Jessie,Inc.has 4-year zero-coupon bonds outstanding,which will pay $1,000 at maturity.The assets are valued at $900,σ = 0.25,r = 0.045,and the company does not pay a dividend.Using a Black-Scholes model,what is the yield on debt?

Question

Quizplus · Accepted Answer

To use the Black-Scholes model to find the yield on debt, we need to find the value of the bond today using the discounted cash flow formula:

Bond Value = $1,000 / (1 + r)^4

where r is the yield on debt.

Using the given values, we can plug in and solve for r:

$900 = $1,000 / (1 + r)^4

(1 + r)^4 = $1,000 / $900
(1 + r)^4 = 1.1111
1 + r = 1.0276
r = 0.0276 = 2.76%

However, this is the annual effective yield, and we're looking for the annual nominal yield. To convert to a nominal yield, we need to multiply by the number of periods per year:

Nominal Yield = 2 * 2.76% = 5.52%

Therefore, the closest answer choice is B, 6.48%.