Question

# Consider a business loan maturing in three years that has three remaining annual payments in one,...

Consider a business loan maturing in three years that has three remaining annual payments in one, two, and three years. The annual payments are all equal to \$3 Million. While analyzing the loan, you are using a YTM equal to 10%.

Determine the duration of the loan and then, using this estimated duration and a duration analysis, predict the percentage change in the value of the loan after a 0.5 percentage point increase in the interest rate. You should assume that a one percentage point change in the rate is approximately equal to a one percent change in the rate.

 Year Cashflow(million) PV @10 PV Proption of bond value Propotion of Bond value *Time(yars) 1 3 0.909 2.727 0.365544698 0.365544698 2 3 0.8264 2.4792 0.332327985 0.66465597 3 3 0.7513 2.2539 0.302127317 0.906381952 7.4601 1 1.93658262
 Duration Years = 1.936583 Volatility             = Duration / (1+YTM) 1.936583/1.10 1.76053 1.76

Value of loan if interest rate incfreases to .5 percentage point thevalue of loan will decrease by .5*1.76 = .88 %

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