Question

Spencer would like to buy a car. He narrowed down his choice into two cars. The first car, RX costs $23,000 and the annual insurance, repair, maintenance, tax, and fuel cost is $3,800 and could be sold for $8,000 at the end of four year. On the other hand, the second car, BZ costs $28,000, the annual costs for this car is $3200 per year and it can be sold for $10 000 at the end of the fifth year. What is the total equivalent annual cost (EAC) for both cars and if you don’t mind driving either of them, which one is more economical? The cost of capital for both choices is 6 percent.

Question 11 options:

	RX=8618.87 and BZ=8073.135, BZ is better
	RX=8608.87 and BZ=8773.135, RX is better
	RX=8608.87 and BZ=8073.135, BZ is better
	RX=8608.87 and BZ=8173.135, BZ is better

Answer 1

Here, we need to find out the equivalent annual cost (EAC) for both the car models. The calculations have been shown in the excel file images below:

Solution. BZ Initial Cost: Salvage Value RX $23,000.00 $8,000.00 $28,000.00 $10,000.00 Cost of capital, r: 6% 4 Useful life(years): Annual insurance, repair, maintenance, tax an fuel cost $3,800.00 $3,200.00 Equivalent annual cost(EAC): O Step 1: Find present value of salvage value: Present value of Salvage value = Salvage value (1 + r) useful life RX $6,336.75 BZ $7,472.58

Step 2: Subtract the present value of salvage from the initial cost: = Initial Cost - Present value of salvage RX $16,663.25 BZ $20,527.42 Step 3: Find the annuity value: Now, taking values calculated in step 2 as NPV in the formula for "Present value of Annuity", find the annuity value: |(1-(1+r)-n NPV for annuity cashflows = Annuity * Cost of capital, r: 6% here, NPV stands for net present value Annuity means periodic cashflows per period r is the rate of interest per period n is the number of years Assuming the values calculated in Step 2 as NPV value here in the formula, we will calculate the value of annuity here $16,663.25= Annuity * (1-(1+6%)* 6% $20,527.42 = Annuity * (1-(1+6%)-5 6% BL RX Annuity = $16,663.25 * 6% |(1-(1+6%)-) Annuity = $20527.42 * 6% |(1-(1+6%)-5)

Assuming the values calculated in Step 2 as NPV value here in the formula, we will calculate the value of annuity here $16,663.25= Annuity * (1-(1+6%)-1 6% -5 $20,527.42 = Annuity * uuta (1-(1+6% RX Annuity = $16,663.25 * 6% |(1-(1+6%)--) Annuity = $20527.42 * |(1-(1+6%)-5) $4,808.87 $4,873.14 Step 4: Add the annuity value and other maintenance costs, etc. to find EAC: Add the value of annuity calculated above and the other annual costs, i.e.the annual insurance, repair, maintenance tax, fuel cost etc. The value you get is the equivalent annual cost(EAC) RX EAC: $8,608.87 $8,073.14

Since, Equivalent Annual Cost value for BZ is less than RX, BZ is more economical. So, the third option is correct.