Question

You are the manager of a local factory that produces plastic bottles for soft drink manufacturers. Your assistant comes to you with exciting news about a new assembly line for the company. He presents the following data to you that he’s researched:

            Estimated life of assembly line:             4 years

            Initial investment cost:                         $800,000

            Estimated salvage value:                       none

            Estimated Cash Flow Analysis

            Year                                        Expected Cash Flow

            1                                              $450,000

            2                                              240,000

            3                                              150,000

            4                                                  60,000

a) If the current interest rate is 3 percent, use net present value analysis to determine whether or not the company should purchase this new machine.

b) Ceteris paribus, what is the relationship between the interest rate and the present value of a given amount of money? What does “present value” even mean?

Answer 1

a)

Present value = (Future value * Present value factor)

Present value factor = 1 / ( 1 + r ) ¹ + 1 / ( 1 + r )² ...........1/ ( 1 + r )ⁿ

Year	Expected cash flow	Present value factor @3%	Present value
1	450000	0.971	436950
2	240000	0.943	226320
3	150000	0.915	137250
4	60000	0.888	53280
Total present value			853800

Net present value = Total present value - Initial investment

= $853800 - $800000  

= $53800

Decision:- Company should purchase the machine as it gives positive net present value.

b)

Interest rate is the required return which an investor wants on its investment. Higher interest rate means investor wants higher return form the investment and vice- versa. If interest rate increases then present value of future benefits will decreases. Since Less amount is required today to gain the given amount in future with higher interest rate. money will grow faster with higher interest rate.

If interest rate is lower then present value is higher . It means due to lower desire return of the investor money will not grow that faster and we need higher present value today to gain the given future value.

Present value :- It shows value of all the future cash flows in today's term. It is calculated by discounting the future cash flows with the desire rate of return of the investors.