The Metchosin Corporation has two different bonds currently outstanding. Bond M
ID: 2790832 • Letter: T
Question
The Metchosin Corporation has two different bonds currently outstanding. Bond M has a face value of $60,000 and matures in 20 years. The bond makes no payments for the first six years, then pays every six months over the subsequent eight years, and d over thenas a face finally pays $3,000 every six months over the last no coupon compounded six years. Bond N also has a face value of $60,000 and a maturity of 20 years; it makes payments over the life of the bond. The required return on both these bonds is 12 percent semiannually, what is the current price of bond M and bond N? (Do not round intermediate calculations. Round the final answer to 2 decimal places.) Current price Bond M Bond NExplanation / Answer
Current price of the bond is just the present valeu of future cash flows that is coupons and repayment of principal amount
Current Price of Bond M = $2,700(PVIFA6%,16)(PVIF6%,12) + 3,000(PVIFA6%,12)(PVIF6%,28) + 60,000(PVIF6%,40)
=$2,700(10.1059)(0.4870) + 3,000(8.3838)(0.1956) + 60,000(0.0972)
= $13,288.24 + 4919.61+5832 = 24,039.85 or 24,040
Current Price of Bond N = Since there are no coupons, we have to find only the present value of principal repayment after 20 years i.e n=40 (n= no. of periods)
Current price of Bond N = $60,000(PVIF6%,40)
= $60,000(0.0972) = $5832
Note: PVIFA = present value interest factor annuity; PVIF = Present value interest factor
For PVIFA and PVIF, we can refer the present value tables or you can apply the forumulas
1. PVIFA6%,16 = 1 x (1+r)n-1/r (1+r) where r = semi annual rate of interst i.e 6% or 0.06; n = no.of periods i.e 16 in 8 years = 1 x (1+0.06)16-1/0.06(1+0.06)16 = 10.1059
2. PVIF6%,12 = 1/(1+0.06)12 = 0.4970
3. PVIFA6%,12 = 1 x (1+0.06)12 -1/0.06(1+0.06)12
3. PVIF6%,40 = 1/(1+0.06)40 = 0.0972
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