Question

What is the net present value of a project that has an initial cash outflow of $7,670 and cash inflows of $1,280 in Year 1, $6,980 in Year 3, and $2,750 in Year 4? The discount rate is 12.5 percent.
a) $249.65
b) $68.20
c) $86.87
d) $270.16
e) $371.02

Answer 1

Answer:

c) $86.87

Explanation:

The computation of the Net present value is shown below

= Present value of all yearly cash inflows after implementation of discount factor - initial investment

The discount factor should be determined by

= 1 ÷ (1 + rate) ^ years

where,  

rate is 12.5%  

Year = 0,1,2,3,4

Discount Factor:

For Year 1 = 1 ÷ 1.125^1 = 0.8889

For Year 2 = 1 ÷ 1.125^2 = 0.7901

For Year 3 = 1 ÷ 1.125^3 = 0.7023

For Year 4 = 1 ÷ 1.125^4 = 0.6243

So, the calculation of a Present value of all yearly cash inflows are shown below

= Year 1 cash inflow × Present Factor of Year 1 + Year 2 cash inflow × Present Factor of Year 2 + Year 3 cash inflow × Present Factor of Year 3 + Year 4 cash inflow × Present Factor of Year 4

= $1,280 × 0.8889 + $0 × 0.7901 + $6,980 × 0.7023 + $2,750 × 0.6243

= $1,137.778 + $0 + $4,902.277 + $1,716.811

= $7,756.87

Therefore, the Net present value equivalent to

= $7,756.87 - $7,670

= $86.87

We take the discount factor's first four digits.