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Question:

A firm issues a 4-year semiannual-pay bond with a face value of $10 million and a coupon rate of 10%. The market interest rate is 11% when the bond is issued. The balance sheet liability at the end of the first semiannual period is closest to:

A $9,715,850.
Explaination

The initial liability is the amount received from the creditor, not the par value of the bond.
N = 8; I/Y = 11/2 = 5.5; PMT = 500,000; FV = 10,000,000; CPT -> PV = $9,683,272. The interest expense is the effective interest rate (the market rate at the time of issue) times the balance sheet liability. $9,683,272 x 0.055 = $532,580. The value of the liability will change over time and is a function of the initial liability, the interest expense and the actual cash payments. In this case, it increases by the difference between the interest expense and the actual cash payment: $532,580 -$500,000 = $32,580 + $9,683,272 = $9,715,852. Tip: Knowing that the liability will increase is enough to select choice C without performing this last calculation. Entering N - 7 and solving for PV also produces $9,715,852.