The Pan American Bottling Co. is considering the purchase of a new machine that would increase the speed of bottling and save money. The net cost of this machine is \(60,000. The annual cash flows have the following projections:

Year	Cashflow
1	\)23,000
2	26,000
3	29,000
4	15,000
5	8,000

a. If the cost of capital is 13 percent, what is the net present value of selecting a new machine?

b. What is the internal rate of return?

c. Should the project be accepted? Why?

Capital budgeting can be defined as the process by which the investors assess the different available investment options. It includes methods such as the payback method, Net present value, and IRR.

$$\begin{gathered} \mathit{A}\mathit{v}\mathit{e}\mathit{r}\mathit{a}\mathit{g}\mathit{e}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{i}\mathit{n}\mathit{f}\mathit{l}\mathit{o}\mathit{w}\mathit{s}\mathbf{=}\frac{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{s}\mathbf{}\mathbf{e}\mathbf{a}\mathbf{c}\mathbf{h}\mathbf{}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}}{\mathbf{N}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{23}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{26}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{29}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{15}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{000}}{\mathbf{5}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{20}\mathbf{,}\mathbf{200} \end{gathered}$$

Calculation of PVIFA:

$$\begin{gathered} \mathit{P}{\mathit{V}}_{\mathbf{I}\mathbf{F}\mathbf{A}}\mathbf{=}\frac{\mathbf{Initial}\mathbf{}\mathbf{investment}}{\mathbf{Average}\mathbf{}\mathbf{cashflow}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{20}\mathbf{,}\mathbf{200}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{97} \end{gathered}$$

For n=5, we will find 2.97 falls, around 20% or 25%.

Calculation of present value under each percent of estimated IRR:

20%:

25%:

The net present value is below the initial investment; the IRR will be around 20% to 25%. Now, we will interpolate:

Calculation of IRR:

$$\begin{gathered} \mathbf{IRR}\mathbf{=}\mathbf{25}\mathbf{\%}\mathbf{+}\frac{\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{440}}{\mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{778}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{25}\mathbf{\%}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{77}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{25}\mathbf{.}\mathbf{77}\mathbf{\%} \end{gathered}$$

The business entity must accept the project because the net present value calculation is positive, and the IRR is higher than the project’s cost of capital.