Question

project k has a cost of 62,125, and its expected nect cash inflwos are 14,000 per year for 8 year .

A- The cost of capital is 12 %. What is the project 's npv?

B- what is the project 's IRR?

Answer 1

A)

Project's NPV

$ 7,421.96

Working:

Present Value of annuity of 1

=

(1-(1+i)^-n)/i

where,

=

(1-(1+0.12)^-8)/0.12

i

12%

=

4.96764

n

8

Present Value of annual cash inflows

=

Annual cash inflows x Present value of annuity of 1

=

$       14,000

x

4.96764

=

$ 69,546.96

Present Value of cash inflows

$ 69,546.96

Less Cost of Project

$ 62,125.00

Net Present Value (NPV)

$   7,421.96

B)

Project's IRR

15.63%

Workings:

IRR (Internal rate of return) is the rate at which NPV is zero.

Discount rate and present value of cash inflows have adverse relation.It means if discount rate increases, present value of

cash iflows decreases and vice versa.

At 12%, NPV us positive. So to reduce NPV to zero, we take another higher discount rate.

At 20% Discount rate:

Present Value of annuity of 1

=

(1-(1+i)^-n)/i

where,

=

(1-(1+0.20)^-8)/0.20

i

20%

=

3.79917

n

8

Present Value of annual cash inflows

=

Annual cash inflows x Present value of annuity of 1

=

$       14,000

x

3.79917

=

$ 53,188.35

Present Value of cash inflows

$ 53,188.35

Less Cost of Project

$ 62,125.00

Net Present Value (NPV)

$ -8,936.65

IRR

=

12%+(20%-12%)*(7421.96/(7421.96+8936.656))

=

15.63%