Question

Companies often invest in training their employees to raise their productivity. Economists sometimes wonder why companies spend money on training employees when this incentivizes other companies to poach their employees with higher salaries since the employees gain human capital from training.

Imagine it costs a company 25,000 dollars to teach their employees Python, but it also raises their output by 2,500 dollars per month. The company discounts the future at rate of ?=0.01r=0.01 per month.

a. For how many full months does an employee need to stay at a company for that company to make a profit for paying for their employees’ Python training?

b. Imagine that 3/4 of the employees stay for 8 months and 1/4 of the employees stay for 24 months. Is it worth it for the company to invest in employee Python training?

Answer 1

Part a)

The employees need to stay in the company untill the NPV becomes positive.

NPV = PV of cash inflows - PV of cash outflows

PV of cash inflows = 2500/(1+0.01)^1 + 2500/(1+0.01)^2 + 2500/(1+0.01)^3...........2500/(1+0.01)^n

where n is the required number of months

PV of cash outflows = 25000

NPV = 2500/(1+0.01)^1 + 2500/(1+0.01)^2 + 2500/(1+0.01)^3...........2500/(1+0.01)^n - 25,000

Since we require NPV to be greater than 0

2500/(1+0.01)^1 + 2500/(1+0.01)^2 + 2500/(1+0.01)^3...........2500/(1+0.01)^n - 25,000 >0

n >10

n should be minimum 11 months

So, the employees need to stay for a minimum of 111 months for the company to make a profit

Part b)

If 3/4th of employees stay for 8 months and 1/4th of employees stay for 24 months,

Total savings of all employees for a month = 2500

So savings of 3/4 employyes for a month will be 2500 *3/4 = 1875 and savings of 1/4 employyes for a month will be 2500 *1/4 = 625

PV of 3/4 employees = 1875/(1+0.01)^1 + 1875/(1+0.01)^2............1875/(1+0.01)^8

PV of 3/4 employees = 14,347

PV of 1/4 employees = 625/(1+0.01)^1 + 625/(1+0.01)^2............625/(1+0.01)^24

PV of 1/4 employees = 13,277

Total PV of inflows = 14,347 + 13,277 = 27,624

NPV = PV of cash inflows - PV of cash outflows

NPV = 27,624 - 25000

NPV = 2,624

Since NPV is positive, it is worth for the company to invest.