Solving for exponent manipulation

[[email protected]]

Hi,

According to the hull notes on swaps we can solve the following for the value of r.

2.46+2.41+2.35+ e^(-2r) = 100 which gives an r = 4.99.

Can someone step me through this solution, and/or provide a reference in the notes or elsewhere on the rules with respect to such problems.

Thanks in advance.

 

[[email protected]]

e^(-2r)=100-2.46-2.41-2.35=92.78
-2r=ln(92.78) which will not yield the answer.

So, i guess, you are missing something in the above eqn.

Alan

 

[David Harper CFA FRM]

Brian,

The notes (according to my read; page 76) give:

2.5*exp(-0.5*3%) + 2.5*exp(-1*3.5%) + 2.5*exp(-1.5*4%) + 102.5*exp(-2*R) = 100, such that
2.46 + 2.41 + 2.35 + 102.5*exp(-2*R) = $100; i.e., PV of cash flows, including final $100, equals par $100, therefore:
102.5*exp(-2*R) = $100 - 2.46 - 2.41 - 2.35;
102.5*exp(-2R) = 92.7688;
exp(-2R) = 92.7688/102.5; take natural log of both sides:
LN[exp(-2R)] = LN[92.7688/102.5];
-2R = LN[92.7688/102.5];
R = LN[92.7688/102.5]/-2 ~= 4.99%

Hope that helps, David

 

[[email protected]]

Perfect, thank you Dave.