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	$925,000
Cash inflows, years 1 through 7	154,000	167,300

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 low  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 5%. 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

Low cost option:

Formula	Year (n)	0	1	2	3	4	5	6	7
	Cash flow (CF)	(775,000)	154,000	154,000	154,000	154,000	154,000	154,000	154,000
(CCFn-1 + CFn)	Cumulative cash flow (CCF)	(775,000)	(621,000)	(467,000)	(313,000)	(159,000)	(5,000)	149,000	303,000
(-CCFn-1/CFn)	Fraction of year 6 (F)							0.03
(5 + F) years	Payback period	5.03
(Using IRR function)	IRR	9.00%

High cost option:

Formula	Year (n)	0	1	2	3	4	5	6	7
	Cash flow (CF)	(925,000)	167,300	167,300	167,300	167,300	167,300	167,300	167,300
(CCFn-1 + CFn)	Cumulative cash flow (CCF)	(925,000)	(757,700)	(590,400)	(423,100)	(255,800)	(88,500)	78,800	2,46,100
(-CCFn-1/CFn)	Fraction of year 6 (F)							0.53
(5 + F) years	Payback period	5.53
(Using IRR function)	IRR	6.27%

a). Payback period: Low cost - 5.03 years; High cost - 5.53 years

Low cost option is better based on payback period.

b). IRR: Low cost - 9%; High cost - 6.27%

Low cost option is better based on IRR also.

c). Based on payback period and IRR, low cost option is a better choice than the high cost option.

d).

		Low cost	High cost
Formula	Life (l) (in years)	7	7
	Discount rate (d)	5%	5%
	Initial cost (a)	(775,000)	(925,000)
	Cash inflow/year (b)	154,000	167,300
(1 - (1+d)^-l)/d	PVFA	5.7864	5.7864
(b*PVFA)	PV of cash inflows ('c)	891,102	968,060
(a+c)	NPV	116,102	43,060
(c/-a)	Profitability Index (PI)	1.15	1.05

Both NPV and PI methods select the low cost plane as the better option of the two.

e).  

Discount rate		Low cost	High cost
2%	NPV	221,687	157,764
	PI	1.29	1.17
4%	NPV	149,316	79,144
	PI	1.19	1.09
6%	NPV	84,687	8,932
	PI	1.11	1.01
8%	NPV	26,781	(53,974)
	PI	1.03	0.94
10%	NPV	(25,264)	(110,514)
	PI	0.97	0.88

(Note: the valuation tables for these scenarios cannot be posted here due to the word answer limit.)

As can be seen from the table, at every discount rate, low cost plane is a better option than the high cost one.

f).