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

Defender

capital cost (P) = 306251$

operating cost (A) = 39998

Salvage value(F) = 0

Number of years = 10

MARR = 4%

Anual Worth (aw) = capital cost(A/P,i,n) - operating cost + Salvage value(A/F,i,n)

where (A/P,i,n) is called the capital recovery factor

(A/P,i,n) =

= 0.04(1+0.04)¹⁰/(1+0.04)¹⁰-1

= 0.04(1.04)¹⁰/1.04¹⁰-1

= 0.04(1.48024428492/1.48024428492-1

= 0.05920977139/.48024428492

= 0.123290944

AWDefender = 306251(0.123290944) - 39998 + 0

= 37757.9749 - 39998

= -2240.0251 (negative value)

Challenger

capital cost (p) = 205569$

Operation cost (A) = 55860$

salvage value (f) = 0

AW_Challenger = 205569(0.123290944) - 55860 + 0

= 25344.7961 - 55860

= - 30515.2039

from the above, the EUAC of the defender is better than the challenger and hence we opted for the option 1

since we have only cash outflows and no inflow over all these periods and all the returns turn to be negative

the rate of return on the defender is = (-2240.0251/306251)*100

= -0.73%

   the rate of return on the challenger is = (-30515.2039/205569)*100

= -14.85%

here the most expensive satellite turns out to be the challenger as it has a very less return compared to the defender

hence the incremental external rate for expensive satellite is 24% (14+10)