Question

A new computer system will require an initial outlay of $21,500, but it will increase the firm’s cash flows by $4,600 a year for each of the next 8 years.

a. Calculate the NPV and decide if the system is worth installing if the required rate of return is 9%. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)

b. Calculate the NPV and decide if the system is worth installing if the required rate of return is 14%. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places

c. How high can the discount rate be before you would reject the project? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

Solution

a. NPV=Present value of future cashflows-Initial investment

Present value of a cashflow=Cashflow/(1+r)^n
where

r-rate of discounting=9%

n=period of cashflow

Calculattionb for total PV of cashflows given below

Excel formula

Thus NPV=25460.1679-21500

=3960.168

Thus NPV=$3960.17

Since NPV>0 THE SYSTEM IS WORTH INSTALLING

b

NPV=Present value of future cashflows-Initial investment

Present value of a cashflow=Cashflow/(1+r)^n
where

r-rate of discounting=14%

n=period of cashflow

Calculattionb for total PV of cashflows given below

Excel formula

Thus NPV=21338.7739-21500

=-161.2261

Thus NPV= -$161.23

Since NPV<0 THE SYSTEM IS NOT WORTH INSTALLING

c To find How high the discount rate can be before rejecting the project, we must find the IRR

IRR is the rate at which NPV is zero ,thus at any rate higher than IRR the NPV will become negative ,thus making the project unfeasible

Calculation of IRR given below

Excel formula

Thus IRR=13.78%

Therefore the Discount rate cannot be more than 13.78% before the project is rejected

If you are satisfied with the answer,please give a thumbs up