Question

An investment has an installed cost of $527,630. The cash flows over the four-year life of the investment are projected to be $212,200, $243,800, $203,500, and $167,410, respectively.

a.	If the discount rate is zero, what is the NPV? (Do not round intermediate calculations.)
b.	If the discount rate is infinite, what is the NPV? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations.)
c.	At what discount rate is the NPV just equal to zero? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a). NPV = PV of Cash Inflows - PV of Cash Outflows

= [$212,200/(1.00)] + [$243,800/(1.00)²] + [$203,500/(1.00)³] + [$167,410/(1.00)⁴] - $527,630

= $212,200 + $243,800 + $203,500 + $167,410 - $527,630 = $299,280

b). If the required return is infinite, future cash flows have no value. Even if the cash flow in one year is $1 trillion, at an infinite rate of interest, the value of this cash flow today is zero. So, if the future cash flows have no value today, the NPV of the project is simply the cash flow today, so at an infinite interest rate:

NPV = −$527,630

c). IRR is the discount rate at which NPV is equal to zero, to find the IRR, we need to put the following values in the following values in the financial calculator:

CF0 =-527,630; C01 = 212,200; F01 = 1; C02 = 243,800; F02 = 1; C03 = 203,500; F03 = 1; C04 = 167,410; F04 = 1;

Press IRR, then CPT, which gives 21.76

So, the discount rate at which NPV just equal to zero is 21.76%