Question

You are considering a project that has been assigned a discount rate of 8 percent. If you start the project today (t=0), you will incur an initial cost of $980 and will receive cash inflows of $475 a year for three years. If you wait one year to start the project, the initial cost will rise to $1,000 (at t=1) and the cash flows will increase to $515 a year for three years (starting from year t=2). Should you wait one year to start the project?

No, because NPV at t=0 is lower by $31.58

No, because NPV at t=0 is lower by $25.42

Yes, because NPV at t=0 is higher by $58.85

Yes, because NPV at t=0 is higher by $37.45

Yes, because NPV at t=0 is higher by $18.66

Answer 1

Option (c) is correct

We will compare the net present value of each project.

Net Present value (NPV) = Present value of cash inflows - Initial investment

First we will check the NPV for starting the project now.

There will be annual cash inflows of $475. Since the annual cash inflows are same, so it is an annuity. We will find the value of present value of ordinary annuity of $1 at 8% interest rate for 3 years.

Present value of cash inflows = $475 * PVIFA (8%, 3 years)

where, PVIFA (8%, 3 years) is the present value of annuity of $1 at 8% for 3 years

The value of PVIFA (8%, 3 years ) from the present value of ordinary annuity table is 2.57710

Now, putting this value in the above equation, we get,

Present value = $475 * 2.57710 = $1224.15

Net Present value = Present value of cash inflows - Initial investment

Initial investment = $980

Net Present value = $1224.15 - $980 = $244.15

Now, we will check the NPV for starting the project one year from now.

Since the annual cash flows will start from t=2, so in calculating the present value of cash flows, we will discount the present value of annuity for one more period with simple present value interest factor of $1 to know the present value at t=0.

Present value of cash inflows = $515 * PVIFA (8%, 3 years) * PVIF (8%,1 year)

where, PVIFA (8%, 3 years) is the present value of annuity of $1 at 8% for 3 years

The value of PVIFA (8%, 3 years ) is 2.57710

and the value of PVIF (8%, 1 year) is $0.926

Now, putting these values in the above equation, we get,

Present value of cash inflows = $515 * 2.57710 * 0.926 = $1229

Also the initial investment will be made after 1 year i.e. t =0, so we will discount the initial investment to 1 year at PVIF(8%, 1 year)

Present value of initial investment = $1000 * 0.926 = $926

Net Present value = Present value of cash inflows - Initial investment

Net Present value = $1229 - $926 = $303

Since the net present value of waiting till year is higher than the present value at t=0, by $58.85 (i.e. $303 - $244.15) so we should wait for 1 year to start the project.