Question

Jupiter Inc. has decided to acquire a new weather satellite. After considering several options it has narrowed its search to two satellites.

Satellite XPTO: purchase cost of $306251 and operating costs of $39998 per year (paid at the end of each year).

Satellite XYZ: purchase cost of $205569 and operating costs of $55860 per year (paid at the end of each year).

Both satellites have a service life of 10 years. Based on the defender-challenger approach and given that the MARR is 4%, reinvestment rate is 9%, and minimum external rate of return is 10%, compute the incremental external rate of return of choosing the most expensive satellite.

PLEASE NO EXCEL CALCULATIONS, INCLUDE STEPS AND FORMULAS.

Answer 1

INCREMENTAL EXTERNAL RATE OF RETURN:

	A	B	C=B-A
	XYZ	XPTO	Incremental cost
Purchase cost	$205,569	$306,251	$100,682
Operating Cost	$55,860	$39,998	($15,862)

For the Option of XPTO(Challanger) Vs XYZ(Defender)

Incremental initial cost=$100,682

Incremental savings=$15,862

Future Value of $15,862 per year for 10 years=15862*CAF

CAF=Uniform Series Compound amount Factor(F/A,i,N)=(((1+i)^N)-1)/i

i=Reinvestment Rate=9%=0.09

N=number of years=10

CAF=((1.09^10)-1)/0.09=15.19293

Future Value of annual savings for 10 years=(15.19293*15862)= $ 240,990.26

Assume External Rate of Return=R

100682*((1+R)^10)=240990.26

(1+R)^10= 240,990.26/100682= 2.393578352

1+R=2.393578352^(1/10)= 1.091201024

R=0.091201024

External Rate of Return=9.12%

Incremental external rate of return of choosing the most expensive satellite=9.12%