Definition

• Treasury bonds auctioning refers to a market-determined price system for investing in the government securities.
• Investors are invited to bid for offered securities by quoting their yields around a fixed coupon rate thus reflecting desired discount prices.
• The coupon rate is the interest percentage charged on the face or nominal value of all quoted securities.
• This interest is paid semi-annually.

Why Treasury Bond Auction?

The re-launch of treasury bonds in May 2001 introduced a better channel for government borrowing and debt management. Since then, performance has remained quite encouraging. Two main objectives were;

• Development of a Yield Curve and,
• Debt Restructuring. National Debt Office has now gone a step further to propose the Issuance of Fixed Coupon Rate Treasury Bonds by auction.

Purpose:

To establish a market-determined yield curve.

Strengths of Bond Auction

• Most efficient way the government can source funds, as the price is purely market- determined.
• Quite good for establishing and maintaining a stable market-determined yield curve.
• Gives an opportunity for investors to maximise profits/returns by competitively bidding for a desired rate of return.
• Best form of investment compared to real sector, especially in a depressed economy.
• Auction-based bonds are self-regulating. When market rates are high, prices are low and investors bid at a discount and when rates fall, prices rise and investors bid at a premium.
• Allows the market to determine acceptable margins within which secondary trading can be carried out.

General Formula for Bond Pricing

Where; P=Price of the bond/security
r=Yield To Maturity (YTM)
I=Interest amount based on a fixed coupon rate and face value (semi-annual)
n= Interest period (annually or semi-annually)

Yield To Maturity (YTM) - Yield refers to the returns from investing in government securities, corporate bonds or even equities. Yield to Maturity is the return an investor expects to gain by investing in a security (bonds) and holding it until maturity. Yield is also the measure of return on future cash flows.

Price - Price is the amount an investor pays for future cash flows. There is inverse relationship between the price and Yield. The higher the quoted Yield, the lower the price paid per face value. The reverse is true. Investors can either quote their yields at par, discount or at a premium.

Par - An Investor can buy a security at par. It is the face or nominal value of the security. For every Kshs 100.00 paid now, the borrower will return Kshs 100.00 upon maturity. This corresponds to the 13% coupon rate or yield at par. This is a security sold at par.

EXAMPLE 1:

Calculate the price (P) of a 3-year bond given the following:

Coupon rate =13%p.a
Investor quotes 13% yield to maturity
Face value =Kshs 100
Semi-annual Interest Amount, I =100*(13/2)/100=6.5 Interest periods=3*2=6 =6.103286385+5.730785338+5.381019097+5.05260009+4.744225437+4.4546718+68.53341188 = 100

Premium - Any Yield quoted below the coupon rate (par) corresponds to a premium price i.e. the price an investor pays is above par price. This means that if an investor pays Kshs 101.220 today, the borrower will refund Kshs 100.00 in future as agreed at 12.5% Yield to Maturity.

EXAMPLE 2:

Calculate the price (P) of a 3-year bond given the following:

Coupon rate =13%p.a
Investor quotes 12.5% yield to maturity
Face value =Kshs 100
Semi-annual Interest Amount, I =100*(13/2)/100=6.5 Interest periods=3*2=6 =6.117647059+5.757785467+5.419092204+5.1003220075+4.800303129+4.5179324+69.50665164 = 101.220

Discount - Any Yield quoted above coupon rate (par), corresponds to a discount price. It is the amount by which a security is priced below its theoretical price (par). For instance for Kshs 100.00 offered in future, an investor pays Kshs 97.617 if the Yield to Maturity is 14%.

EXAMPLE 3:

Calculate the price (P) of a 3-year bond given the following:
Coupon rate =13%p.a
Investor quotes 14% yield to maturity
Face value =Kshs 100
Semi-annual Interest Amount, I =100*(13/2)/100=6.5
Interest periods=3*2=6 =6.074766355+5.677351734+5.3059362+4.958818878+4.634410167+4.3312245+66.63422238 = 97.617

NB: Refer to the table below generated from the formula above.