# JAIIB AFB Unit 2 - Calculation of YTM (Part 1)

## JAIIB AFB Unit 2 - Calculation of YTM (Part 1) (Year: 2019)

Bond Value

Debt

DEBT means a sum of money due by certain and expresses agreement. In a less technical sense, it means a claim for money. Loans from banks or financial institutions are one of the popular forms of debt.

Bonds

Debt capital consists of mainly bonds and debentures. The holder of debt capital does not receive a share of ownership of the company when they provide funds to the firm. Rather, when a company first issues debt capital, the providers of debt capital purchase a debenture, which involves lending money to the firm. In return for loaning this money, bond holders have a right to certain guaranteed payments during the life of the bond.

For example : a company issued a bond of a face value of Rs. 100 carrying a coupon rate of 10 per cent for ten years. This entitles the bondholder to receive Rs. 10 (10 per cent of Rs. 100) for ten years as interest. At the end of tenth year, the bondholder is also entitled to receive back the invested amount of Rs. 100. Irrespective of the level of profits or losses, which company makes during that period of ten years, the bondholder is entitled to receive the coupon interest during that period.

TERMS ASSOCIATED WITH BONDS

Face Value: Also known as the par value and stated on the face of the bond. It represents the amount borrowed by the firm, which it promises to repay after a specified period.

Coupon rate: A bond carries a specific rate of interest, which is also called as the coupon rate.

Maturity: A bond is issued for a specified period. It is to be repaid on maturity.

Redemption Value: The value, which the bondholder gets on maturity, is called the redemption value. A bond is generally issued at a discount (less than par value) and redeemed at par.

Market Value: A bond may be traded on a stock exchange. Market value is the price at which the bond is usually bought or sold in the market.

Bond Value

A bond, whose par value is Rs. 1,000, bears a coupon rate of 12 per cent and has a maturity period of 3 years. The required rate of return on the bond is 10 per cent. What is the value of this bond?

Solution

Annual interest payable = 1,000 * 12% = 120
Principal repayment at the end of 3 years = Rs. 1,000
The value of the bond
= 120 (PVIFA 10%, 3 yrs) + Rs. 1,000 (PVIF 10%, 3 yrs)
= 120 (2.487)+1,000 (0.751)
= 298.44 + 751
= Rs. 1,049.44

A bond, whose par value is Rs. 1000, bears a coupon rate of 12 per cent payable semi-annually and has a maturity period of 3 years. The required rate of return on bond is 10 per cent. What is the value of this bond?

Solution

Semi-annual interest payable = 1,000 x 12 per cent/2= 60
Principal repayment at the end of 3 years = Rs. 1,000

The value of the bond
= 60 (PVIFA 10%/2, 6 pds) + Rs. 1,000 (PVIF 10%/2, 6 pds) =
60 (5.0746) + 1,000 (0.746) = 304.48 + 746 = 1,050.48

The face value of the bond is Rs. 1,000, coupon rate is 11 per cent, years to maturity is seven years. The required rate of return is 13 per cent, and then the present value of the bond is

110 x PVIFA (13 per cent, 7) + 1,000 (PVIF 13 per cent, 7)
110(4.423)+1,000 (0.425) = 911.53

One year from now, when the maturity period will be six years, the present value of the bond will be

110 x PVIFA (13 per cent, 6) + 1,000 (PVIF 13 per cent, 6)
110 (3.998) + 1,000 (0.480) = 919.78

Similarly, when maturity period is 5, 4, 3, 2, 1 the Bond value will become 929.87, 940.14, 952.71, 966.48, 982.35, respectively.