Question

urgent

Firm Y’s corporate jet is not fully utilized. You estimate that its use by other officers would increase direct operating costs by only $20,000 a year and would save $90,000 a year in airline bills. However, the increase in usage of the jet will make the firm to replace the jet at the end of three years rather than four. A new jet (at the current low rate of use) has a life of six years, and the equivalent annual cost (EAC) of $240,000. Assume the tax rate is zero and the cost of capital is 8%.

Calculate the NPV of allowing other officers to use the jet.

Answer 1

Solution:

Calculation of Present value / discounted cash inflows :

As per the information given in the question

Use of Firm Y’s corporate jet by other officers would increase direct operating costs by only $ 20,000 a year and would save $ 90,000 a year in airline bills.

This implies the net annual savings shall be equal to

= Savings in airline bills – Increase in direct operating costs

= $ 90,000 - $ 20,000

= $ 70,000

Thus net annual savings = $ 70,000

These savings will be generated for a period of 3 years

Thus the Present Value of the savings for 3 years discounted at the rate of 8 % is

= $ 70,000 * PVIFA ( 8 % , 3 )

= $ 70,000 * [ ( ( 1 / ( 1 + 0.08 ) 1 ) + ( 1 / ( 1 + 0.08 ) 2 ) + ( 1 / ( 1 + 0.08 ) 3) ]

= $ 70,000 * [ ( ( 1 / ( 1.08 ) 1 ) + ( 1 / ( 1.08 ) 2 ) + ( 1 / ( 1.08 ) 3) ]

= $ 70,000 * [ ( 1/1.08 ) + ( 1 / 1.166400) + ( 1 /1.259712)

= $ 70,000 * ( 0.925926 + 0.857339 +0.793832 )

= $ 70,000 * 2.577097

= $ 180,396.790000

Thus the present value of cash inflows for 3 years = $ 180,396.7900

Calculation of Present value / discounted cash out flows :

As per the information given in the question the Corporate jet of Firm Y will have to be replaced with a new jet. This would entail a cash outflow of $ 240,000 in year 4 i.e., yearly EAC on purchase of the new jet.

Thus discounted cash outflow in Year 4 = Cash outflow in Year 4 * PVF ( 8 %, 4)

= Cash outflow in Year 4 * ( 1 / ( 1 + r ) 4 )

We know that Cash outflow in Year 4 = $ 240,000 ; r = 8 % = 0.08

Applying the above information we have discounted cash outflow in Year 4 as

= $ 240,000 * ( 1 / ( 1 + 0.08 ) 4 )

= $ 240,000 * ( 1 / ( 1.08 ) 4 )

= $ 240,000 * ( 1 / 1.360489 )

= $ 240,000 * 0.735030

= $ 176,407.2000

Thus the present value cash outflow in Year 4 = $ 176,407.2000

Calculation of the NPV of allowing other officers to use the jet :

The NPV of allowing other officers to use the jet is

= Present value of cash inflows from Year 1 to Year 3 - Present value cash outflow in Year 4

= $ 180,396.7900 - $ 176,407.2000

= $ 3,989.5900

= $ 3,989.60 ( when rounded off two decimal places )

= $ 3,990 ( When rounded off to the nearest dollar )

Thus the NPV of allowing other officers to use the jet = $ 3,990

Note : The value of ( 1.08 ) 2   has been calculated using the excel function =POWER(Number,Power). Thus =POWER(1.08,2) = 1.166400

PV factors for Year 1, 3 and 4 can be calculated in a similar manner.