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. (8 points) 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? (5 points)

Answer 1

Solution

Present Value is the present worth (in terms of present prices) of future value .

If the interest rates increase,the present value of the money decreases.That is the reason,the interest rates are also called discount rates.So,interest rates and present value are inversely proportional to each other.

Estimated life of assembly = 4 years ; Initial investment (Cash Ouflow)=$8,00,000 ; Interest Rate = 3%

No Salvage value=> depreciation cost per year = $8,00,000 / 4 i.e., $2,00,000 per year.

Estimated cash flow in year 1,2,3 and 4 = $450,000 ; 240,000 ;150,000 and $60,000

Subtracting the depreciation cost from the estimated cash flow at the end of each year we get the Net Estimated Cash inflow per year

At the end of Year 1 = $450,000 - $2,00,000 i.e., $250,000

At the end of Year 2 =  $240,000 - $2,00,000 i.e., $40,000

At the end of Year 3 = $150,000 -$2,00,000 i.e., -$50,000

At the end of Year 4 = $60,000 - $2,00,000 i.e., -$1,40,000

Net Present Value is the present value of all the future cash flows i.e.,

NPV = -$8,00,000 + ($2,50,000 / 1.03) + ($40,000 / (1.03^2)) +(-$50,000 / (1.03^3)) +(-1,40,000 / (1.03^4))

= -$8,00,000 +$2,42,718.44 + $37,703.83 - $45,757.08 -$1,24,388.18

= -$6,89,722.99

No,the company should not purchase the new machine as the NET PRESENT VALUE IS NEGATIVE

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