Question

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	$510,000	$980,000
Cash inflows, years 1 through 7	102,000	167,156

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 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.

   	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.
   
   
6. Use the results of parts (b) and (e) to sketch the NPV profiles of the two proposed planes on the same set of axes. Show the IRRs on the graph.

Answer 1

Ans a)

Payback period = Initial Investment / Annual cash flows

Payback period for Low cost = 5 years ($510,000 / $102,000)

Payback period for High cost = 5.86 years ($980,000 / $167,156)

Ans b)

IRR is the rate at which NPV of the project is zero. Using excel sheet,

IRR of Low cost = 9.2%

IRR of High cost = 4.64%

Ans c)'

Higher the IRR, better the project is and lower the payback period, better the project is.

As Payback period of Low cost is lower and IRR of Low cost is higher, Low cost is acceptable project.

Ans d)

NPV of Low cost = ($102,000 * 4.8684) - $510,000

= -$13,423

PI of Low cost = ($102,000 * 4.8684) / $510,000

= 0.97

NPV of High cost = ($167,156 * 4.8684) - $980,000

= -$166,218

PI of High cost = ($167,156 * 4.8684) / $980,000

= 0.83

Ans e)

Discount Rate		Low Cost	High Cost
2%	NPV	1,50,144	1,01,834
PI	1.29	1.10
4%	NPV	1,02,214	23,287
PI	1.20	1.02
6%	NPV	59,405	-46,868
PI	1.12	0.95
8%	NPV	21,053	-1,09,719
PI	1.04	0.89
10%	NPV	-13,423	-1,66,218
PI	0.97	0.83