(present value) Suppose an entrepreneur considers to invest in a project. It needs a cash

investment $I at year t = 0. If she/he invests, the project will generate an annual cash flow $x

from year t = 1 to year t = T. The annual interest rate is r (that is, if she/he deposits cash I in a bank, she/he will have I (1 + r) one year after).

(a) What is the present discounted value of the annual cash

ow at year t = 0?

(b) Suppose I = 0; x = ; T = 10; and r = 5%: If you are the entrepreneur, will you

invest in the project? Why?

## Discounted Sum, Present Value?

March 2nd, 2014 admin

a) What is the present discounted value of the annual cash

ow at year t = 0?

Answer: casflow and its present value will be negative: present value will be – $1 ( if spent in the beginning of the year).

(b) Suppose I = $100; x = $12; T = 10; and r = 5%: If you are the entrepreneur, will you

invest in the project? Why?

Answer: I will not invest. Asume that I borrowed $100 from the bank for 10 years at the given r=5%. So from each years annual cash flows I will be able to make the interest payment. After paying interest, I will be left with $7 each year and therefore in 10 years I will have 70 dollars. If I had put this surplus cash in the ban I would have earned interest of 5% on my outstanding deposit balanecs. My average deposit balance would have been $35 for 10 years.Iwould have earned 5% for 10 years, ie. 50% of $35 or $17.5. This together with my final deposit balance of $70 will not equal to $100 to repat my loan to the bank. So, why should I invest. I did nt calculate the present vale of $12 each year for 10 years at a discount rate of 5% by the usual method. That would have shown that the prsent value of $12 each year for 10 years would have been less than $100, the cost of the project. I just made a shortcut believing I am right].