Question

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.

Answer 1

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 %