Question

Problem 10-15

Island Airlines Inc. needs to replace a short-haul commuter plane on one of its busier routes. Two aircraft are on the market that satisfy the general requirements of the route. One is more expensive than the other but has better fuel efficiency and load-bearing characteristics, which result in better long-term profitability. The useful life of both planes is expected to be about seven years, after which time both are assumed to have no value. Cash flow projections for the two aircraft follow.

	Low Cost	High Cost
Initial cost	$753,400	$971,000
Cash inflows, years 1 through 7	153,000	159,600

1. Calculate the payback period for each plane and select the best choice. Round your answers to one decimal place.

   Low Cost	years
   High Cost	years

   
   
2. Calculate the IRR for each plane and select the best option. Use the fact that all the inflows can be represented by an annuity. Round your answers to one decimal place.

   Low Cost	%
   High Cost	%

   
   IRR also selects the   cost plane.
   
3. Compare the results of parts (a) and (b). Both should select the same option, but does one method result in a clearer choice than the other based on the relative sizes of the two payback periods versus the relative sizes of the two IRRs?
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
4. Calculate the NPV and PI of each project assuming a cost of capital of 8%. Use annuity methods. Do not round intermediate calculations. Round PVFA values in intermediate calculations to four decimal places. Round NPV to the nearest dollar, round PI to two decimal places.

   	Low Cost	High Cost
   NPV	$	$
   PI

   
   Which plane is selected by NPV?
     cost plane.
   By PI?
     cost plane.
   
5. Calculate the NPV and PI of each project, assuming the following costs of capital: 2%, 4%, 6%, 8%, and 10%. Use annuity methods. Do not round intermediate calculations. Round PVFA values in intermediate calculations to four decimal places. Round NPV to the nearest dollar, round PI to two decimal places. Use a minus sign to indicate a negative NPV.

   		Low Cost	High Cost
   2%	NPV	$	$
   	PI
   4%	NPV	$	$
   	PI
   6%	NPV	$	$
   	PI
   8%	NPV	$	$
   	PI
   10%	NPV	$	$
   	PI

   
   Is the same plane selected by NPV and PI at every level of cost of capital? Investigate the relative attractiveness of the two planes under each method.
   

Answer 1

a. Payback period tells us in how many years firm can retain the money they have invested.

Low cost (payback period): In 4 years company receives 612,000 and the remaining 141,400 (753,400-612,000) in 5th year.

5th year=141,400/153,000=0.924

Low cost (pay back period)=4.924 years

in similar way, High cost project receives cashflow 957,600 in 6 years and the remaining 13,400 in 0.084 years

High cost (pay back period)=6.084 years.

Hence, firm should accept low cost plane which has low payback period.

b. IRR can be found using IRR function in EXCEL

=IRR(values)=IRR(year0 to Year7 cashflows)

IRR of low cost =9.66%

IRR of high cost=3.63%

Company should accept the low cost plane because of having higher IRR.

c. Both the methods gives us the same result, company should accept the low cost plane because of its low payback period and high IRR.

d. =NPV(rate,Year1 to Year7 cashflows)-Cost

PI=NPV(rate,Year1 to Year7 cashflows)/Cost

Please find the below sheet with clear cashflows and NPV and PI

NPV is positive and PI is greater than 1 for Low cost plane. Hence accept that

e. Please find the NPV and PI for 2%,4%,6%,8% and 10% for both low and high cost plane

Yes, from 2% to 8% cost of capital, based on NPV and PI, low cost plane should be accepted. But with 10% cost of capital both the projects have negative NPV and PI less than 1. Hence, both should be rejected at only 10% cost of capital. At remaining cost of capital, low cost plane should be selected.