The Frush Corporation has two different bonds currently outstanding. Bond M has
ID: 2766399 • Letter: T
Question
The Frush Corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $2,300 every six months over the subsequent eight years, and finally pays $2,600 every six months over the last six years. Bond N also has a face value of $20,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. The required return on both these bonds is 12 percent compounded semiannually.
What is the current price of Bond M and Bond N? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
The Frush Corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $2,300 every six months over the subsequent eight years, and finally pays $2,600 every six months over the last six years. Bond N also has a face value of $20,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. The required return on both these bonds is 12 percent compounded semiannually.
Explanation / Answer
Price of Bond M = $$15815.68
Price of Bond N = $ 2,073.34
Bond M
Face Value = 2000
Time to Matuirty = 20 years
Payment schedule
No payments = First 6 years
Payment for Next 8 years = 2300 every six months
Payment for last 6 years = 2600 every six months
Required rate of return = 12%
Present Value of Payment in last 6 years at the beginning of last 6 year period
= 2600*[(1-(1.06^-6*2)/0.06]
= 2600*[(1-0.49696936)/0.06]
= 2600 *0.50303064/0.06
= 2600 * 8.383844
= 21797.9944
Present value of this amount today = 21797.9944 / 1.06^14*2 (20 years – 6 years = 14 years remaining)
= 21797.9944 / 5.11168669
= 4264.344764 ---------(A)
Present value of first annuity payment of 2300 every six months for 8 years at the beginning of 8 years
= 2300 * [(1-(1.06^-8*2)/0.06]
= 2300*[(1-0.3936463)/0.06]
= 2300 * 0.6063537/0.06
= 2300 * 10.105895
= 23243.5585
Present value of the first annuity payment today = 23243.5585 / 1.06^6*2
(first annuity starts 6 years from today)
= 23243.5585 / 2.0121964
= 11551.336475 ------(B)
Present Value of the bond = (A) + (B) = 4264.344764 + 11551.336475 = 15815.681239
Current Price of the Bond = $15815.68 (rounded off)
Bond N
Face Value = 20000
Period = 20 years
Required rate of return = 12%
Current Price / Present Value of the bond = 20000/1.12^20 = 20000 / 9.646293
= 2073.3353 = $ 2,073.34 (rounded off)
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