When your firm hires a new employee this year, it is obligated to contribute $5,000 to a defined contribution plan for that employee, one year after the hire date. The contribution must be
Adjusted annually for inflation. Assume that inflation will be a constant 2.5% a year from this
Point forward. What is the cost to you of hiring a 30-year old who will be with the company
For 32 years if the appropriate discount rate is 10%? Round your answer to the nearest dollar.

Question

Quizplus · Accepted Answer

The cost of hiring a new employee can be calculated by finding the present value of the contributions that the firm will have to make over the period of the employee's tenure.

Given:
- Annual contribution = $5,000
- Inflation rate = 2.5%
- Discount rate = 10%
- Time period = 32 years

First, we need to adjust the annual contribution for inflation for each year. Using the formula for real interest rate, we get:
Real interest rate = (1 + nominal interest rate)/(1 + inflation rate) - 1
= (1 + 10%)/(1 + 2.5%) - 1
= 7.32%

Adjusted annual contribution = $5,000 * (1 + 2.5%)^(n-1) * (1 + 7.32%)^(32-n)
where n is the number of years since the employee was hired.

Next, we can sum up the present value of all the contributions using the formula for present value of an annuity:
PV annuity = C * [(1 - (1 + r)^(-n))/r]
where C is the annual contribution, r is the discount rate, and n is the number of years.

PV of contributions = Σ [Adjusted annual contribution] * [(1 - (1 + 10%)^(-32))/10%]
= Σ [$5,000 * (1 + 2.5%)^(n-1) * (1 + 7.32%)^(32-n)] * [(1 - (1 + 10%)^(-32))/10%]
= $152,835.24

Therefore, the cost to the firm of hiring a new employee who will be with the company for 32 years is $59,708 (rounded to the nearest dollar). First, we need to calculate the present value of the contribution using the formula:
PV = CF/((1+r)^n)
where PV is present value, CF is cash flow, r is the discount rate, and n is the number of years from the hire date.

The cash flow is $5,000 adjusted for inflation at 2.5% annually, so in the first year it will be $5,125 (5,000 * 1.025). In the second year, it will be $5,253.13 (5,125 * 1.025), and so on.

We need to calculate the present value of 32 cash flows, starting from one year after the hire date. Using a financial calculator or spreadsheet, we get the present value of the contribution to be $59,708.

Therefore, the cost of hiring a 30-year-old who will be with the company for 32 years, with a defined contribution plan that requires a $5,000 contribution adjusted for inflation each year, and a discount rate of 10% is $59,708. Answer (C) is correct.

When Your Firm Hires a New Employee This Year, It