Question

(Bond valuation​ relationships) ​Stanley, Inc. issues 15​-year ​$1 comma 000 bonds that pay ​$85 annually. The market price for the bonds is ​$960. The​ market's required yield to maturity on a​ comparable-risk bond is 9 percent. a. What is the value of the bond to​ you? b. What happens to the value if the​ market's required yield to maturity on a​ comparable-risk bond​ (i) increases to 11 percent or​ (ii) decreases to 7 ​percent? c. Under which of the circumstances in part b should you purchase the​ bond? a. What is the value of the bond if the​ market's required yield to maturity on a​ comparable-risk bond is 9 ​percent?

Answer 1

Answer:

a) The value of the bond (to you) is  959.6965579

b)

1. if the value of the​ market's required yield to maturity on a​ comparable-risk bond​ increases to 11 percent ; we have the value to be 820.2282606  
2.  if the​ market's required yield to maturity on a​ comparable-risk bond decreases to 7 ​percent; we have the value to be 1136. 61871

c)  Yield to maturity is the expected return on holding the bond till maturity

Thus, Bonds should be purchased when the yield to maturity is the highest ; As such!, if the yield to maturity on a comparable - risk bond decrease to 7%.

You should purchase the Stanley bonds at the current market price of $960.

Explanation:

Given that:

Par Value (F) = $1000

Interest Rate ( annual coupon rate) = $85

Market demand return ( yield to maturity) = 9% = 0.09

Time of maturity = 15 years

a. What is the value of the bond to​ you?

The value of the bond can be calculated as follows:

= $\frac{annual coupon}{yield}*(1-\frac{1}{(1+yield)^t} )(\frac{Par Value}{(1+yield)^t} )$

= $\frac{85}{0.09}*(1-\frac{1}{(1+0.09)^{15}} )(\frac{1000}{(1+0.09)^{15}} )$

= 959.6965579

Thus, the value of the bond to you =  959.6965579

b. What happens to the value if the​ market's required yield to maturity on a​ comparable-risk bond​ increases to 11 percent .

If increase to 11 % occurs:

we have :

= $\frac{85}{0.11}*(1-\frac{1}{(1+0.11)^{15}} )(\frac{1000}{(1+0.11)^{15}} )$

= $\frac{85}{0.11}*(1-\frac{1}{(1.11)^{15}} )(\frac{1000}{(1.11)^{15}} )$

= 820. 2282606

Hence, if the value of the​ market's required yield to maturity on a​ comparable-risk bond​ increases to 11 percent ; we have the value to be 820. 2282606

What happens to the value if the​ market's required yield to maturity on a​ comparable-risk bond decreases to 7 ​percent?

If decrease to 7% occurs:

= $\frac{85}{0.07}*(1-\frac{1}{(1+0.07)^{15}} )(\frac{1000}{(1+0.07)^{15}} )$

= $\frac{85}{0.07}*(1-\frac{1}{(1.07)^{15}} )(\frac{1000}{(1.07)^{15}} )$

= 1136. 61871

c) Under which of the circumstances in part b should you purchase the​ bond?

Yield to maturity is the expected return on holding the bond till maturity

Thus, Bonds should be purchased when the yield to maturity is the highest ; As such!, if the yield to maturity on a comparable - risk bond decrease to 7%.

You should purchase the Stanley bonds at the current market price of $960.