Accounting

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11.2
a. Determine the current value of the bond if present market conditions justify a 14 percent required rate of return.

PV = CF^n / (1 +i) ^n
PV = CF n / (1 + i)^4
PV = 70 / (1 + .14) ^4
PV = 70 / (1.14) ^4
PV = 70/ 1.14 + 70/ 1.30 + 70/ 1.48 + 70/ 1.69
PV = 61.40 + 53.85 + 47.30 + 41.42 = $203.97
PV of the par value = 1,000
PV = $203.97 + 1,000 = $1203.97

b. Now, suppose Twin Oaks' four-year bond had semiannual coupon payments. What would be its current value? (Assume a 7 percent semiannual required rate of return. However, the actual rate would be slightly less than 7 percent because a semiannual coupon bond is slightly less risky than an annual coupon bond).

PV = 35/ (1+ i/2) ^n*2

PV = 35/ (1 + .7/2) ^4*2

PV = 35/ (1 +.035)^8

PV = 35/ 1.035 ^8

PV= $240.44

PV of the par value = $1,000 + $240.44 = $1,240.44

c. Assume that Twin Oaks' bond had a semiannual coupon but 20 years remaining to maturity. What is the current value under these conditions? (Again, assume a 7 percent semiannual required rate of return, although the actual rate would probably be greater than 7 percent because of increased price risk).

PV= CFn/ (1 + i/2) ^n*2

PV= 35/ (1+.7/2) ^20*2

PV= 35/ (1.035)^40

PV= $746.26

PV = $1,000 + $746.26

PV of the par value = $1746.26

Thank you for your questions.

(A) 2(1.05)/(1.15-1.05) = $21

(B) 2(1.05)/(1.13-1.05) = $26.25

(C) 2(1.07)/(1.15-1.07) = $26.75
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