Sunburn Sunscreen has a zero coupon bond issue outstanding with a $20,000 face value that matures in one year. The current market value of the firm’s assets is $21,700. The standard deviation of the return on the firm’s assets is 38 percent per year, and the annual risk-free rate is 5 per cent per year, compounded continuously. Based on the Black–Scholes model, what is the market value of the firm’s equity and debt?
Cost of Capital
Shareholders and investors who invest into the capital of the firm desire to have a suitable return on their investment funding. The cost of capital reflects what shareholders expect. It is a discount rate for converting expected cash flow into present cash flow.
Capital Structure
Capital structure is the combination of debt and equity employed by an organization in order to take care of its operations. It is an important concept in corporate finance and is expressed in the form of a debt-equity ratio.
Weighted Average Cost of Capital
The Weighted Average Cost of Capital is a tool used for calculating the cost of capital for a firm wherein proportional weightage is assigned to each category of capital. It can also be defined as the average amount that a firm needs to pay its stakeholders and for its security to finance the assets. The most commonly used sources of capital include common stocks, bonds, long-term debts, etc. The increase in weighted average cost of capital is an indicator of a decrease in the valuation of a firm and an increase in its risk.
Equity as an OptionSunburn Sunscreen has a zero coupon bond issue outstanding with a $20,000 face value that matures in one year. The current market value of the firm’s assets is $21,700. The standard deviation of the
Q.How do find the value of N(1) and N(2) from the table? Please explain clearly. In the answer, how did they get the value from the table? Shouldn't the value be N(1) = 0.7054 and N(2) = 0.5596? I am very confused.
In the answer the values are -
N(d1) = .7041
N(d2) = .5621
The answer to this question is attached.
![2. Equity as an Option
We can use the Black-Scholes model to value the equity of a firm. Using the asset
value of $21,700 as the stock price, and the face value of debt of $20,000 as the
exercise price, the value of the firm's equity is:
di = [In($21,700/$20,000) + (.05 + .38²/2) × 1] / (.38 x v1) = .5363
d2 = .5363 – (.38 × v1 ) =
N(d1) = .7041
N(d2) = .5621
Putting these values into the Black-Scholes model, we find the equity value is:
Equity = $21,700(.7041) – ($20,000e-05(1))(.5621)
Equity = $4,585.75
The value of the debt is the firm value minus the value of the equity, so:
Debt = $21,700 – 4,585.75
Debt = $17,114.25](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86997bfb-28ac-4959-a677-70ac8b7f32b8%2Fce16cb67-0ca9-42a0-8345-de7fca588f6a%2Fb1eb9gs_processed.png&w=3840&q=75)
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