Question

PLEASE SHOW CALCULATIONS

1. Find the real return, nominal after-tax return, and real after-tax return for each of the following stocks:

Stock	Nominal Return	Inflation	Tax Rate
X	13.5%	5%	15%
Y	8.7%	4.7%	25%
Z	5.2%	2.5%	28%

2.)

Compute the holding period returns for each security below:

Security	Price Today	Price One Year Ago	Dividends Received	Interest Received
RR	$20.05	$18.67	$0.50
WC	$33.42	$45.79	$1.10
AC	$1,015.38	$991.78		$100.00

Answer 1

1)

Formula for nominal return

(1+ nominal return) = (1+ Real return)*(1+ inflation)

For stock X

(1+0.135) = (1+Real return)*(1+0.05)

1+ real return = 1.135/1.05 = 1.080952381

real return = 1.080952381 - 1 = 0.080952381 = 8.0952381%

OR

if we use approximate formula to calculate real return

Nominal return = real return + inflation

0.135 = real return + 0.05

real return = 0.135-0.05 = 0.085 = 8.5%

Nominal after tax return = Nominal return*(1-tax rate) = 13.5*(1-0.15) = 13.5*0.85 = 11.475%

Real after tax return when calculated from actual formula = real return from actual formula*(1-Tax rate)

= 8.0952381*(1-0.15) = 8.0952381*0.85 = 6.880952385%

Real after tax return when calculated from approximate formula = real return from approximate formula*(1-0.15) = 8.5*0.85 = 7.225%

For stock Y

(1+0.087) = (1+Real return)*(1+0.047)

1+ real return = 1.087/1.047 = 1.038204394

real return = 1.038204394 - 1 = 0.038204394 = 3.8204394 %

OR

if we use approximate formula to calculate real return

Nominal return = real return + inflation

0.087 = real return + 0.047

real return = 0.087-0.047 = 0.04 = 4%

Nominal after tax return = Nominal return*(1-tax rate) = 8.7*(1-0.25) = 8.7*0.75 = 6.525%

Real after tax return when calculated from actual formula = real return from actual formula*(1-Tax rate)

= 3.8204394*(1-0.25) = 3.8204394*0.75 = 2.86532955%

Real after tax return when calculated from approximate formula = real return from approximate formula*(1-0.15) = 4*0.75 = 3%

For stock Z

(1+0.052) = (1+Real return)*(1+0.025)

1+ real return = 1.052/1.025 = 1.026341463

real return = 1.026341463 - 1 = 0.026341463 = 2.6341463 %

OR

if we use approximate formula to calculate real return

Nominal return = real return + inflation

0.052 = real return + 0.025

real return = 0.027 = 2.7%

Nominal after tax return = Nominal return*(1-tax rate) = 5.2*(1-0.28) = 5.2*0.72 = 3.744%

Real after tax return when calculated from actual formula = real return from actual formula*(1-Tax rate)

= 2.6341463*(1-0.28) = 2.6341463*0.72 = 1.896585336%

Real after tax return when calculated from approximate formula = real return from approximate formula*(1-0.28) = 2.7*0.72 = 1.944%