Question

Tom can choose when he is to receive $100,000 of fully taxable bonus. If he receives the bonus at the end of 2016, his bonus will be $100,000. If he postpones receipt of the bonus until the end of 2017, the amount will be $110,000. If Tom receives the bonus at the end of 2016, he can invest the proceeds with a pre-tax return of 10% over the next year.

If the marginal tax rate of Tom is 31% in 2016 and 2017, when should he elect to receive the bonus?

At what pre-tax rate of return will Tom be indifferent to receiving the bonus in the alternative years?

If the marginal tax rate of Tom increases to 35% in 2017, when should he elect to receive the bonus?

What would the tax rate need to be in 2017 to make Tom indifferent to the two options?

Answer 1

1. To decide when to receive bonus

Particulars	2016	2017
Bonus received	100,000	110,000
Less: Tax @ 31%	31,000	34,100
Post tax amount received (A)	69,000	75,900
Proceeds of 2016 reinvested @10%	6,900	0
Tax on amount reinvested @ 31%	2,139	0
Post tax amount received from reinvestment (B)	4,761	0
Total cash receipts (A+B)	73,761	75,900

Tom should elect to receive bonus in 2017

2.Pre-tax rate of return

Amount of bonus received if elected to received in 2017 = 75,900

Amount of bonus received if elected to received in 2016 = 69,000

Difference in amount = 6,900

Amount of bonus to be reinvested to earn post tax return of 6,900 = 69,000

Post tax return rate = 6,900/69,000*100 = 10%

Pre tax return - 31%* Pre tax return = 6,900

Pre tax retuen = 10,000

Pre tax return rate = 10,000/69,000*100= 14.49%

3. To decide when to receive bonus

Particulars	2016	2017
Bonus received	100,000	110,000
Less: Tax @ 31% for 2016 and 35% for 2017	31,000	38,500
Post tax amount received (A)	69,000	71,500
Proceeds of 2016 reinvested @10%	6,900	0
Tax on amount reinvested @ 35%	2,415	0
Post tax amount received from reinvestment (B)	4,485	0
Total cash receipts (A+B)	73,485	71,500

Tom should elect to receive bonus in 2016

4. Tax rate in 2017

Let tax rate be x%

69,000+(6,900 - x% *6,900) = 110,000- x% *110,000

x% *110,000 - x% *6,900 = 110,000-69,000-6,900

103,100 *x% = 34,100

x% =34,100/103,100

x=33.07%

tax rate in 2017 = 33.07%