Assume Chen Inc. has an outstanding bond with the following characteristics: 10

Question

Assume Chen Inc. has an outstanding bond with the following characteristics: 10 years to maturity; 5% coupon paid annually;
yield = 4%; par value = $1000. The bond has a conversion ratio of 20.

1. Suppose you have a 10-year mortgage for $100,000 with annual payments beginning in exactly one year at an interest rate of 6%. What is your annual payment?

2. Suppose you have a 10 year mortgage for $100,000 with annual payment beginning today at an interest rate of 6%. The mortgage also requires a balloon payment (payment on the last date) of $50,000. What is your annual payment?

3. Suppose you have a 10 year mortgage for $100,000 with annual payment beginning in exactly one year at an interest rate of 6%. What is your outstanding mortgage balance after you have made 3 payments?

Suppose we have $1 million invested in 10-year zero coupon bonds and $1 million invested in 4-year zero coupon bonds. If interest rates fall by 1%, approximately what will be the percentage change in this investment’s value?

Explanation / Answer

Question 1. Annual Payment = P x r(1+r)^n/((1+r)^n-1) Here P = 100,000 n = 10 years r = 6/100 = 0.06 Hence Annual EMI = 100,000 x 0.06 x 1.06^10/(1.06^10-1) Or EMI = 100,000 x 0.06 x 1.79085/0.79085 Therfore EMI = 100,000 x 0.13587 = 13586.80 Question 2 Let the EMI amount be A. Therefore A = (P-A) x r(r+1)^(n-1)/((1+r)^(n-1)-1) Hence A = (100,000-A) x 0.06 x 1.06^9/(1.06^9-1) OR A =( 100,000-A) x 0.06 x 1.689479/(1.689479-1) Or A = (100,000 - A ) x 0.101369/0.689479 Or, A = (100000-A) x 0.147022 Or A = 100,000 x 0.147022 - A x 0.147022 OR A +0.147022A = 14702.2 Therefor A = 14702.20/(1.147022) Hence A = 12,817.71 Question 3 Year Beginning Interest @6% Installment Outstanding 1 100000 6000 13586.8 92413.20 2 92413.20 5544.792 13586.8 84371.19 3 84371.19 5062.27152 13587.8 75845.66 4 75845.66 4550.739811 13588.8 66807.60 5 66807.60 4008.4562 13589.8 57226.26 6 57226.26 3433.575572 13590.8 47069.04 7 47069.04 2824.142106 13591.8 36301.38 8 36301.38 2178.082633 13592.8 24886.66 9 24886.66 1493.19959 13593.8 12786.06 10 12786.06 767.1635659 13594.8 -41.58 Outstanding After 3 Installment payment = $75,845.66

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