Question

Suppose you buy a bond with a coupon of 8.2 percent today for $1,100. The bond has 7 years to maturity. Assume interest payments are reinvested at the original YTM.

a. What rate of return do you expect to earn on your investment? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

b. Two years from now, the YTM on your bond has increased by 2 percent, and you decide to sell. What price will your bond sell for? (Do not round intermediate calculations. Round your answer to 2 decimal places.)    

     

Answer 1

(a)-The rate of return earned on the investment

The rate of return expected to earn is the Yield to Maturity of the Bond

The Yield to maturity of (YTM) of the Bond is calculated using financial calculator as follows (Normally, the YTM is calculated either using EXCEL Functions or by using Financial Calculator)

Variables	Financial Calculator Keys	Figure
Face Value [$1,000]	FV	1,000
Coupon Amount [$1,000 x 8.20%]	PMT	82
Yield to Maturity [YTM]	1/Y	?
Time to Maturity [7 Years]	N	7
Bond Price [-$1,100]	PV	-1,100

We need to set the above figures into the financial calculator to find out the Yield to Maturity of the Bond. After entering the above keys in the financial calculator, we get the yield to maturity (YTM) on the bond = 6.38%.

Therefore, the rate of return earned on the investment will be 6.38%.

(b)-Selling price of the Bond

The Selling Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Par Value of the bond = $10000

Annual Coupon Amount = $82 [$1,000 x 8.20%]

Annual Yield to Maturity = 8.38% [6.38% + 2.00%]

Maturity Period = 5 Year [7 Year – 2 Year]

Therefore, the Selling Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $82[PVIFA 8.38%, 5 Years] + $1,000[PVIF 8.38%, 5 Years]

= [$82 x 3.95304] + [$1,000 x 0.66874]

= $324.14 + $668.74

= $992.88

Hence, the selling price of the Bond will be $992.88.

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.  

-The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.