash outflows discounted at 6% will be equal to the present value of cash inflows discounted ast 6%. THus, we calculate both as following:

Present value of cash outflows= (1,05,000*1) + 3,500*[(1/1.06)+(1/1.06)²+(1/1.06)³+...........+(1/1.06)¹⁰] = 1,05,000 + 3,500*7.36 = $130,760

Present value of cash inflows= X*[(1/1.06)¹¹+(1/1.06)¹²+(1/1.06)¹³+.................+(1/1.06)³⁰] = X*6.405

Thus, equating the two we get as follows:

X*6.405 = 130,760

X= $20,415.3