You are analyzing the cost of debt for a firm. You know that the firm’s 14-year
ID: 2789290 • Letter: Y
Question
You are analyzing the cost of debt for a firm. You know that the firm’s 14-year maturity, 9.75 percent coupon bonds are selling at a price of $885.92. The bonds pay interest semiannually. If these bonds are the only debt outstanding for the firm.
What is the current YTM of the bonds? (Round intermediate calculations to 4 decimal places, e.g. 1.2514 and final answer to 2 decimal places, e.g. 15.25%.)
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You are analyzing the cost of debt for a firm. You know that the firm’s 14-year maturity, 9.75 percent coupon bonds are selling at a price of $885.92. The bonds pay interest semiannually. If these bonds are the only debt outstanding for the firm.
Explanation / Answer
Answer 1.
Approx YTM = (C+ (F-P)/n)/(F+P)/2
Where,
C = Coupon/Interest payment
F = Face Value
P = Price
n = Periods to maturity
So, In this case
Coupon = 9.75% of Face value (which should be 1000) = 97.5 but since it will paid semiannualy and we want Coupon amount for a period i.e. for 6 months. Therefor Coupon amount for 1 period = 97.5/2 = $48.75
F = 1000
P = 885.92 (given)
n (No. of periods) = 14*2 = 28 (no. of 6 months)
Therefor Putting value into the formulla we get =
(48.75+ (1000-885.92)/28)/(1000+885.92)/2 = 5.60% But this is for 6 months
Therefore For 1 year = YTM = 5.6*2 = 11.20%
Answer 2
After Tax Cost of Debt = YTM rate * (100-Tax rate)
=11.20% * (100-30%)
= 7.84%
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