The Hudson Corporation makes an investment of \(24,000 that provides the following cash flow:

Year	Cash flow
1	\)13,000
2	13,000
3	4,000

a. What is the net present value at an 8 percent discount rate?

b. What is the internal rate of return?

c. In this problem, would you make the same decision under both parts a and b?

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.

$\begin{array}{c}\mathbf{Average}\mathbf{}\mathbf{of}\mathbf{}\mathbf{inflows}\mathbf{=}\frac{\mathbf{Total}\mathbf{}\mathbf{of}\mathbf{}\mathbf{cash}\mathbf{}\mathbf{flows}\mathbf{}\mathbf{each}\mathbf{}\mathbf{year}}{\mathbf{Number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{years}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{13}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{13}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{000}}{\mathbf{3}}\\ \mathbf{=}\mathbf{\$}\mathbf{10}\mathbf{,}\mathbf{000}\end{array}$

Calculation of PVIFA:

$\begin{array}{c}{\mathbf{PV}}_{\mathbf{IFA}}\mathbf{=}\frac{\mathbf{Initial}\mathbf{}\mathbf{investment}}{\mathbf{Average}\mathbf{}\mathbf{cash}\mathbf{}\mathbf{flow}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{24}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{10}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{2}\mathbf{.}\mathbf{4}\end{array}$

For n=3, we will find 2.4 falls, around 14% or 15%.

Calculation of present value under each percent of estimated IRR:

14%:

15%:

The net present value is below the initial investment; the IRR will be between 14% and 15%. Now, we will interpolate:

Calculation of IRR:

$\begin{array}{c}\mathbf{IRR}\mathbf{=}\mathbf{14}\mathbf{\%}\mathbf{+}\frac{\mathbf{\$}\mathbf{98}}{\mathbf{\$}\mathbf{345}}\\ \mathbf{=}\mathbf{14}\mathbf{\%}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{28}\mathbf{\%}\\ \mathbf{=}\mathbf{14}\mathbf{.}\mathbf{28}\mathbf{\%}\end{array}$

For parts (a) and (b), the business entity must accept the project because the net present value is positive and the internal rate of return is higher than the cost of capital.