Question

Block B. A company is considering the purchase of a generating set to supply the electrical needs of his office during brownouts. The first offer he received is for a gasoline-driven unit with an estimated life of 5 years and would cost the company $52,000. The annual maintenance cost is estimated to be $8,300, annual operating costs would be $27,600 and the salvage value would be $7,200. The second offer the company received is for a diesel engine-driven unit with an estimated life span of 10 years, annual maintenance cost of $5,800, operating costs of $18,800 and a salvage value of $11,900. The price offered for the unit is $98,250. The cost of money is 20%. What is the annual cost of the better alternative?

CHOICES:

A. $50,344

B. $43,595

C. 47,575

D. $52,321

Answer 1

Answer : C ) : $47,575

See calculations for answer above :

Alternative 1 :

NPV = CF₀ + CF₁/(1+r)¹ + CF₂/(1+r)² + .......................................................+ CF_n/(1+r)ⁿ

= -52,000 + ( -27,600 - 8,300) / (1+0.20)¹ + .( -27,600 - 8,300) / (1+0.20)² +..................................... .......+ ( - 27,600 - 8,300 + 7,200)/(1+0.20)⁵

= -$156,469.46

Equivalent annual cost = r(NPV) / (1 - (1+r)^-n)

= 0.20(-$156,469.46) / (1-(1+0.20)^-5)

= $-52,320.21

Alternative 2 :

NPV = = -98,250 + ( -24,600) / (1+0.20)¹ + .( -24,600) / (1+0.20)² +..................................+ ( -12,700)/(1+0.20)¹⁰

= -$199,462.90

Equivalent annual cost = 0.20(-$199,462.90)/(1-(1+0.20)^-10)

= $-47,576.44

= $-47,575 (Rounded off)

Therefore it is clear that alternative 2 is better with annual cost equal to $47,575.

Negative sign above is just a representative of cost. Do not get confused with that sign above in the formulas.