Question

A project needs an initial outlay of $3000 for equipment and will net a cash flow of $250 for the next 15 years. At the end of the 15th year, there is a Salvage Value of $1000 for the equipment. What is the NPV of the project if the cost of capital is 15% p.a. effective (to the nearest dollar)?

Select one:

a. -$945

b. -$1415

c. $2250

d. $1585

Answer 1

Net Present value

= Present value of inflows – Present value of outflows

Inflows are yearly cash inflow of $250 each for next 15 years and terminal cash inflow of salvage value of $1,000

The stream of cash inflows of $250 each for 15 years is an annuity and we have to calculate present value of annuity for 15 years

Annuity factor

= [ 1 – ( 1 + r ) ^ - n] / r

Where,

r = Rate of interest = 15% or 0.15

n = Time period = 15 years

So, Annuity factor

= [ 1 – ( 1.15 ^ -15)] / 0.15

= [ 1 - 0.122894] / 0.15

= 5.847370

So, Present value of $250 to be received each year for 15 years

= Cash flow each year x Annuity factor

= $250 x 5.847370

= $1,461.84

Present value factor

= 1 / ( 1 + r) ^ n

So, present value factor for 15^th year cash inflow of salvage value

= 1 / (1.15^15)

= 1 / 8.137061

= 0.122894

So, present value of salvage value

= Salvage value x Present value factor

= $1,000 x 0.122894

= $122.89

So, Present value of inflows

= $1,461.84 + $122.89

= $1,584.73

So, Net Present value

= $1,584.73 - $3,000

= -$1,415.26 or -$-1,415

So, as per above calculations, option b is the correct option