Question

The management of XYZ Company is considering the purchase of a $25,000 machine that would reduce operating
costs by $4,000 per year. At the end of the machine’s 10‐year useful life, it will have a zero salvage value. The
company requires a 14% on all investment projects.

Answer 1

"Answer on question #59001- Economics - Accounting "

The management of XYZ Company is considering the purchase of a $25,000 machine that would reduce operating costs by $4,000 per year.

At the end of the machine's 10-year useful life, it will have a zero salvage value. The company requires a 14% on all investment projects.

Solution

Company's investing is $I = \$25,000$

The interest rate is $r = 14\%$

Company's investing will create additional cash flow \$4,000 per year over the ten years.

Net present value's cash flow is calculated following

$$NPV = -I + \sum_{n=1}^{10} \frac{\text{Cash Flow}}{(1+r)^n}$$

I – initial investment, r – discount rate by investment, n – number of periods the investment will be needed.

$$\begin{array}{l} NPV = -25000 + 4000/(1,14) + 4000/(1,14)^2 + 4000/(1,14)^3 + 4000/(1,14)^4 \\ \quad + 4000/(1,14)^5 + 4000/(1,14)^6 + 4000/(1,14)^7 + 4000/(1,14)^8 \\ \quad + 4000/(1,14)^9 + 4000/(1,14)^{10} = -25000 + 20864 = -4136 \\ \end{array}$$

Suppose the equivalent annual cost is $x$, then

$$\begin{array}{l} x/(1,14) + x/(1,14)^2 + x/(1,14)^3 + x/(1,14)^4 + x/(1,14)^5 + x/(1,14)^6 + x/(1,14)^7 \\ \quad + x/(1,14)^8 + x/(1,14)^9 + x/(1,14)^{10} = -4136 \\ \end{array}$$ $$x = -793$$

Answer

Net present value is negative \$4136, annual equivalent cost is \$793.

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