Answer:
- No, he will not accumulate sufficient funds to purchase his delivery truck after 6 years.
Explanation:
To determine how much money Earl Miller—the owner of the Papa Gino's franchise—will have available in 6 years, it's necessary to assess the worth of the $20,000 he plans to invest at a 5% interest rate compounded semiannually:
With semiannual interest: 5% / 2 = 0.05/2 = 0.025
Equation:
Here, r/n was calculated previously: r/n = 0.05/2 = 0.025; and t refers to the time in years: 6.
Thus, the future value of the investment would fall short of the truck's price, meaning
he will not be able to afford the delivery truck after 6 years.
A) he is unable to identify the proper problem
B) he neglects to assign numerical values to various criteria
C) he resolves the issue ineffectively
D) he does not correctly identify the procedure steps
Response:
A. He fails to identify the proper problem.
Clarification:
In option B, assigning numerical values to decision criteria could assist in the decision-making process, yet it's not essential for achieving a successful outcome.
Regarding option C, solving a problem ineffectively is not optimal, but it does hold some value.
As for option D, recognizing the procedure's steps doesn't significantly impact the success of the process.
This directs us to option A as the correct response; addressing a problem is futile if it's the incorrect one. Resolving an erroneous problem yields no benefit for the organization.
Opting for the lease is a more favorable choice. To illustrate, we examine the calculations for both options. First, we calculate the Net Present Value (NPV) for the Lease Option:
Year n Details CF ($) DF=1/(1.1)^n PV ($)
1 - Lease payment (30,000) 0.9091 (27,273)
2 - Lease payment (30,000) 0.8264 (24,793)
3 - Lease payment (30,000) 0.7513 (22,539)
4 - Lease payment (30,000) 0.6830 (20,490)
The NPV for the lease option equals (95,096).
For the Buy Option, we carry out the following calculations:
Year n Details CF ($) DF=1/(1.1)^n PV
0 Purchase cost (80,000) 1.0000 (80,000)
1 Maintenance costs (10,000) 0.9091 (9,091)
2 Maintenance costs (10,000) 0.8264 (8,264)
3 Maintenance costs (10,000) 0.7513 (7,513)
4 Maintenance costs (10,000) 0.6830 (6,830)
Residual value at end of year 4 20,000 0.6830 13,660
The NPV for the buy option results in (98,038).
To determine the equivalent annual annuity (EAA) for each option:
EAA = (r × NPV) / (1 - (1 + r)^-n)
where r is the discount rate per period and n shows the number of periods.
Calculating:
Lease option EAA = (0.1 × -95,096) / (1 - (1 + 0.1)^-4) = -30,000.
Buy option EAA = (0.1 × 98,038) / (1 - (1 + 0.1)^-4) = -30,928.
Since the lease option manifests a lower EAA of $30,000 compared to the buy option's $30,928, the lease is deemed the superior choice.
