Q50971d The bonds of the Premier Company Ltd (PCL) are currently selling at Rs.10, 800. Assuming (i) coupon rate of interest, 10 per cent, (ii) par value, Rs 10,000, (iii) maturity 10 years and (iv) annual interest payment, compute the YTM.

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Solution:

Substituting the values in following Equation

B = I x (PVIFA_kdn) + M x

Rs 10,800 = [Rs 1,000 x (PVIFA_{kd, 10}) + Rs 10,000 x (PVIF_{kd, 10})

If k_d= 10 per cent, that is, equal to’ the coupon rate, the value of the bond would be Rs 10,000. Since the value of the bond is Rs 10,800, the k_d must be less than 10 per cent.

Using 9 per cent discount rate gets

= [Rs 1,000 x (PVIFA_9,10) + Rs 10,000 x (PVIF_9,10)

= (Rs 1,000 x 6.418) + (Rs 10,000 x 0.422) = Rs 6,418 + Rs 4,220 = Rs 10,638

Since the value of the bond (Rs 10,638) at k_d = 9 per cent is less than Rs 10,800 (current market price). Try a lower rate of discount (kd). Using 8 per cent, we get

(Rs 1,000 x 6.710) + (Rs 10,000 x 0.463)

= Rs 6,710 + Rs 4,630 = Rs 11,340

Since the bond value (Rs 11,340) is higher than the current price of Rs 10,800, the k_d (YI’M)

between 8 and 9 per cent. The exact value can be found by interpolation, which is 8.77% `

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