Question

Salary vs. Deferred Compensation Exercise (Turn in Solutions)

1. It is now 10 years after you have graduated. You are advising a large company regarding its compensation and tax planning for its highly-compensated employees. Suppose that the top personal tax rate and the corporate tax rate are both 35%. Suppose Congress increases the top personal tax rate to 40% decreases the corporate tax rate to 31%, but the changes will not take effect for another three years.

(Assume r = 6.5% throughout this problem.)

a. What is the amount of deferred compensation that the employer could offer and be indifferent between deferred compensation and $1 of salary?

b. The employer is aware that, if he offers the deferred compensation computed in (a), then the employee will choose salary. In fact, the employer recognizes that the employee would choose salary over deferred compensation even if his salary was reduced a bit. Using the deferred compensation figure computed in (a), how much of a pay cut would the employee accept and still prefer salary over deferred compensation?

           c. Same facts as #1. However, the company is short on cash and must pay deferred compensation. How much deferred compensation will the employee demand three years from today to be indifferent between salary today and deferred compensation three years from today?

Answer 1

(a)
For the employer to be indifferent the FV of the salary should be equal to the PV of deferred compensation
after three years
The net salary cost to the company = Salary * (1- tax rate)
Tax benefit on Salary at current tax rate			35%
Net cost to company for $ 1 Salary
Salary			$1.00
Less: Tax benefit @ 35%			$0.35
Net salary cost to Company			$0.65
Tax benefit on Deferred compensation after 3 years			31%
The deferred compensation should be an amount whose PV at rate of return of 6.50% should be $ 0.65
so that the employer remains indifferent between salary and deferred compensation.
Hence, we will calculate the future value of the after tax salary cost to company for $ 1 salary paid.
After tax cost to the Company			$0.65
FV = PV * (1+r) ^ n
where, PV is the present value of the after tax salary cost
r = rate of return( which is 6.50% as stated in the problem)
n = period (which is 3 years as stated in the problem)
= 0.65 * (1+.065) ^ 3
=0.65 * (1.065) ^ 3
= 0.65 * 1.21
= $ 0.79
The value derived above is the after tax cost of deferred compensation to the Company.We will calculate the
gross deferred tax cost to the company after considering the tax rate after 3 years
After tax value of deferred compensation			$0.79
Tax rate for the company (after 3 years)			31%
Deferred tax compensation (After tax value/(1 - tax rate))			$1.14
The company would be offering $ 1.14 as deferred compensation after 3 years for every $ 1 of salary it offers
at the present and would be indifferent between the two offers.
(b)
The company would be offering $ 1.14 as deferred compensation after 3 years for every $ 1 of salary it offers
at the present.
The net deferred compensation receivable by the employees after deducting tax at the rates applicable after
3 years would be as under
Deferred tax compensation offerred by the Company			$1.14
Tax rate after 3 years for employees			40%
Net deferred compensation receivable by the employees			$0.68
The employees would prefer salary in the current year if the future value of the salary after 3 years is not
less than deferred compensation they will receive after three years
Net deferred compensation receivable by the employees			0.68
The employee would agree to salary in the current at lower amounts if the future value after 3 years is
not less than $ 0.68
Hence, to calculate the minimum acceptable salary, we would calculate the present value if the
future value after 3 years at rate of return of 6.50% is $ 0.68
Calculation of the PV if the future value is $ 0.68
PV = FV/(1+r) ^ n
= 0.68/(1+0.065) ^ 3
= 0.68/1.21
= $ 0.56
The value derived above is the after tax value of salary to the employee.We will calculate the
gross salary receivable by the employee after considering the tax rate after 3 years
After tax value			$0.56
Tax rate on salary for current year for employees			35%
Gross salary(After tax salary/(1-tax rate))			$0.86
Hence, the employee would be ready to take a salary cut of $ 0.14 per $ 1 of salary
The pay cut which would agreeable to the employee would be 14% of their current salary
(c.)
PV of deferred compensation should be $ 0.65 for the employee to be indifferent
FV = PV * (1+r) ^ n
= $ 0.65 * (1+.065) ^ 3
= $ 0.65 * (1.065) ^ 3
= $ 0.65 * 1.21
= $ 0.79
The value derived above is the after tax value of salary to the employee.We will calculate the
gross salary receivable by the employee after considering the tax rate for the current year
After tax value of deferred compensation			$0.79
Tax rate for current year for the employees			40%
Deferred tax compensation(After tax salary/(1-tax rate))			$1.32