Question

Prices of zero-coupon bonds reveal the following pattern of forward rates:

Year	Forward Rate
1	6%
2	7
3	8

   

In addition to the zero-coupon bond, investors also may purchase a 3-year bond making annual payments of $60 with par value $1,000.

  

a.	What is the price of the coupon bond?(Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)

  

Price

$

  

b.	What is the yield to maturity of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.)

  

Yield to maturity

%

  

c.	Under the expectations hypothesis, what is the expected realized compound yield of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.)

  

Realized compound yield

%

   

d.	If you forecast that the yield curve in 1 year will be flat at 8.0%, what is your forecast for the expected rate of return on the coupon bond for the 1-year holding period? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.)

  

Holding period return

%

Answer 1

a.

Cash Flows	60	60	1060
Forward Rate	6%	7%	8%
Present value	56.60377	52.90072	865.3513
Price	$                                             974.86

b.

YTM=[ C+((F-P)/n)] / [(F+P)/2]
Where,
C=	Coupon Rate
F=	Face Value
P=	Price
Ytm=	6.93%

c.

Expected Compounded Yield=	(1.06x1.07x1.08)-1
	= 22.49%

d.

Expected Rate of return by holding bond for 1 year= (Price of bond at end of 1st year - Price of bond today + Coupon) / Price of bond today

= (964.33*-974.86+60)/974.86 = 5.08

* price of bond after 1 year

Cash Flows	60	1060
Forward Rate	8%	8%
Present value	55.55556	908.7791
Price	$ 964.33