Question

3.

A What was the real rate of return over the past year (from one year ago to today) for a stock if the inflation rate over the past year was 4.57 percent, the risk-free return over the past year was 6.99 percent, the stock is currently priced at 78.89 dollars, the stock was priced at 71.24 dollars 1 year ago, and the stock just paid a dividend of 2.47 dollars? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

B. Over the past year (from one year ago to today), the inflation rate was 4.13%, the risk-free rate was 6.08%, and the real rate of return for a bond was 3.17%. The bond is currently priced at $974.00, pays annual coupons of $84.70, and just made a coupon payment. What was the price of the bond one year ago

C Over the past year (from 1 year ago to today), the inflation rate was 6.09 percent, the risk-free rate was 8.98 percent, and the real rate of return for a bond was 8.62 percent. The bond was priced at 1,288.18 dollars one year ago and 1,316.75 dollars two years ago, pays annual coupons of 55.58 dollars, and just made a coupon payment. What is the price of the bond today?

Answer 1

a. Following information are given in the question:

Inflation rate	4.57%
Risk free return	6.99%
Stock price now	$78.89
Stock price 1 year ago	$71.24
Dividend	$2.47

Step 1: Calculation of nominal rate of return

Nominal rate of return = ((Stock price now - Stock price 1 year ago)+Dividend) / Stock price 1 year ago

= ((78.89-71.24)+2.47)/71.24 = 10.12/71.24 = 14.21%

Step 2: Calculation of real rate of return over the past year

Real rate of return = (Nominal rate of return - Inflation rate) / (1+Inflation rate)

= (14.21%-4.57%)/(1+4.57%) = 9.64%/1.0457 = 9.21% or .0921

Thus, real rate of return = .0921

b. Following information are given in the question:

Inflation rate	4.13%
Risk free return	6.08%
Bond price now	$974
Real rate of return	3.17%
Coupon	$84.7

Step 1: Calculation of nominal rate of return

From the above equation we saw, Real rate of return = (Nominal rate of return - Inflation rate) / (1+Inflation rate).

Thus, Nominal Rate of return = (Real rate of return * (1+Inflation rate)) + Inflation rate

= (3.17%*(1+4.13%))+4.13% = 7.43%

Step 2: Calculation of price of bond one year ago

From the above equation we saw, Nominal rate of return = ((Bond price now - Bond price 1 year ago)+Coupon) / Bond price 1 year ago

Let Bond price 1 year ago be X

Thus, 7.43% = ($974-X+$84.7) / X

=7.43%*X = $1058.70-X

=.0743X = $1058.70-X

=.0743X+X = $1058.70

=1.0743X = $1058.70

X = $1058.70/1.0743 = $985.47

Thus, price of the bond one year ago = $985.47

c. Following information are given in the question:

Inflation rate	6.09%
Risk free return	8.98%
Bond price 1 year ago	$ 1,288.18
Bond price 2 year ago	$1,316.75
Real rate of return	8.62%
Coupon	$55.58

Step 1: Calculation of nominal rate of return :

From the above equation we saw,  Nominal Rate of return = (Real rate of return * (1+Inflation rate)) + Inflation rate

Nominal rate of return = (8.98%*(1+6.09%))+6.09% = 15.62%

Step 2: Calculation of price of bond today

From the above equation we saw, Nominal rate of return = ((Bond price now - Bond price 1 year ago)+Coupon) / Bond price 1 year ago

Let Bond price now be X

Thus, 15.62% = (X-$1288.18+$55.58) /1288.18

15.62%*$1288.18 = X-

$201.17=X-$1232.6

$201.17+$1232.6 = X

X = $1,433.77

Thus, price of the bond now = $1,433.77