B2b co. is considering the purchase of equipment that would allow the company to add a new product to its line. the equipment is expected to cost $384,000 with a 8-year life and no salvage value. it will be depreciated on a straight-line basis. the company expects to sell 153,600 units of the equipment’s product each year. the expected annual income related to this equipment follows. if at least an 9% return on this investment must be earned, compute the net present value. (pv of $1, fv of $1, pva of $1, and fva of $1) (use appropriate factor(s) from the tables provided.)

sales $ 240,000
costs
materials, labor, and overhead (except depreciation on new equipment) 84,000
depreciation on new equipment 48,000
selling and administrative expenses 24,000
total costs and expenses 156,000

pretax income 84,000
income taxes (20%) 16,800
net income $ 67,200
compute the net present value of this investment.

Net present value=-$127,294.283, since the net present value is negative, this means the investment will be a loss

Explanation:

The net present value is a way of determining the time value of money to assess whether an investment is worthwhile. By converting the future cash flow value to a present value cash flow, and subtracting from the initial investment, one can determine if the profit was profitable or not. A positive Net present value denotes that the investment will be profitable, a net present value of zero means there are no gains or losses and a negative net present value means that the investment will be a loss. We can calculate the NPV as shown below;

Step 1: Determine Net income

Annual net income=$67,200

Step 2: Determine present value of future cash flows

PV=C/(1+r)^n

where;

PV=present value of future cash flow

C=future cash flows

r=annual interest rate

n=number of years

In our case;

PV=unknown

C=$67,200 per year

r=9%=9/100=0.09

n=from 1 to 8 years

Replacing for each year;

Present value of future cash flows={67,200/(1+0.09)^1}+{67,200/(1+0.09)^2}+{67,200/(1+0.09)^3}+{67,200/(1+0.09)^4}+{67,200/(1+0.09)^5}+{67,200/(1+0.09)^6}+ {67,200/(1+0.09)^7}+{67,200/(1+0.09)^8}

Present value of future cash flows=61,651.376+56,560.896+51,890.730+36,760.701+23,891.934+14,245.979+7,793.038+3,911.063=$256,705.717

The present cash flow value=$256,705.717

Step 3: Determine the net present value

Net present value=Present cash flow value-equipment cost

where;

present cash flow value=$256,705.717

equipment cost=$384,000

replacing;

Net present value=256,705.717-384,000=-$127,294.283, since the net present value is negative, this means the investment will be a loss