Question

Calisto Launch Services is an independent space corporation and has been contracted to develop and launch one of two different satellites. Initial equipment will cost $800,000 for the first satellite and $900,000 for the second. Development will take 5 years at an expected cost of $110,000 per year for the first satellite; $160,000 per year for the second. The same launch can be used for either satellite and will cost $285,000 at the time of the launch 5 years from now. At the conclusion of the launch, the contracting company will pay Calisto $2,350,000 for either satellite. Calisto is also considering whether they should consider launching both satellites. Because Calisto would have to upgrade its facilities to handle two concurrent projects, the initial costs would rise by $200,000 in addition to the first costs of each satellite. Calisto would need to hire additional engineers and workers, raising the yearly costs to a total of $390,000. An additional compartment would be added to the launch vehicle at an additional cost of $65,000. As an incentive to do both, the contracting company will pay for both launches plus a bonus of $1,050,000. Using a present worth analysis (PW) with a MARR of 10.00 percent/year, what should Calisto Launch Services do? (Do all calculations to 5 decimal places and round final answer to 2 decimal places in terms of k (1 k - 1,000). Tolerance is +/- 1.oo.) (I) Calculate PW of first satellite (in thousands) (I) Calculate PW of second satellite (in thousands) (III) Calculate PW of both satellites S: (in thousands) (IV) Which satellite should be selected based on PW analysis?

Answer 1

Present Worth of Satellite 1

Initial Cost = -$800,000

Development Cost = -$110000 for each of 5 years

Launch Cost at the end of year 5 = -$285000

Payment at the end of year 5 = $2,350,000

n=5 years, r= 10%

PW of Development Cost = P * (1-(1+r)^-n)/r

=- 110000 *(1-(1+10%)^-5)/10%

= -110000 *(1-(1+0.1)^-5)/0.1

= -110000 *(1-(1.1)^-5)/0.1

=-110000 *(1-0.62092)/0.1

=-110000 * 0.37908/0.1

= -$416986.54463

PW of Launch Cost = P/(1+r)^n

= -285000/(1+10%)^5

=-285000/(1.1)^5

=-285000/  1.61051

=-$176962.57707

PW of Payment = P/(1+r)^n

= 2350000/(1+10%)^5

=2350000/(1.1)^5

=2350000/  1.61051

=$1459165.10919

Hence PW of Satellite 1 = Initial Cost + Development Cost + Launch Cost + Payment

= -800,000-416986.54463-176962.57707+1459165.10919=$65215.98749

Hence PW of Satellite 1 is $65.22 thousand

Present Worth of Satellite 2

Initial Cost = -$900,000

Development Cost = -$160000 for each of 5 years

Launch Cost at the end of year 5 = -$285000

Payment at the end of year 5 = $2,350,000

n=5 years, r= 10%

PW of Development Cost = P * (1-(1+r)^-n)/r

=- 160000 *(1-(1+10%)^-5)/10%

= -160000 *(1-(1+0.1)^-5)/0.1

= -160000 *(1-(1.1)^-5)/0.1

=-160000 *(1-0.62092)/0.1

=-160000 * 0.37908/0.1

= -$606528

PW of Launch Cost will be same as above =-$176962.57707

PW of Payment will be same as above = $1459165.10919

Hence PW of Satellite 2 = Initial Cost + Development Cost + Launch Cost + Payment

= -900000-606528-176962.57707+1459165.10919=-$224325.46788

Hence PW of Satellite 2 is -$224.32 thousands

PV of Both Satellites

Initial Cost = -800,000-900000-200000=-$1,900,000

Development Cost = -$390000 for each of 5 years

Launch Cost at the end of year 5 = -285000-65000 = -$350,000

Payment at the end of year 5 = 2,350,000*2+1050000= $5,750,000

n=5 years, r= 10%

PW of Development Cost = P * (1-(1+r)^-n)/r

=- 390000 *(1-(1+10%)^-5)/10%

= -390000 *(1-(1+0.1)^-5)/0.1

= -390000 *(1-(1.1)^-5)/0.1

=-390000 *(1-0.62092)/0.1

=-390000 * 0.37908/0.1

= -$1478412

PW of Launch Cost = P/(1+r)^n

= -350000/(1+10%)^5

=-350000/(1.1)^5

=-350000/  1.61051

=-$217322.46307

PW of Payment = P/(1+r)^n

= 5750000/(1+10%)^5

=5750000/(1.1)^5

=5750000/  1.61051

=$3570297.60759

Hence PW of Satellite 1 = Initial Cost + Development Cost + Launch Cost + Payment

= -1900,000-1478412-217322.46307+3570297.60759=-$25436.85548

Hence PW of both Satellites is -$25.44 thousands

Since the PW of Satellite 1 is highest and positive it should be selected.