Question

You have been offered a unique investment opportunity. If you invest $ 11 comma 300 $11,300 ​today, you will receive $ 565 $565 one year from​ now, $ 1 comma 695 $1,695 two years from​ now, and $ 11 comma 300 $11,300 ten years from now. a. What is the NPV of the opportunity if the cost of capital is 5.6 % 5.6% per​ year? Should you take the​ opportunity? b. What is the NPV of the opportunity if the cost of capital is 1.6 % 1.6% per​ year? Should you take it​ now?

Answer 1

(a)-Net Present Value (NPV) of the opportunity if the cost of capital is 5.60%

Net Present Value = Present Value of annual cash inflows – Initial Investment

= CF1/(1 + r)¹ + CF2/(1 + r)² + CF10/(1 + r)¹⁰ - Initial Investment

= [$565/(1 + 0.056)¹ + $1,695/(1 + 0.056)² + $11,300/(1 + 0.056)¹⁰] - $11,300

= [($565 / 1.056) + ($1,695 / 1.11514) + ($11,300 / 1.72440)] - $11,300

= [$535.04 + $1,519.99 + 6,552.99] - $11,300

= $8,608.02 - $11,300

= -$2,691.98 (Negative NPV)

Decision

“NO”. The Project should not be accepted, since the Net Present Value (NPV) of the opportunity is negative $2,691.98 (Negative NPV)

(b)-Net Present Value (NPV) of the opportunity if the cost of capital is 1.60%

Net Present Value = Present Value of annual cash inflows – Initial Investment

= CF1/(1 + r)¹ + CF2/(1 + r)² + CF10/(1 + r)¹⁰ - Initial Investment

= [$565/(1 + 0.016)¹ + $1,695/(1 + 0.016)² + $11,300/(1 + 0.016)¹⁰] - $11,300

= [($565 / 1.016) + ($1,695 / 1.03226) + ($11,300 / 1.17203)] - $11,300

= [$556.10 + $1,642.03 + 9,641.43] - $11,300

= $11,839.56 - $11,300

= $539.56

Decision

“YES”. The Project should be accepted, since the Net Present Value (NPV) of the opportunity is Positive $539.56