Question

You know that the assets of a firm BIG are today worth 100mil. You reasonably feel that in a year they will be either worth 110mil or 90mil. You also know that a riskless zero coupon bond maturing in one year is offering today a yield of 5%. The firm has issued a zero-coupon bond that matures in one year and has a face value of 100mil.

What should be the value of this corporate bond today? What should be its yield to maturity? What should be the value of the equity of the firm? Can you do a further analysis of this problem? How are the above affected by the yield of the one year zero and the volatility of the asset value?

Answer 1

a. .Face value of zero coupon bond = 100 million

Yield of zero coupon bond maturing in one year = 5%

Since, it is a zero coupon bond, there will not be any coupons issued but only the repayment of the face value on maturity. And these will be issued at a discount since coupon payments are not made.

Thus, Value of the bond today = Face value (to be repaid on maturity which is 1 year)* Discount factor at 5% = 100 million * (1/(1+5%)^1) = 100 million * 0.9524 = 95.24 million

b. Maturity of the zero coupon bond 1 year

Yield to maturity = (Future Value / Value of the bond today -1 ) = (100 milion/95.24 million)-1 = 5%

c. The assets of the firm today are 100 million. Zero coupon bonds has face value of 100 million. Thus, it implies that bond equals the total assets and there are no equity in the firm.

Thus, value of the equity = 0

(Value of the equity typically becomes zero when the firm had accumulated loses eroding its networth fully).

d. Yield impacts the current price of the bond. Yield represent the return expected when the bond is held into maturity. Thus, if the yield increases, the value of the bond comes down and if the yield reduces, the value of the bond now increases.

Assets of the firm today is 100 million and in one year, it will be 110 million or 90 million. If the firm is worth 110 million in 1 year, it implies the firm has generated additional value (earnings in one year) and thus the value of the equity would be 10 million.

Similarly, if the firm is worth 90 million in 1 year, it implies the firm has generated negative value in one year and thus the value of the equity would be negative 10 million .

However, assuming probability of the assets being 110 million or 90 million is equal in one year, there will be no change to the value now and will remain at 100 million (110 million * 50%+90 million * 50%).