Question

Upon graduation, you receive two very different – job offers that will result in two different career trajectories. To keep things simple, let’s assume your salaries are paid once a year at the end of each year.

A. Option A (company A) is a job related to your background. It starts with a decent salary $75,000 per year, and increases by 3% per year after that.

B. Option B (company B) requires some initial learning, so the first 3 years has a low salary that starts at $42,000 and increases by 2% per year. At the end of year 3 (beginning of year 4), the salary increases by a factor of 2 (it doubles), and then it will increase by 6% per year every year after that.

Assume your TVOM is 5%. We want to compare these two options in short term and long term. Assume you quit both jobs after 3 years.

1. What are the present worth of each job?

2. Which offer (A or B) should you choose, if you are going to work for 10 years? 20 years? 30 years?

3. What is the minimum number of years that you become indifferent between the two job offers?

4. Generate a plot that shows the difference in the present worth of the two options (PW(A)-PW(B)) as a function of the number of years you are planning to work [from 3 years to 30 years)].

Now, we want to look into the impact of your time value of money. Suppose you will be working for 20 years.

5. What will be the level of TVOM that makes you indifferent between the two job offers?

Annual Worth Equivalent: 6. Suppose again that your TVOM is 4%, and that you are going to work for 20 years for company B. Company B can pay you using a different payment plan from what was described earlier, in which they pay you equal monthly payments for the duration of your (in this case it will be 240 equal monthly payments). What should be the size of those payments to make you indifferent between the two payment plans? (Note that the original payment plan is still based on annual payments)

Answer 1

Bases on given information assuming I quit both jobs after 3 years the Present worth of each job will be the Net Present Value of salaries drawn from each company discounted with discounting factor of 5% as my TVOM is 5%

1. What are the present worth of each job?

Years	Salary of Company A	Salary of Company B	PVF @ TVOM of 5%	PV of Company A	PV of Company B
1	75,000	42,000	0.9524	71,429	40,000
2	77,250	42,840	0.9070	70,068	38,857
3	79,568	85,680	0.8638	68,733	74,014
	Total			2,10,230	1,52,871

So the Net Present Value of the salaries given by company A at the end of 3 years id $210,230 and for Company B is $ 152,871

If I quit job in 3 years then I will select Company A as it gives highest value among the 2 companies

2. Which offer (A or B) should you choose, if you are going to work for 10 years? 20 years? 30 years?

To answer this we will need to find NPV of both company’s salary for 10, 20 and 30 years

NPV for 10 years of working:

Years	Salary of Company A	Salary of Company B	PVF @ TVOM of 5%	PV of Company A	PV of Company B
1	75,000	42,000	0.9524	71,429	40,000
2	77,250	42,840	0.9070	70,068	38,857
3	79,568	85,680	0.8638	68,733	74,014
4	81,955	90,821	0.8227	67,424	74,718
5	84,413	96,270	0.7835	66,140	75,430
6	86,946	1,02,046	0.7462	64,880	76,148
7	89,554	1,08,169	0.7107	63,644	76,874
8	92,241	1,14,659	0.6768	62,432	77,606
9	95,008	1,21,539	0.6446	61,243	78,345
10	97,858	1,28,831	0.6139	60,076	79,091
	Total			6,56,070	6,91,083

NPV for 20 years of working:

Years	Salary of Company A	Salary of Company B	PVF @ TVOM of 5%	PV of Company A	PV of Company B
1	75,000	42,000	0.9524	71,429	40,000
2	77,250	42,840	0.9070	70,068	38,857
3	79,568	85,680	0.8638	68,733	74,014
4	81,955	90,821	0.8227	67,424	74,718
5	84,413	96,270	0.7835	66,140	75,430
6	86,946	1,02,046	0.7462	64,880	76,148
7	89,554	1,08,169	0.7107	63,644	76,874
8	92,241	1,14,659	0.6768	62,432	77,606
9	95,008	1,21,539	0.6446	61,243	78,345
10	97,858	1,28,831	0.6139	60,076	79,091
11	1,00,794	1,36,561	0.5847	58,932	79,844
12	1,03,818	1,44,755	0.5568	57,809	80,605
13	1,06,932	1,53,440	0.5303	56,708	81,372
14	1,10,140	1,62,646	0.5051	55,628	82,147
15	1,13,444	1,72,405	0.4810	54,569	82,930
16	1,16,848	1,82,749	0.4581	53,529	83,720
17	1,20,353	1,93,714	0.4363	52,510	84,517
18	1,23,964	2,05,337	0.4155	51,509	85,322
19	1,27,682	2,17,657	0.3957	50,528	86,134
20	1,31,513	2,30,717	0.3769	49,566	86,955
	Total			11,97,359	15,24,629

NPV for 30 years of working:

Years	Salary of Company A	Salary of Company B	PVF @ TVOM of 5%	PV of Company A	PV of Company B
1	75,000	42,000	0.9524	71,429	40,000
2	77,250	42,840	0.9070	70,068	38,857
3	79,568	85,680	0.8638	68,733	74,014
4	81,955	90,821	0.8227	67,424	74,718
5	84,413	96,270	0.7835	66,140	75,430
6	86,946	1,02,046	0.7462	64,880	76,148
7	89,554	1,08,169	0.7107	63,644	76,874
8	92,241	1,14,659	0.6768	62,432	77,606
9	95,008	1,21,539	0.6446	61,243	78,345
10	97,858	1,28,831	0.6139	60,076	79,091
11	1,00,794	1,36,561	0.5847	58,932	79,844
12	1,03,818	1,44,755	0.5568	57,809	80,605
13	1,06,932	1,53,440	0.5303	56,708	81,372
14	1,10,140	1,62,646	0.5051	55,628	82,147
15	1,13,444	1,72,405	0.4810	54,569	82,930
16	1,16,848	1,82,749	0.4581	53,529	83,720
17	1,20,353	1,93,714	0.4363	52,510	84,517
18	1,23,964	2,05,337	0.4155	51,509	85,322
19	1,27,682	2,17,657	0.3957	50,528	86,134
20	1,31,513	2,30,717	0.3769	49,566	86,955
21	1,35,458	2,44,560	0.3589	48,622	87,783
22	1,39,522	2,59,233	0.3418	47,696	88,619
23	1,43,708	2,74,787	0.3256	46,787	89,463
24	1,48,019	2,91,275	0.3101	45,896	90,315
25	1,52,460	3,08,751	0.2953	45,022	91,175
26	1,57,033	3,27,276	0.2812	44,164	92,043
27	1,61,744	3,46,913	0.2678	43,323	92,920
28	1,66,597	3,67,727	0.2551	42,498	93,805
29	1,71,595	3,89,791	0.2429	41,688	94,698
30	1,76,742	4,13,179	0.2314	40,894	95,600
	Total			16,43,948	24,41,051

From the above tables the NPV for 10 years working for Company A is $ 656,070 and for Company B is $ 691,038. For 20 years working for Company A is $ 1,197,359 and for Company B is $ 1,524,629. For 30 years working for Company A is $ 1,643,948 and for Company B is $ 2,441,051.

As we can see Company B offers highest NPV in all 3 cases so we should choose Option B or Company B

Note: I have not pasted 3rd answers as the error showing as "answer cannot be longer than 65000 characters".