Question 4 Neo purchases a bond issued by the Smith corporation. The bond 8% sem

Question

Question 4 Neo purchases a bond issued by the Smith corporation. The bond 8% semiannual Smit has a face value of $1,000, with coupons, and is callable at the end of the 10th through the 15th years at par. The h corporation sells the bond at the maximum price that guarantees the investor to yield 6% convertible semiannually. If the yield rate is lower than 6%, Neo would rather invest his money in the bank. Determine the price that Neo pays to purchase the bond from Smith corporation. (a) 1248.77 (b) 1198.77 (c) 1148.77 (d) 1098.77 (e) 1048.77

Explanation / Answer

Face Value of Bond = 1000

Coupon Rate = 8% semi-annually

So, periodic coupon payment = 1000 * 8% / 2 =40

YTM = 6% convertible semiannually. So, semi-annual YTM = 6%/2 = 3%

The bond is callable at the end of 10th through 15th year.

As an Investor, Neo should expect the bonds to be called at the end of 10 years and calculate the price he would pay to purchase the bond.

Calculation

The present value of all the periodic coupon payments can be calculated using the formula pf PV of Annuity:

PV = C * ((1-1/(1+r)T)/r) where C = Annuity payment, r = Periodic Interest Rate, T = Number of periods

Here, C = 40, r = 3%, T = 10*2 = 20 (Semi-annual payment for 10 years, so number of payments = 10*2)

So, PV of coupon payments = 40 * ((1-1/(1+3%)20)/3%) = 595.0990 [rounded-off to 4 decimals]

PV of the redemption amount at the end of 10th year = 1000/(1+3%)20 = 553.6758   [rounded-off to 4 decimals]

Price, Neo will pay to purchase the Bond = PV of coupon payments + PV of Redemption Amount
= 595.0990 + 553.6758 = 1148.77 [rounded-off to 2 decimals]

So, the answer will be (c) 1148.77

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