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	$775,000	$950,000
Cash inflows, years 1 through 7	154,000	176,275

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 9%. 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?
   high or low cost plane?
   By PI?
   high or low 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.

   Select the correct graph.

   a,b,c or d

   The correct graph is  .

   Would NPV and IRR ever give conflicting results? Why?
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Answer 1

(a). Payback period for two different capacity planes:

Initial Cost for Low cost plane = $775,000

Initial Cost for High cost plane = $950,000

Year	Cashflow for Low cost planes	Cashflow for High cost planes	Cumulative Cashflows for high cost planes
1	$154,000	$176,275	$176,275
2	$154,000	$176,275	$352,550
3	$154,000	$176,275	$528,825
4	$154,000	$176,275	$705,100
5	$154,000	$176,275	$881,375
6	$154,000	$176,275	$1,057,650
7	$154,000	$176,275	$1,233,925

To Calculate Payback Period we will have find out the period at which the Cashflows from the planes will recover its initial cost of buying.

For that purpose we will add the cashflows for respectives planes and will check at which year it is able to recover its cost fully.

Therefore, Payback Period for Low Cost planes : Sum of the Cashflows till the period where it is able to recover the cost.

So, by adding cashflows till year 5 we are able to get a total amount of $770,000 from cashflows. But our initial investment in Low Cost Planes was $775,000 which means we have recovered $770,000 till year five and we have to still recover $5,000 in the 6th year.

Hence, Payback Period = 5year + $5,000 / $154,000 = 5.032 years or 5years 12 days approx.

Similarly, Payback period for High cost planes :

Now see the above table and column "Cumulative Cashflows" if see the values there for different years as mentioned along, we are able to see that till 5th year we are able to recover $881,375 of the initial cost of $950,000.

and we have to still recover $68,625 in 6th year.

Therefore, Payback Period for High cost planes = 5 + $68,625/$176,275 = 5.39 years

In the above Low cost planes are good alternative based on the Payback Period Calculation.

(b). Calculation of IRR :

To calculate IRR we have taken two Discount rate to reachout the required IRR at which the Planes NPV becomes ZERO. The two discount rates are 10% and 8% for both types of planes.

Below is the Excel Image for reference:

IRR for Low cost Planes:

For 8% discount rate NPV is positive(see the above attached excel image ) = $801,781 - $775,000 = $26,781

For 10% Discount Rate NPV is Negative ( See the above attached image) = $749,736.50 - $775,000 = -$25263.5

IRR using Trial & Error :

Lower rate + (Upper rate - Lower Rate) * Positive NPV / Negative NPV = 8% + (10% - 8%) * $26,781 / $25,263.5 = 8% + 2.12% = 10.12%

IRR for High cost Planes:

For 8% discount rate NPV is positive(see the above attached excel image ) = $984,034.3 - $950,000 = $34034.3

For 10% Discount Rate NPV is Negative ( See the above attached image) = $858,180.53 - $950,000 = -$91819.47

IRR using Trial & Error :

Lower rate + (Upper rate - Lower Rate) * Positive NPV / Negative NPV = 8% + (10% - 8%) * $34034.3 / $91819.47 = 8% + 0.741 = 8.741%

Hence, IRR for Low cost plane is Higher than the High Cost plane which is a desirable opportunity.

(c). After comparing the results obtained in part(a) and part(b) it is observed that for both the methods of evaluation we arrive at the same result that the Low Cost Plane is more profitable as compared to High Cost planes. Because using payback period method we have seen that the recovery of initial cost for Low Cost Plane is lower than the High Cost plane.

And by IRR we have seen that the IRR for low Cost plane is higher than the high cost plane.

(d). NPV Calculation for Both types of Planes:

Please see attached image of Excel calculation for NPV:

PI for low cost plane @ 9% = Discounted cashflow / Initial cost of the project = $775,074.74 / $775,000 = 1.00096

PI for high cost plane @9% = Discounted Cashflow / Initial Cost of the project = $887183.76 / $950,000 = 0.934

Hence, here it is also obvious that the High Cost plane is not a Good investement alternative so purchasing of High cost palne may be avoid by the Firm.