Question

Suppose you are considering investing in a Telus Corp. corporate bond with a ​$15,000 face value maturing on July​ 23, 2020. The​ bond's coupon or bond rate is 5.05 ​percent, and interest is paid​ semi-annually. The current required market rate or yield to market​ (YTM) for a bond of this type is 2.74 percent.

​(a) Explain if and why this bond should sell at​ par, at a​ premium, or at a discount.

​(b) Determine the purchase price or​ "clean price" for this bond if the purchase was made on July​ 23, 2014.

​(c) Determine the cash price or​ "dirty price" for this bond if the purchase is instead made on September​ 28, 2014.

Answer 1

(a)This bond will sell at a premium.

Whenever a new bond is issued in the market it is always issued at par value, not at any premium or discount. A bond became premium/discount once it starts trading in the secondary market. A bond trading above its par value will be known as premium bond as it offers coupon rate higher than YTM and investor's demand for such a bond will high, which will increase the price of the bond.

If Coupon rate > YTM, the bond will sell over par value or at a premium.

If coupon rate = YTM, the bond will sell at par.

If coupon rate < YTM, the bond will sell below par value or at a discount.

(b)

Step1:- We will discount all the future value to 23rd July 2014.

Step 2:- We will not consider coupon payment received on 23rd July 2014 as this coupon is already received by the seller.

FV 15000 Coupon Rate 5.05% YTM 2.74% Coupon Amour 378.75 =C1*E1/2 Payment PV of payment 23-Jul 378.75 23-Jan 378.75 373.6312518 =C5/(1+$C$2/2)^A5 2 23-Jul 378.75 368.5816828 =C6/(1+$C$2/2)^A6 23-Jan 318.75 378.75 305. 363.6003579 =C7/(1+$C$2/2)^AZ 4 23-Jul 378.75 358.6863548 =C8/(1+$C$2/2)^A8 5 23-Jan 378.75 353.8387638 =C9/(1+$C$2/2)^A9 6 23-Jul 378.75 349.0566872 =C10/(1+$C$2/2)^A10 23-Jan 378.75 344.3392396 =C11/(1+$C$2/2)^A11 8 23-Jul 378.75 339.6855476 =C12/(1+$C$2/2)^A12 9 23-Jan 378.75 335.0947495 =C13/(1+$C$2/2)^A13 23-Jul 378.75 330.5659954 =C14/(1+$C$2/2)^A14 23-Jan 378.75 326.0984466 =C15/(1+$C$2/2)^A15 12 23-Jul 15378.75 13061.93984 =C16/(1+$C$2/2)^A16 Dirty price 16905.11891 7

Step 3:- As the seller is selling the bond on one of the coupon dates, there would be no accrued interest.

Step 4: Dirty Price = Clean Price + Accrued Interest (Accrued interest = 0)

Dirty Price = Clean Price = 16905.11891 Answer

(c)

The price of the bond on 23rd July 2014 =16905.11891

The price of the bond on 28th Sept 2014 = 16991.32563

Dirty price = 16991.32563
Accrued Interest = 140.9791667 (Interest accrued between 28th Sept 2014 and 23rd July 2014)

Clean Price = 16850.34646

А в FV 15000 Coupon Rate 5.05% YTM 2.74% Coupon Amour 378.75 =C1*E1/2 Payment PV of payment 23-Jul 378.75 28-Sep 23-Jan 378.75 373.6312518 =C6/(1+$C$2/2)^A6 23-Jul 378.75 368.5816828 =C7/(1+$C$2/2)^AZ 23-Jan 378.75 363.6003579 =C8/(1+$C$2/2)^A8 23-Jul 378.75 358.6863548 =C9/(1+$C$2/2)^A9 23-Jan 378.75 353.8387638 =C10/(1+$C$2/2)^A10 23-Jul 378.75 349.0566872 =C11/(1+$C$2/2)^A11 7 23-Jan 378.75 344.3392396 =C12/(1+$C$2/2)^A12 23-Jul 378.75 339.6855476 =C13/(1+$C$2/2)^A13 9 23-Jan 378.75 335.0947495 =C14/(1+$C$2/2)^A14 10 23-Jul 378.75 330.5659954 =C15/(1+$C$2/2)^A15 11 23-Jan 378.75 326.0984466 =C16/(1+$C$2/2)^A16 12 23-Jul 15378.75 13061.93984 =C17/(1+$C$2/2)^A17 Price of bond on 23 July 2014 16905.11891 Price of the bond on 28th sept 2014 16991.32563 =D18*(1+(C2/2)* (B5-B4)/180) Dirty Price 16991.32563 Accrued Interest 140.9791667 =E2*(B5-B4)/180 Clean Price 16850.34646! =D20-D21 14 21