Bond valuation
The process of bond valuation is based on the fundamental concept that the current price of a security can be determined by calculating the present value of the cash flows that the security will generate in the future.
There is a consistent and predictable relationship between a bondâÂÂs coupon rate, its par value, a bondholderâÂÂs required return, and the bondâÂÂs resulting intrinsic value. Trading at a discount, trading at a premium, and trading at par refer to particular relationships between a bondâÂÂs intrinsic value and its par value. These result from the relationship between a bondâÂÂs coupon rate and a bondholderâÂÂs required rate of return.
Remember, a bondâÂÂs coupon rate partially determines the interest-based return that a bond (might/will)...........pay, and a bondholderâÂÂs required return reflects the return that a bondholder(would like/is obligated).............to receive from a given investment.
The mathematics of bond valuation imply a predictable relationship between the bondâÂÂs coupon rate, the bondholderâÂÂs required return, the bondâÂÂs par value, and its intrinsic value. These relationships can be summarized as follows:
| ⢠| When the bondâÂÂs coupon rate is equal to the bondholderâÂÂs required return, the bondâÂÂs intrinsic value will equal its par value, and the bond will trade at par. |
| ⢠| When the bondâÂÂs coupon rate is greater to the bondholderâÂÂs required return, the bondâÂÂs intrinsic value will (be less than/exceed/equal)................
its par value, and the bond will trade at a premium. |
| ⢠| When the bondâÂÂs coupon rate is less than the bondholderâÂÂs required return, the bondâÂÂs intrinsic value will be less than its par value, and the bond will trade (at a premium/at par/at a discount)............................. |
For example, assume Liam wants to earn a return of 5.00% and is offered the opportunity to purchase a $1,000 par value bond that pays a 8.75% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bondâÂÂs intrinsic value(Link to the formula : http://q4pws.aplia.com/q4pws/rest/1.0/image/image9594/img.png?data=q4%3AREMOTE_URL%3Ahttp%3A%2F%2Faplia-prod-webjboss-372923237.us-east-1.elb.amazonaws.com%2Fproblemsetassets%2Fq4_export%2Ffinance%2Fq4problems%2F3061500.08.xml%2CV5%2C291%2C1%2CSTUDENT%2CSTUDENT%2C0%2Cq4pws-aplia-7.6.4-G2f8d8babd91356776c6b2ec65d5e2a2153b4d346-B36-2015.12.16-03%3A57-PM-PST&oauth_signature=jG%2Fu63kSgI9xRhXign5JItWfpAQ%3D&oauth_version=1.0&oauth_nonce=3573483745&oauth_signature_method=HMAC-SHA1&oauth_consumer_key=q4-callback&oauth_timestamp=1454953012
Complete the following table by identifying the appropriate corresponding variables used in the equation.
unknown --------------------- variable name ---------------------variable value
A --------------------- (Bondholders required return/Bonds annual coupon payment/Bonds semiannual coupon payment)---------------------($21.88/$65.63/$87.50/$43.75)
B--------------------- (Bonds par value/bonds annual coupon payment/semiannual coupon payment) ---------------------$1000
C--------------------- semiannual required return -------------------- ($5.75/$3.81/$4.38/$2.5)
Based on this equation and the data, it is (reasonable/unreasonable)...................to expect that LiamâÂÂs potential bond investment is currently exhibiting an intrinsic value greater than $1,000.
Now, consider the situation in which Liam wants to earn a return of 5.75%, but the bond being considered for purchase offers a coupon rate of 8.75%. Again, assume that the bond pays semiannual interest payments and has three years to maturity. If you round the bond's intrinsic value to the nearest whole dollar, then its intrinsic value of ($757/$866/$1407/$1082).................is (equal to/greater than/less than).............................its par value, so that the bond is trading at (par/a discount/a premium)..............................
Given your computation and conclusions, which of the following statements is true?
(a)When the coupon rate is greater than LiamâÂÂs required return, the bond should trade at a discount.
(b)A bond should trade at a par value when the coupon rate is greater than Liam's required return
(c) When the coupon rate is greater than LiamâÂÂs required return, the bond's intrinsic value will be less than it's par value
(d) When the coupon rate is greater than LiamâÂÂs required return, the bond should trade at a premium
