Question

Discuss the genralized principle in valuing a financial asset.
Calculate price of bonds. Show your fomular in calculation.

Answer 1

Solution:- Valuation is the process of determining the fair value of a financial asset. The process is also referred to as “valuing” or “pricing” a financial asset. The fundamental principle of valuation is that the value of any financial asset is the present value of the expected cash flows. This principle applies regardless of the financial asset. Thus, the valuation of a financial asset involves the following three steps:

(1) estimate the expected cash flows;

(2) determine the appropriate interest rate or interest rates that should be used to discount the cash flows; and

(3) calculate the present value of the expected cash flows using the interest rate or interest rates.

Bond pricing is an empirical matter in the field of financial instruments. The price of a bond depends on several characteristics inherent in every bond issued. These characteristics are:

• Coupon, or lack thereof
• Principal/par value
• Yield to maturity
• Periods to maturity

Bond Pricing: Coupons

A bond may or may not come with attached coupons. A coupon is stated as a nominal percentage of the par value (principal amount) of the bond. Each coupon is redeemable per period for that percentage. For example, a 10% coupon on a $1000 par bond is redeemable each period.

A bond may also come with no coupon. In this case, the bond is known as a zero-coupon bond. Zero-coupon bonds are typically priced lower than bonds with coupons.

Bond Pricing: Principal/Par Value

Each bond must come with a par value that is repaid at maturity. Without the principal value, a bond would have no use. The principal value is to be repaid to the lender (the bond purchaser) by the borrower (the bond issuer). A zero-coupon bond pays no coupons but will guarantee the principal at maturity. Purchasers of zero-coupon bonds earn interest by the bond being sold at a discount to its par value.

A coupon-bearing bond pays coupons each period, and a coupon plus principal at maturity. The price of a bond comprises all these payments discounted at the yield to maturity.

Bond Pricing: Yield to Maturity

Bonds are priced to yield a certain return to investors. A bond that sells at a premium (where price is above par value) will have a yield to maturity that is lower than the coupon rate. Alternatively, the causality of the relationship between yield to maturity and price may be reversed. A bond could be sold at a higher price if the intended yield (market interest rate) is lower than the coupon rate. This is because the bondholder will receive coupon payments that are higher than the market interest rate, and will, therefore, pay a premium for the difference.

Bond Pricing: Periods to Maturity

Bonds will have a number of periods to maturity. These are typically annual periods, but may also be semi-annual or quarterly. The number of periods will equal the number of coupon payments.

The Time Value of Money

Bonds are priced based on the time value of money. Each payment is discounted to the current time based on the yield to maturity (market interest rate). The price of a bond is usually found by:

P(T0) = [PMT(T1) / (1 + r)^1] + [PMT(T2) / (1 + r)^2] … [(PMT(Tn) + FV) / (1 + r)^n]

Where:

• P(T0) = Price at Time 0
• PMT(Tn) = Coupon Payment at Time N
• FV = Future Value, Par Value, Principal Value
• R = Yield to Maturity, Market Interest Rates
• N = Number of Periods