Principal 100000 55839 PV 1 for 10 periods at 6 5583900 Interest 5000 736009

Principal 100000 55839 pv 1 for 10 periods at 6

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Principal: \$100,000 * .55839 (PV \$1 for 10 periods at 6%) = \$55,839.00 Interest: \$5,000 * 7.36009 (PVoA for 10 periods at 6%) = 36,800.45 Price of bond 92,639.45 Now, let’s look what would happen if we had a \$100,000, 5-year, 12% bond. Other similar instruments in the market are selling for 10%. (I flipped the face and market rates for this problem) We know that this bond will sell at a PREMIUM because the face rate (12%) is greater than the market rate (10%). Remember, the interest PAID is \$100,000 * 12% = \$12,000 per year. Given the factors below, which do we use for our pricing formula? The PV of \$1 for 5 periods at 10% is .62092 use this for the principal The PV of \$1 for 5 periods at 12% is .56743 The PVoA of 1 for 5 periods at 10% is 3.79079 use this for the interest The PVoA of 1 for 5 periods at 12% is 3.60478 Assuming the bond pays interest annually , the price of the bond is: Principal \$100,000 * .62092 (PV \$1 for 5, 10%) = 62,092.00 Interest: \$12,000 * 3.79079 (PVoA for 5, 10%) = 45,489.48 Price of bond 107,581.48 Assuming that the bond pays interest semi-annually, we have to adjust the interest payments (rents), time periods and interest rates accordingly. The factors are: The PV of \$1 for 10 periods at 5% is .61391 use this for the principal The PV of \$1 for 10 periods at 6% is .55839 The PVoA of 1 for 10 periods at 5% is 7.72173 use this for the interest The PVoA of 1 for 10 periods at 6% is 7.36009 Since we pay interest semi-annually, the interest paid each period is \$100,000 * 12%/2 = \$6,000 per period.
To price our bond: Principal: \$100,000 * .61391 (PV \$1 for 10 periods, 5%) = 61,391.00 Interest: \$6,000 * 7.72173 (PVoA for 10 periods, 5%) = 46,330.38 Price of bond 107,721.38 AMORTIZATION OF PREMIUM/DISCOUNT When amortizing a discount, we are bringing the bond UP TO its face value. So, each year, the amount amortized is ADDED to the carrying value of the bond from the previous year. When amortizing a premium, we are bringing the bond DOWN TO face value. So, each year, the amount amortized is subtracted from the carrying value of the bond from the previous year. There are two methods of amortization – Effective interest and straight-line. The straight line method is found by taking the amount of premium or discount and dividing it by the number of interest payment periods. This gives us the amount of amortization for the period. The difference between this amount and the interest paid (in cash) is the interest expense for the period. To find the effective interest each period, we multiply the MARKET rate by the carrying value of the bond at the beginning of each period. (The carrying value of the bond is the carrying value from the previous period, plus any discount amortized or less any premium amortized in the given period). Here are some examples (these are from the problems that I sent you in that file): Foreman Company issued \$800,000 of 10%, 20-year bonds on January 1, 2011, at 102. Interest is payable semiannually on July 1 and January 1. Foreman Company uses the straight-line method of amortization for bond premium or discount.

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