Question

A project that provides annual cash flows of $17,300 for nine years costs $78,000 today.

  

What is the NPV for the project if the required return is 8 percent? (Do not round intermediate calculations. Round the final answer to 2 decimal places.)

  

NPV

$

  

At a required return of 8 percent, should the firm accept this project?

Accept or Reject

  

What is the NPV for the project if the required return is 20 percent? (Do not round intermediate calculations. Negative answer should be indicated by a minus sign. Round final the answer to 2 decimal places.)

  

NPV

$

  

At a required return of 20 percent, should the firm accept this project?

Accept or Reject

  

At what discount rate would you be indifferent between accepting the project and rejecting it? (Do not round intermediate calculations. Round the final answer to 2 decimal places.)

  

Discount rate

%

Answer 1

1)

Present value = Annuity * [ 1 - 1 / ( 1 + R)ⁿ]] / R

Present value = 17,300 * [ 1 - 1 / ( 1 + 0.08)⁹]] / 0.08

Present value = 17,300 * [ 0.499751 / 0.08]

Present value = 17,300 * 6.246888

Present value = 108,071.1609

NPV = present value of cash inflows - present value of cash outflows

NPV = 108,071.1609 - 78,000

NPV =$30,071.16

b)

At required rate of return of 8%, company should accept the project the as it has a positive NPV.

c)

NPV when required rate is 20%:

Present value = Annuity * [ 1 - 1 / ( 1 + R)ⁿ]] / R

Present value = 17,300 * [ 1 - 1 / ( 1 + 0.2)⁹]] / 0.2

Present value = 17,300 * [ 0.806193 / 0.02]

Present value = 17,300 * 4.030967

Present value = 69,735.7205

NPV = present value of cash inflows - present value of cash outflows

NPV = 69,735.7205 - 78,000

NPV = -$8,264.28

d)

At the required rate of 20%, project should not be accepted as it has a negative NPV.

e)

IRR would be the discount rate that the company would be indifferent between accepting and rejecting project

IRR is the discount rate that makes NPV equal to zero.

-78,000 + 17,300 * [ 1 - 1 / ( 1 + R⁹]] / R = 0

Using trial and error method i.e, after trying different values for R, let try 16.62

-78,000 + 17,300 * [ 1 - 1 / ( 1 + 0.1662)⁹] / 0.1662 = 0

0 = 0

Therefore IRR is 16.62%