Question

Suppose your project is worth $952 with a probability of 0.92 and $523 with a probability of 1-0.92. The appropriate cost of capital is 9.5% for the overall project. If you want to raise $610 today and promise to bond investors a rate of return of 6.6%, what's the expected rate of return of this bond?

Answer 1

Given

Amount of Debt Raised = $610

Promised rate of return to bond investors = 6.6%

Expected Value of bond after one year = 610 * (1 + 0.066) = $650.26

Note that the bond holders are paid the full amount if project worth is higher than the total debt value, and if the project value is lower than the value of debt, then the bondholders are paid the project value itself.

Probability	Project Worth	Debt Value
0.92	$952	$650.26
0.08	$523	$523

Return to bond holders = (debt value – amount of debt raised)/ amount of debt raised

So, for probability of 0.92, the Return to bond holders = ($650.26- $610)/$610 = 0.066 = 6.6%

for probability of 0.08, the Return to bond holders = ($523- $610)/$610 = -0.1426 = -14.26%

Therefore expected return to bond investors = (0.92 * 6.6%) + (0.08 * -14.26%) = 0.0493 = 4.93%

Expected rate of return of this bond = 4.93%