Question

Hugh has the choice between investing in a city of heflin bond at 6.60 percent investing in a surething bond at 10.00 percent. assuming that both bonds have the same nontax characteristics and that hugh has a 40 percent marginal tax rate, what interest rate does surething inc., need to offer to make hugh indifferent between investing in the two bonds?

Answer 1

Answer: Surething Inc, needs to issue bonds with 11% interest rate in order to make Hugh indifferent between investing in two bonds.

We arrive at the answer in the following manner:

The City of Helfin bonds are municipal bonds and hence they are tax free. This means that Hugh will get an after - tax return of 6.6%.

The bonds of Surething Inc offering a 10% interest, however are taxed at 40%. So, the current after-tax returns of the bond is:

$After - tax return= Pre- tax return * (1 -tax rate)$

$After-tax return= 0.1 * (1-0.4)$

Current after tax return = 0.06 or 6%

However Hugh will be indifferent to investing in these two bonds only if they offer the same after-tax return of 6.6%.

Given this, we can calculate the indifference rate as follows:

$After - tax return= Pre- tax return * (1 -tax rate)$

$0.066= Pre- tax return * (1 -0.4)$

$\frac{0.066}{0.6}= Pre-tax return$

Pre-tax return = 0.11 or 11%.