Question

The president’s executive jet is not fully utilized. You judge that its use by other officers would increase direct operating costs by only $26,000 a year and would save $100,000 a year in airline bills. On the other hand, you believe that with the increased use the company will need to replace the jet at the end of three years rather than four. A new jet costs $1.16 million and (at its current low rate of use) has a life of six years. Assume that the company does not pay taxes. All cash flows are forecasted in real terms. The real opportunity cost of capital is 9%.

a. Calculate the equivalent annual cost of a new jet. (Do not round intermediate calculations. Enter your answer as a negative value rounded to 2 decimal places.)

   

Equivalent annual cost            $

b. Calculate the present value of the additional cost of replacing the jet one year earlier than under its current usage.(Do not round intermediate calculations. Enter your answer as a negative value rounded to 2 decimal places.)

     

Present value            $

c. Calculate the present value of the savings. (Do not round intermediate calculations. Enter your answer as a positive value rounded to 2 decimal places.)

    

Present value            $

d. Should you try to persuade the president to allow other officers to use the plane?

Answer 1

Given:

Purchase price of new jet = $ 1,160,000

Increase in direct Operating costs = $26,000 per year

Savings per year = $100,000

Life term = 6 years

Discount rate = 9%

Solution a:

Equivalent annual cost of new jet can be found using annuity formula for the cost of new jet, considering 6 periods.

Here, Annuity Factor of 6 years and 9 % is =

Upon calculating, we get, Annuity Factor = $ 4.49

Hence, PMT = 1,100,000 / 4.49 = $ 245,211.76

When the jet is relaced at the end of year 3 rather than at the end of year 4, the incremental cost is occured at the end of year 4.

Hence, Equivalent Annual cost of new Jet is given as:

Hence, Equivalent Annual cost of new jet is given as $ 173,714.19

Solution b:

Net present value of additional cost of replacing the jet one year earlier than under its current usage:

If jet is relaced at the end of year 3, rather than at the end of year 4, the Equivalent annual cost is given by:

The Present value of its equivalent annual cost considering 3 years:

Hence, the additional cost is =189,348.47 -  173,714.19 (taken from Solution a) = $ 15,634.28

Present value of the additional cost of replacing the jet one year earlier than under its current usage is $ 15,634.28

Solution c:

Additional Cost per year = $ 26,000

Savings per year = $ 100,000

Net Savings = $ 100,000 - $ 26,000 = $ 74,000

These savings are incurred in Years 1,2 and 3 before the jet is relaced.

Present Value of these savings =

= 67,889.91+ 62,284.32 + 57,141.58

=$ 187,315.81

Hence, Present Value of Savings = $ 187,315.81

Solution d:

Figures taken from above Solutions.

When other officers use the plane, the Net Savings on the plane are $ 187,315.81 and the additional cost of replacing the jet one year earlier is $ 15,634.28. Net Savings account for $ 171,681.53 ($ 187,315.81 - $ 15,634.28). Hence, other officers must be allowed to use the plane.