Question

Flo's Frozen Yogurt shop is evaluating new dispensing machines. The Flownator has a first cost of $31279 and annual expenses of $9501 that will increase by $467 per year. It will require an overhaul at the end of year 6 at a cost of $6107. The Flownator will save $19262 per year in labor costs. The Flownator has a salvage value of $8475 and a lifespan of 10 years. The YogGoo300 has a first cost of $24866 and annual expenses of $3522 that will increase by 7% per year. The YogGoo300 will save Flo's $10561 per year in labor costs. The YogGoo300 has a lifespan of 6 years. What must the salvage value of the YogGoo30 be to make it equally desirable to the Flownator? Use a MARR of 7% to make your calculation. Enter your answer as follows: 12345 Round your answer. Do not use a dollar sign ("$"), any commas (","), or a decimal point (".").

Answer 1

MARR = 7%

Flownator option

first cost = 31279

annual expenses = 9501 increase by 467 per year.

overhaul at the end of year 6 at a cost of 6107.

Annual savings = 19262 per year in labor costs.

salvage value = 8475

life = 10 years.

Annual worth = -31279 *(A/P,7%,10) - 9501 - 467 * (A/G, 7%, 10) - 6107 *(P/F, 7%, 6) *(A/P,7%,10) + 19262+ 8475 * (A/F, 7%, 10)

= -31279 *0.1423775 - 9501 - 467 * 3.946071 - 6107 *0.666342 *0.1423775 + 19262 + 8475*0.072377

= 3498.77

YogGoo300 option

first cost = 24866

annual expenses = 3522 that will increase by 7% per year.

here g= 7% = 0.07 and i =7% too

Annual savings = 10561 per year in labor costs.

life = 6 years.

Let salvage value = S

Present value of geometric series, when g=i is given by C*n / (1+i)

where C is first payment and n is no of years and i is interest rate

Present value of annual cost = 3522 * 6 / (1+0.07) = 19749.53

Annual worth = -24866 *(A/P,7%,6) - 19749.53*(A/P,7%,6) + 10561 + S * (A/F, 7%, 6)

= -24866 *0.2097958 - 19749.53*0.2097958 + 10561 + S*0.1397958

= 1200.849 + S*0.1397958

As per the condition given in the ques

1200.849 + S*0.1397958 = 3498.77

S = (3498.77 - 1200.849) / 0.1397958

S = 16437.696 = 16438 (rounding off)