Question

Julio Company is considering the purchase of a new bubble packaging machine. If the machine will provide $20,000 annual savings for 10 years and can be sold for $50,000 at the end of the period, what is the present value of the machine investment at a 9% interest rate with savings realized at year end?

Answer 1

Present value of the machine is the sum of the present values of the annual savings of $20000 and terminal cash flow (by sale of machine) of $50000 at the end of the period.

Annual savings will be same every year, so it is an annuity. Terminal cash inflow at the end of the period is a one time payment.

Now,

First we will calculate the present value of annual savings:

For calculating the present value, we will use the following formula:

PVA = P * (1 - (1 + r)^-n / r)

where, PVA = Present value of annuity, P is the periodical amount = $20000, r is the rate of interest = 9% and n is the time period = 10

Now, putting these values in the above formula, we get,

PVA = $20000 * (1 - (1 + 9%)^-10 / 9%)

PVA = $20000 * (1 - ( 1+ 0.09)^-10 / 0.09)

PVA = $20000 * (1 - ( 1.09)^-10 / 0.09)

PVA = $20000 * ((1 - 0.42241080689) / 0.09)

PVA = $20000 * (0.5775891931 / 0.09)

PVA = $20000 * 6.41765770116

PVA = $128353.15

Next, we will calculate the present value of terminal cash flow:

For calculating present value, we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value = $50000, PV = Present value, r = rate of interest = 9%, n= time period = 10

now, putting theses values in the above equation, we get,

$50000 = PV * (1 + 9%)¹⁰

$50000 = PV * (1 + 0.09)¹⁰

$50000 = PV * (1.09)¹⁰

$50000 = PV * 2.36736367459

PV = $50000 / 2.36736367459

PV = $21120.54

Now,

Present value of the machine investment = Present value of annual savings+ Present value of terminal cash flow

Present value of the machine investment = $128353.15 + $21120.54 = $149473.69