Question

9. Consider the following bond quotes for ABC and XYZ Corp.
It is June 27, 2020. You must provide equations for each of the questions.
Issuer Name Coupon Maturity Last Change Yield%
ABC Corp. 4.375 12/27/2038 92.5133 -0.315 ?????
XYZ Corp 0.000 06/27/ 2031 46.9150 +0.234 ?????
Note that yields for ABC and XYZ Corp bonds are all semiannually compounded.
a. (6 points) Supply the missing information (yield%) for each of the bonds.
b. (6 points) What are the current yield and expected capital gains yield for the next
year for ABC Corp bond?
c. (2 points) What was the yesterday’s price for ABC Corp bond?

Could you explain the question in detail with formula plz! I don't understand others poster answers. Thanks!

Answer 1

a.Yield % = $ annual coupon/Current market price

For ABC Corp.

4.375/92.5133=

4.73%

For XYZ Corp.

No coupons -- so $ 0

But some bond quotes, have YTM, ie Yield to Maturity , on their quotes

which can be calculated as follows:

Yiled is the Yield to maturity, ie. YTM

ABC Corp.

Current market price is given as--- 92.5133

Pmt.=Semi-annual $ coupon=4.375%*100=4.375/2= 2.1875

n=no.of semi-annual periods pending till maturity--ie. From Jun 27,2020 to Dec 27,2038---- 37 s/a periods

FV=Face value= $ 100

So,using the formula to find the current market price of the bond

which is the Present Value of its coupon cashflows PLUS face value to be received at maturity

ie. PV/Price=(Pmt.*(1-(1+r)^-n)/r)+(FV/(1+r)^n

here, r, is the semi-annual yield , we need to find out--- ??

so, with this we will equate the available values.

92.5133=(2.1875*(1-(1+r)^-37)/r)+(100/(1+r)^37

Solving for r, we get the semi-annual Yield/YTM as

2.50%

The annual yield/YTM on the bond=

(1+2.5%)^2-1=

5.06%

XYZ Corp.

Current market price is given as--- 46.9150

Pmt.=Semi-annual $ coupon=0

n=no.of semi-annual periods pending till maturity--ie. From Jun 27,2020 to Jun 27,2031---- 22 s/a periods

FV=Face value= $ 100

So,using the formula to find the current market price of the bond

which is the Present Value of its face value to be received at maturity

ie. PV/Price=(FV/(1+r)^n

here, r, is the semi-annual yield , we need to find out--- ??

so, with this we will equate the available values.

46.9150=100/(1+r)^22

Solving for r, we get the semi-annual Yield/YTM as

3.50%

The annual yield/YTM on the bond=

(1+3.5%)^2-1=

7.12%

b To calculate both for ABC Corp. , we need to know the bond's price next year, ie. After 2 coupons

So, using the above formula, at 2.5% semi-annual YTM

Price (end of next yr.)=(2.1875*(1-(1.025)^-35)/0.025)+(100/(1+0.025)^35)

92.7671

So, the expected current yield over the next year=

4.375/92.7671=

4.72%

& the expected Capital gains Yield=

(Price , end of next yr.-Current price)/Current price

(92.7671-92.5133)/92.5133=

0.27%

c. Yesterday’s price for ABC Corp bond

92.5133+0.315=

92.8283

Yesterday's price has decreased by 0.315 (denoted as -0.315) under change column & the result is the last price