Finance Numericals

Example: Find out the duration of a bond if the interest 9.8% p.a. semi-annually for 4 year bond. The coupon rate is 9% p.a. semi- annually. The face value of bond is Rs. 10, 000. Solution: The semi annual yield rate = 9.8/200 = 0.049 The semi- annual coupon rate = 9/200 = 0.045 The coupon payment = 0.045*10000 = Rs. 450 Year Cash flows Interest rate @ 4.9% Present value of cash flows (C/ (1+r) n Present value of cash flows * time 1 450 1.049 428.979 428.979 2 450 1.100 409.090 818.18 3 450 1.154 389.948 1, 169.844 4 450 1.210 371.900 1, 487.6 5 450 1.270 354.330 1, 771.65 6 450 1.332 337.837 2, 027.022 7 450 1.397 322.118 2, 254.826 8 10, 450 1.466 7, 128.240 57, 025.62 Total 9, 742.442 66, 98

Bond Duration: It is expressed in number of years. It tells the time an investment in a debt security will take to repay its value.   There is an inverse relationship between bond price and interest rate. It means when the interest rate increases then there will be the decrease in bond price. There are two types of duration Macaulay duration and modified duration. Macaulay Duration is a weighted average maturity period of all cash flows of a bond. Formula : D = Ʃ t t=1 PV CF * t / Ʃ t t=1 PV CF Where, D = Duration PV CF = Present Value of all cash flows T = Time period Factors that affects the duration of a bond: Maturity: There is a direct relationship between maturity and duration.   If the maturity of a bond increases then there is also increase in duration of bond. Coupon rate: There is an inverse relationship between coupon rate and duration. It means if the coupon rate increases then there will be increase in duration. The duration of zero c

The bond price does not remain stable. The price of bond is important for investor who wants to invest in bond market or who wants to sell the bond before maturity. To determine the fair price of the bond is calculate by discounting the cash flow to ascertain the present value of all the cash flows. Formula: P = Ʃ n n=1 C / (1+r) t +... M / (1+r) n There is another method which makes easy to calculate bond price is: P = C [1-(1/ (1+r) n ) / r] + M / (1+r) n Or P = C /r [1-(1/ (1+r) n )] + M / (1+r) n Where, P = Bond Price C = Coupon amount r = required rate of return M = Maturity value n = Number of years If the coupon bond paid in semi-annually then the formula will be: P = C /r [1- (1/ (1+0.5r) 2n )] + M/ (1+0.5r) 2n Or P = C /2 [1- (1/ (1+0.5r) 2n )/ r/2] + M/ (1+0.5r) 2n Zero coupon bonds are a bond which does not give any interest during the bond period. The benefit of the bond is that the investor can purchase it at discount on fair pri

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