Question

(Bond valuation​) You own a 15-year, $1000 par value bond paying 7 percent interest annually. The market price of the bond is $850, and your required rate of return is 10 percent.

a. Compute the​ bond's expected rate of return.

b. Determine the value of the bond to​ you, given your required rate of return.

c. Should you sell the bond or continue to own​ it?

a. What is the expected rate of return of the 15-year, ​$1000 par value bond paying 7 percent interest annually if its market price is $850?

Answer 1

(a)-Bond's expected rate of return

· The Bond's expected rate of return is the Yield to maturity of (YTM) of the Bond.

· The Yield to maturity of (YTM) of the Bond is the discount rate at which the Bond’s price equals to the present value of the coupon payments plus the present value of the Face Value/Par Value

· The Yield to maturity of (YTM) of the Bond is the estimated annual rate of return expected by the bondholders for the bond assuming that the they hold the Bonds until it’s maturity period/date.

· 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
Par Value/Face Value of the Bond [$1,000]	FV	1,000
Coupon Amount [$1,000 x 7.00%]	PMT	70
Market Interest Rate or Yield to maturity on the Bond	1/Y	?
Maturity period/Time to Maturity [15 Years]	N	15
Bond Price/Current Market Price of the Bond [-$850]	PV	-850

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 annual yield to maturity (I/Y) on the bond = 8.84%.

Hence, the Bond's expected rate of return will be 8.84%.

(b)-Value of the Bond at required rate of return of 10.00%.

· The Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the Face Value/Par Value.

· The Price of the Bond is normally calculated either by using EXCEL Functions or by using Financial Calculator.

· Here, the calculation of the Bond Price using financial calculator is as follows

Variables	Financial Calculator Keys	Figure
Par Value/Face Value of the Bond [$1,000]	FV	1,000
Coupon Amount [$1,000 x 7.00%]	PMT	70
Market Interest Rate or Yield to maturity on the Bond [10.00%]	1/Y	10
Maturity period/Time to Maturity [15 Years]	N	15
Bond Price/Current Market Price of the Bond	PV	?

Here, we need to set the above key variables into the financial calculator to find out the Price of the Bond. After entering the above keys in the financial calculator, we get the Price of the Bond (PV) = $771.82.

Hence, the Value of the Bond will be $771.82.

(c)-Sell/Own Decision

“WE SHOULD SELL THE BOND”. If the Present Value of the Bond is less than the Par Value of the Bond, then we should sell the bond and else continue to own.