You are in charge of hiring for the sales department of Nature’s Own chemical co

Question

You are in charge of hiring for the sales department of Nature’s Own chemical company. You are choosing between two workers, a “safe” worker who will produce 250 thousand dollars in sales (net of variable costs) in each of the next four years. The “risky” worker produces 500 thousand dollars in annual sales with probability p, and will cost the company 250 thousand dollars in sales with probability (1-p). Both workers will stay with Nature’s Own for one year for sure, and will leave after four years for sure. There is, however, a 50 percent chance that either type of worker will quit between the end of the first and the start of the second period. If they don’t quit at that moment then they will stay for sure till the end of year 4. (Note to the wise: this is a crude way of modeling a declining quit rate over the worker’s career; it is different from the constant quit rate we modeled in class). If hired, the salary of each type of worker will be $100,000 per year. The discount rate is zero. A risky worker’s “type” (good or bad; i.e. high or low sales) becomes known after the end of his/her first year with Nature’s Own.

a.) Set up a spreadsheet to calculate the firm’s expected present value of hiring each type of worker. Allow for “inputable” values of all the parameters above (the productivities of both worker types in both years, the probability the risky worker is the “good” type, and the probability that workers quit after the first year.

b.) If p = 0.5, which worker should you hire? Is this the worker with the highest expected value of sales in the first year?

c.) Now raise the “riskiness” of the risky worker by raising her sales if she is “good” to 700 thousand, and increasing her net losses if she is “bad” from 250 to 450 thousand dollars. What does this do to her expected value of sales in the first year? Does this change your recommendation on which worker to hire? Why or why not?

d.) Keeping workers’ productivities at the levels in part c above, raise the probability that workers of either type quit after year 1 from .5 to .75. Which worker would you hire now? Why?

Explanation / Answer

a)

For safe worker

Net Sales=250k

If he quits after 1 year, then Sales=250k

If he don’t quit after 1 year then he will work for 4 years, thus Sales=250k+250k+250k+250k=1000k

Since there is 50% probability that he will quit after 1 year

Thus expected sales=0.5*250k+0.5*1000k=625k

Salary=100k per year

If he quits after 1 year, then Salary he receives=100k

If he don’t quit after 1 year then he will work for 4 years, thus Salary he receives=100K*4=400k

Expected salary=0.5*100k+0.5*400k=250k

Expected P.V of safe worker=Expected sales-Expected Salary=625k-250k=375k

For Risky worker

Sales= p*500K

Cost=(1-p)*250K

Net Sales= p*500K-(1-p)*250K=p*750k-250k

If he quits after 1 year, then Sales= p*750k-250k

If he don’t quit after 1 year then he will work for 4 years, thus Sales= (p*750k-250k )*4=p*3000k-1000k

Since there is 50% probability that he will quit after 1 year

Thus expected sales=0.5*( p*750k-250k )+0.5*( p*3000k-1000k )=p*1875k-625k

Salary=100k per year

If he quits after 1 year, then Salary he receives=100k

If he don’t quit after 1 year then he will work for 4 years, thus Salary he receives=100K*4=400k

Expected salary=0.5*100k+0.5*400k=250k

Expected P.V=Expected sales-Expected Salary= p*1875k-625k -250k = p*1875k-875k

b)

For p=0.5

Expected P.V of risky worker= 0.5*1875k-875k=62.5k

Expected P.V of safe worker= 375k

Since Expected P.V of safe worker > Expected P.V of risky worker

So I will hire safe worker at p=0.5

c)

For Risky worker

Sales= p*700K

Cost=(1-p)*450K

Net Sales= p*700K-(1-p)*450K=p*1150k-450k

If he quits after 1 year, then Sales= p*1150k-450k

If he don’t quit after 1 year then he will work for 4 years, thus Sales= (p*1150k-450k)*4=p*4600k-1800k

Since there is 50% probability that he will quit after 1 year

Thus expected sales=0.5*( p*1150k-450k)+0.5*( p*4600k-1800k)=p*2875k-1125k

Salary=100k per year

If he quits after 1 year, then Salary he receives=100k

If he don’t quit after 1 year then he will work for 4 years, thus Salary he receives=100K*4=400k

Expected salary=0.5*100k+0.5*400k=250k

Expected P.V=Expected sales-Expected Salary= p*2875k-1125k-250k = p*2875k-1375k

For p=0.5

Expected P.V=0.5*2875k-1375k=62.5K

Still Expected P.V of safe worker > Expected P.V of risky worker

So I will hire safe worker and my decision will not change

d)

Probability at which I will hire risky worker, when

Expected P.V of Risky worker > Expected P.V of Safe worker

p*2875k-1375k>375k

p>(1375+375)/2875=0.61

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