Employee benefits can be rated in terms of Frequency and Instance Cost. The frequency of a benefit is the average...
GMAT Two Part Analysis : (TPA) Questions
Employee benefits can be rated in terms of Frequency and Instance Cost. The frequency of a benefit is the average number of times a single employee would be expected to receive the benefit over the span of a 20-year career with the company. Instance cost is the average cost incurred by the employer to provide the benefit to a single employee at the moment it is delivered. The frequency/oost ratio (\(\mathrm{F/C}\) ratio) is computed by dividing the frequency by the instance cost. A business is considering various benefits to attract and retain employees.
From the following list of benefits, select the benefit with the highest \(\mathrm{F/C}\) ratio and select the benefit with the lowest \(\mathrm{F/C}\) ratio. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Creating Our Comparison Table
Since we're comparing multiple benefits with different properties (frequency and instance cost), a comparison table is the perfect visualization:
| Benefit | Frequency over 20 years | Instance Cost | F/C Ratio |
| Daily coffee voucher | Daily × 20 years | Cost of 1 coffee | Very High |
| Monthly breakfast | Monthly × 20 years | Cost of 1 breakfast | High |
| Annual 10% raise (10% of employees) | ? | 10% of annual salary | ? |
| First child bonus | ? | 25% of annual salary | Low |
| Annual food reimbursement | Yearly × 20 years | 1 month of food | Moderate |
Calculating Frequencies
Let's calculate the exact frequency for each benefit:
- Daily coffee voucher: 365 days/year × 20 years = 7,300 times
- Monthly breakfast: 12 months/year × 20 years = 240 times
- Annual 10% raise: Each employee has 10% chance each year = 0.10 × 20 years = 2 times (expected value)
- First child bonus: Most employees have 0-2 first children = approximately 1 time
- Annual food reimbursement: 1 time/year × 20 years = 20 times
Estimating Instance Costs
While we don't have exact costs, we can rank them relatively:
- Coffee: Lowest (~$3-5)
- Breakfast: Low (~$15-20)
- Month of food: Moderate (~$300-500)
- 10% annual raise: High (10% of salary)
- 25% salary bonus: Highest (25% of salary)
Phase 2: Understanding the Question
We need to find:
- Highest F/C ratio: High frequency AND low instance cost
- Lowest F/C ratio: Low frequency AND high instance cost
Key Insight
The F/C ratio increases when:
- Frequency goes UP
- Instance cost goes DOWN
Let's update our table with relative F/C ratios:
| Benefit | Frequency | Instance Cost | F/C Ratio |
| Daily coffee | 7,300 | Lowest | Highest |
| Monthly breakfast | 240 | Low | High |
| Annual raise (10%) | 2 | High | Low |
| First child bonus | 1 | Highest | Lowest |
| Annual food | 20 | Moderate | Moderate |
Phase 3: Finding the Answer
For Highest F/C Ratio:
The daily coffee voucher has:
- Highest frequency: 7,300 times
- Lowest instance cost: ~$3-5 per coffee
- Therefore: Highest F/C ratio
For Lowest F/C Ratio:
The first child bonus has:
- Lowest frequency: ~1 time (many employees may never receive it)
- Highest instance cost: 25% of annual salary
- Therefore: Lowest F/C ratio
Phase 4: Solution
Final Answer:
- Highest F/C: Every day, each employee receives a voucher for a free cup of coffee
- Lowest F/C: Upon the birth of an employee's first child, the employee receives a lump-sum bonus equal to 25% of the company's average annual salary
These selections make perfect sense: the coffee benefit combines maximum frequency with minimum cost, while the first child bonus combines minimum frequency with maximum cost.