Question

The aged but cenrally located golf course you manage does not have a in-ground automated water sprinkling system. Instead, to properly water the course, sprinklers and hoses must be repeatedly set, moved, and put away by some of the grounds crew a tedious and laborious task. If over the next 12 years, you project annual savings of about $40,000 from having an automated system, what is the maximum price you would be willing to pay today for an installed, automated golf course sprinkler system? (Assume a interest rate of 6% and you may ignore income taxes)

VARIABLES MUST BE SHOWN

A. Redo your calculation using a 10-year time period and $48,000 in annual savings.

B. Redo your inital calculation one more time using $50,000 in annual savings for the first six years and $30,000 in annual savings for the next six years.

Answer 1

The Maximum price that will be paid is present value of all the future saving

PMT = $40000

N=12 Years

Rate = 6%

PV= PMT(((1-(1+r)^-n)/r)

=40000*(((1-(1.06^-12)/0.06)

=$335353.76

A.  

PMT = $48000

N=10 Years

Rate = 6%

PV= PMT(((1-(1+r)^-n)/r)

=48000*(((1-(1.06^-10)/0.06)

=$353284.18

B. We will calculate two seperate present value then add them

PMT = $0000

N=6 Years

Rate = 6%

PV= PMT(((1-(1+r)^-n)/r)

=50000*(((1-(1.06^-6)/0.06)

=$245866.22

for next 6 years:-

PMT = $30000

N=6 Years

Rate = 6%

PV= PMT(((1-(1+r)^-n)/r)/(1+r)^n

=30000*(((1-(1.06^-6)/0.06)*(1.06^6)

=$103995.59

Total= $103995.59+$245866.22= $349861.81