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How to calculate types of bond Yield with examples?


Yield to maturity: The bondholder earn return on bond after a fixed period of time is known as Yield to maturity. There are two ways to calculate yield to maturity first method is:
YTM = C / (1+r) 1 + C / (1+r) 2... + M / (1+r) n
And the second method is:
YTM = (C + ((F – P)/ n)) / F + P / 2
Where,
C = Coupon amount
F = Face value
P = Market price
N = number of years
M = maturity value

Current Yield: It is calculate by annual interest rate and market price of a bond. It does not consider the time value of money and it also doesn’t show the capital gain or loss earn by an investors.

Formula:
Current Yield = Annual interest rate / Market price

Yield to call: It is a right not an obligation of an issuer to call back its bond at a fixed price and on fixed date before the maturity of the bond. The bondholder should keep the bond till the call date. The yield to call is higher than yield to maturity.

Formula:
Yield to call = (Annual coupon amount (Call price – market price) / number of years till call date) / (call price + market price) / 2

Example: Find out the current yield if the bond selling price is Rs.990. The coupon rate is 8% of 10 year bond. The face value of bond is Rs. 1, 000.

Solution: Current Yield = Annual interest rate / Market price
= 80 / 990
= 0.08 or 8%
Example: Mr. X has purchased 5 year bond of Rs. 1, 160. The coupon rate is 7% semi-annually. The par value of bond is Rs. 1, 000. Find out the yield to maturity.

Solution: YTM = (C + ((F – P)/ n)) / F + P / 2
= (35 + ((1, 000 – 1,160)/ 10)) / 1, 000 + 1,160/ 2
= (35 – 16) / 1, 080
= 19 / 1, 080
= 1.75%

Let’s assume r =1.75% in method second:
YTM = C / (1+r) 1 + C / (1+r) 2 +... M / (1+r) n
1, 160 = 35 / (1+r) 1 + 35 / (1+r) 2 + 35 / (1+r) 3 + 35 / (1+r) 4 + 35 / (1+r) 5 + 35 / (1+r) 6 + 35 / (1+r) 7+ 35 / (1+r) 8 + 1, 035 / (1+r) 9 + 1035 / (1+r) 10
= 35 / (1.0175) 1 + 35 / (1.0175) 2 + 35 / (1.0175) 3 + 35 / (1.0175) 4 + 1, 035 / (1.0175) 5 + 35 / (1.0175) 6 + 35 / (1.0175) 7 + 35 / (1.0175) 8 + 35 / (1.0175) 9 + 1, 035 / (1.0175) 10
= 34.398 + 33.81 + 33.238 + 32.655 + 32.092 + 31.540 + 30.998 + 30.466 + 29.942 + 870.186
= 1, 160
= 1,160 – 1,160
= 0
Yield to maturity = 1.75%

Example: An investor purchased a 10 year bond on Rs. 980@ 8.2% annually. But after 2 years bond is call back at the price of Rs.1, 010. Find out the yield to call if the face value of bond is Rs. 1, 000.

Solution: yield to call = (Annual coupon amount + (Call price – market price) / number of years till call date) / (call price + market price) / 2
= (82 + (1, 010 – 980) /2) / (1, 010 +980) / 2
= 82 + 15 / 995
= 97 / 995
= 9.74%



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