The value of a bond- or any asset, real or financial- is equal to the present value of the cash flows expected from it. Hence, determining the value of a bond requires:
Given these assumptions, the cash flow for a non-callable bond comprises an annuity of a fixed coupon interest payable annually and the principal amount payable at maturity. Hence the value of a bond is:
P =nΣ (t=1) C/ (1 + r)t + M/(1 + r)n (10.1)
Where P = value (in rupees)
n = number of years
C = annual coupon payment (in rupees)
r = periodic required return
M = maturity value
t = time period when the payment is received.
Since the stream of semi-annual coupon payments is an ordinary annuity, we can apply the formula for the present value of an ordinary annuity. Hence the bond value is given by the formula:
P = C × PVIFAr, n + M × PVIFr, n (10.1 a)
To illustrate how to compute the value of a bond, consider a 10-year, 12 per cent coupon bond with a par value of Rs. 1000. Let us assume that the required yield on this bond is 13 per cent. The cash flows for this bond are as follows:
The value of the bond is:P = 120×PVIFA13%, 10 yr + 1,000×PVIF13%, 10yr = 120 × 5.426 + 1000 × 0.295 = 651.1 + 295 = Rs. 946.1
Bond values with semi-annual interest
Most bonds pay interest semi-annually. To value such bonds, we have to work with a unit period of six months, and not one year. This means that the bond valuation equation has to be modified along the following lines:
2n = maturity period expressed in terms of half-yearly periods. Illustration Illustration 10.1: Consider a 8-year, 12 per cent coupon bond with a par value of Rs. 100 on which interest is payable semi-annually. The required return on this bond is 14 per cent.
Solution: Applying Eq. 10.2, the value of the bond is:P =16 Σ (t=1) 6/(1.07)t + 100/ (1.07)+ 16 = 6 (PVIFA7%, 16 yr) + 100 (PVIF7%, 16 yr) = Rs. 6 (9.447) + Rs. 100 (0.388) = Rs. 95.5.
Illustration 10.2: At an annual rate of compounding of 9 per cent, how long does it take for a given sum to become double and triple its original value?
Solution: Pt = P0 (1 + r)n
When the n value is not given it can be solved by using log lnn ln (1 + r) = ln Pt n ln (1 + 0.09) = ln 2 n. ln 0.0862 = ln 0.6931 n = 8.04 years To triple n ln (1 + 09) = ln 3 n. ln 0.0862 = ln 1.0986 = 12.74 years
Illustration 10.3: Of the following which amount is worth more at 16 per cent; Rs. 1000 today or Rs. 2100 after five years.
Solution: The present worth of Rs. 2100 = 2100 (1 + r) n = 2100 (1 + 0.16)5
= 2100 × 0.476 = 999.60
The present worth of Rs. 2100 is Rs. 999.60 which is less than Rs. 1,000. Hence Rs. 2100 after five years is not worthful.
Illustration 10.4: Determine the price of Rs. 1,000 zero coupon bond with yield to maturity of 18 per cent and 10 years to maturity. What is YTM of this bond if its price is Rs. 220?
Illustration 10.5: Arvind considers Rs. 1000 par value bond bearing a coupon rate of 11% that matures after 5 years. He wants a minimum yield to maturity of 15%. The bond is currently sold at Rs. 870. Should he buy the bond?
Solution:P0 =Coupon / (1+ Y) + … + Coupon + Face value/ (1+ Y)5 (Or) P0 = (Coupon) (PVIFA, n) + (Principal amount) (PVIF/k,n) P0 = 110 (PVIFA 15%, 5 years) + 1000 (PVIF/15%, 5 yrs) = 110 (3.352) + 1000 (0.497) = 368.7 + 497 = 865.7.
At Arvind’s anticipated minimum yield of 15% the price should be Rs. 865.70 but the market price is higher. Hence, he should not buy.
Illustration 10.6: Anand owns Rs. 1,000 face value bond with five years to maturity. The bond has an annual coupon of Rs. 75. The bond is currently priced at Rs. 970. Given an appropriate discount rate of 10%, should Anand hold or sell the bond?
Solution:P0 = Coupon (PVIFA k, n) + Principal amount (PVIF k, n) = 75 (PVIFA 10%, 5 yrs) + 1000 (PVIF 10%, 5 yrs) = 75 × 3.7908 + 1000 (0.6209) = Rs. 284.31 + 620.9 = Rs. 905.21.
The market price Rs. 970 is higher than the estimated price Rs. 905.2. It is better for Anand to sell the bond.
Security Analysis and Investment Management Related Interview Questions
|Financial Accounting&Financial Statement Analysis Interview Questions||Network Security Interview Questions|
|Management Accounting Interview Questions||Risk Management Interview Questions|
|Finance Interview Questions||Information Security Audits Interview Questions|
|RSA Archer GRC Interview Questions||Business Investments Interview Questions|
|Accounting Principles Interview Questions||Investment Banking Interview Questions|
|Information Security Analyst Interview Questions|
Security Analysis and Investment Management Related Practice Tests
|Financial Accounting&Financial Statement Analysis Practice Tests||Network Security Practice Tests|
|Management Accounting Practice Tests||Risk Management Practice Tests|
|Finance Practice Tests||Information Security Audits Practice Tests|
|Accounting Principles Practice Tests|
Security Analysis And Investment Management Tutorial
Introduction To Security Analysis
Risk And Return Concepts
New Issue Market (nim)
Stock Exchanges In India – Operations
Listing Of Securities
Stock Brokers And Other Intermediaries
Stock Market Indices
Valuation Of Fixed Income Securities Or Valuation Of Bonds
Valuation Of Variable Income Securities Or Equity Share Valuation
Fundamental Analysis: I
Fundamental Analysis: Ii
Efficient Market Theory
Securities And Exchange Board Of India And Stock Market Regulation
All rights reserved © 2018 Wisdom IT Services India Pvt. Ltd
Wisdomjobs.com is one of the best job search sites in India.