Respuesta :
Answer:
Present Value of annual savings=$274,428
Explanation:
In order to get $72,000 annual savings, Almendarez first has to purchase a machine at a cost of $320,000. This machine will have a salvage value of $51,000 at the end of 7 years. if we are to evaluate if this a worthwile investment, the ideal approach would be to calculate the net present value of the investment, ie take int account all cash-flows (inflows and outflows) from t=0 to t=7.
The question however is just asking for the PV of the annual cost savings only. The annual cost savings are 72 000, every year for seven years and are therefore an annuity.
[tex]PVof An Ordinary Annuity= \frac{PMT[1-(1+i)^{-n} ] }{i}[/tex]
where PMT is the the equal payment cash inflow received at the end of each period and
[tex]\frac{[1-(1+i)^{-n} ] }{i}[/tex] = The present value of an annuity factor for n years at i%
The present value of an annuity factor for 7 years at 18% equals
[tex]\frac{[1-(1+0.18)^{-7} ] }{0.18}=3.8115[/tex]
Therefore: Present value of annual cost savings given an 18% return on investments equals [tex] 72000*3.8115=274428[/tex]
The present value of the annual cost savings is $274,430.
What is the present value of the annual cost savings?
The first step is to determine the future value of the annuity.
Future value = amount x annuity value
Annuity factor = {[(1+r)^n] - 1} / r
Where:
- r = discount rate
- n = number of years
Annuity factor = [{1.18^7) - 1} / 0.18 = 12.141522
Future value = 12.141522 x $72,000 = $874,189,56
Now determine the present value = $874,189,56 / (1.18^7) = $274,430
To learn more about present value, please check: https://brainly.com/question/26537392
