Question

Assume a machine costs \$108,000 and lasts seven years before it is replaced. The operating cost...

Assume a machine costs \$108,000 and lasts seven years before it is replaced. The operating cost is \$17,600 a year. Ignore taxes. What is the equivalent annual cost if the required rate of return is 14 percent? (Hint: the EAC should account for both initial investment and annual operating costs)

 \$33,218.72 \$35,610.58 \$38,127.49 \$42,784.78 \$46,412.03

Present value of outflows=cash outflows*Present value of discounting factor(rate%,time period)

=108000+17600/1.14+17600/1.14^2+.........17600/1.14^7

=108000+17600[1/1.14+1/1.14^2+1/1.14^3+............+1/1.14^7]

=108000+(17600*4.288304839)

which is equal to

=\$183,474,1652(Approx)

Hence equivalent annual cost=[required rate*Present value of outflows]/[1-(1+rate)^-time period]

=[\$183,474,1652*0.14]/[1-(1.14)^-7]

=25686.38313/[1-0.399637322]

=25686.38313/0.600362678

which is equal to

=\$42784.78(Approx).

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