Answer:
Package K offers the lower present worth analysis.
Explanation:
This can be determined using the following 3 steps.
Step 1: Calculations of present worth of Package K
First cost = $200,000
Present value of quarterly operating cost = quarterly operating cost * ((1- (1/(1 + r))^n)/r) ....... (1)
Where;
r = quarterly interest rate = interest rate per year / Number of quarters in a year = 20% / 4 = 5%, or 0.05
n = number of quarters = Number of years * Number of quarters in a year = 2 * 4 = 8
Substituting the values into equation (1), we have:
Present value of quarterly operating cost = $6,000 * ((1- (1/(1 + 0.05))^8)/0.05) = $38,779.28
Present value of salvage value = Salvage value / (1 + quarterly interest rate)^Number of quarters = $30,000 / (1 + 0.05)^8 = $20,305.18
Present worth of package K = First cost + Present value of quarterly operating cost - Present value of salvage value = $200,000 + $38,779.28 - $20,305.18 = $218,474.10
Step 2: Calculations of present worth of Package L
First cost = $280,000
Present value of quarterly operating cost = quarterly operating cost * ((1- (1/(1 + r))^n)/r) ....... (1)
Where;
r = quarterly interest rate = interest rate per year / Number of quarters in a year = 20% / 4 = 5%, or 0.05
n = number of quarters = Number of years * Number of quarters in a year = 4 * 4 = 16
Substituting the values into equation (1), we have:
Present value of quarterly operating cost = $2,200 * ((1- (1/(1 + 0.05))^16)/0.05) = $23,843.09
Present value of salvage value = Salvage value / (1 + quarterly interest rate)^Number of quarters = $30,000 / (1 + 0.05)^16 = $13,743.35
Present worth of package L = First cost + Present value of quarterly operating cost - Present value of salvage value = $280,000 + $23,843.09 - $13,743.35 = $218,474.10 = $269,900.25
Step 3: Comparison of present worth
Present worth of package K = $218,474.10
Present worth of package L = $269,900.25
Therefore, Package K offers the lower present worth analysis.
