Question

Joey receives two job offers: Job A has a starting annual salary of $80,000 and an expected annual salary growth of 7%. Job B has a starting annual salary of $100,000 and an expected salary growth of 5%. Joey is 30 years old and plans to retire when he turns 65. Ignore bonuses, pensions, other compensations and taxes; all cash flows will be made at the end of each year. Joey discounts future cash flows at an effective annual rate of 10%.

1. Which offer has a greater present value?
2. If Joey plans to retire when he turns 55 years old, which offer has a greater present value?
3. If we consider income taxes, could your answers to (a) and (b) be different? Why? Note: qualitative analysis without numbers would suffice for (c).

Answer 1

Hello. Though the present value can be calculated manually, we have used Excel as the tool for the calculations since the values were more. The Excel sheets are provided with the answer.

Present value is the discounted value of future cash flows using a given discount rate. It helps in comparing two options or projects easily.

It is computed as:

where,

CF are the cash Inflows

n = Time period

Co= Cash outflow, i.e. initial investment

Since in this case, there are salaries which means there is no Initial investment so we take that as 0.

PART (A) In the sheet given below,

Column A includes the AGE.

Column B includes the salary from job A which is growing at 7%. Thus we used the formula, =B2*(1.07) For cell B3. And B3*(1.07) for cell B4 and dragged it to generate the salary for rest years.

Same procedure was followed for Job B.

Cell F3 has the discount rate i.e.10%.

For NPV Computation of JOB A, the formula =NPV(rate,cash flows) i.e

=NPV(F3, B2:B37) as highlighted at the top was used.

Same procedure was used for Job B.

Hence, it can be seen , JOB A has Present Value of $1,681,186.10 while JOB B has present value of $1,625,278.94.

JOB A HAS GREATER PRESENT VALUE.

PART(B) We used the same procedure as computed above to calculate the present value by reducing the number of years.

JOB A has a present value of $1,367,283.79 and JOB B has present value of $1,403,319.35.

JOB B HAS A GREATER PRESENT VALUE IF JOEY RETIRES AT 55 YEARS.

PART(C) YES. The answer will be different. Income taxes have an impact while calculating the Net present value of cash flows. It is called the Net present value because it is the difference between present value of cash outflows and inflows.When taxes are involved, the tax effect is shown in cash inflows by calculating the after-tax inflows. Since in this case, salary is a cash inflow and there are no cash outflows, and also salary is an income therefore the Income tax amount will be deducted from these values and then the present value would be computed on the after tax income.

For example, Joey at 31 years Salary is 85600 for Job A and 105000 for Job B, suppose the Income tax rate is 30%. The after tax salary will be 85600*0.7= 59,920 for JOB A and 105000*0.7=73,500 for JOB B. Similarly with all the cash flows, the Present value results will be different.