BMW Corporation has a bond issue outstanding with an annual coupon rate of 8.2 percent paid...

BMW Corporation has a bond issue outstanding with an annual coupon rate of 8.2 percent paid quarterly and four years remaining until maturity. The par value of the bond is $1,000. Determine the fair present value of the bond if market conditions justify a 12.5 percent, compounded quarterly, required rate of return. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Fair present value: ??

Expert Solution

End of quarter	Cash Flow (8.2/4=2.05% of par value per quarter plus the par value at maturity)	PV of Cash Flow (12.5/4=3.125% discounting)
1	20.5	20.5/(1+3.125/100)¹=19.88
2	20.5	20.5/(1+3.125/100)²=19.28
3	20.5	20.5/(1+3.125/100)³=18.69
4	20.5	20.5/(1+3.125/100)⁴=18.13
5	20.5	20.5/(1+3.125/100)⁵=17.58
6	20.5	20.5/(1+3.125/100)⁶=17.04
7	20.5	20.5/(1+3.125/100)⁷=16.53
8	20.5	20.5/(1+3.125/100)⁸=16.03
9	20.5	20.5/(1+3.125/100)⁹=15.54
10	20.5	20.5/(1+3.125/100)¹⁰=15.07
11	20.5	20.5/(1+3.125/100)¹¹=14.61
12	20.5	20.5/(1+3.125/100)¹²=14.17
13	20.5	20.5/(1+3.125/100)¹³=13.74
14	20.5	20.5/(1+3.125/100)¹⁴=13.32
15	20.5	20.5/(1+3.125/100)¹⁵=12.92
16	20.5 + 1000	20.5/(1+3.125/100)¹⁶+1000/(1+3.125/100)¹⁶=12.53+611.19=623.72

Therefore the fair present value of the bond is the sum of present values of all the cash flows

=$ (19.88+19.28+18.69+18.13+17.58+17.04+16.53+16.03+15.54+15.07+14.61+14.17+13.74+13.32+12.92+623.72)

=$ 866.25

Hence the fair price considering a 12.5% required rate of return, compounded quarterly

jeff jeffy answered 3 months ago

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