1. Assume you buy a $1,000 face value bond with 7 years until maturity, a coupon
ID: 2801976 • Letter: 1
Question
1. Assume you buy a $1,000 face value bond with 7 years until maturity, a coupon rate of 5% paid semiannually, and a yield to maturity of 8%.
A) What is the price of this bond?
B) Assume that the yield to maturity falls to 7% after one year, and the investor decides to sell the bond. What would be the holding period return for the investor?
2. Assume you buy 800 shares of a stock selling for $15 a share, borrowing $4,000 at an interest rate of 6% to help finance the purchase. Your account has a maintenance margin of 40%.
A. At what price would you receive a margin call?
B. If, after one year, the price increased to $20 a share, what would be your rate of return?
Explanation / Answer
1)
A) Price of bond = Interest*PVIFA(r%,n ) + Redemption value*PVIF(r%,nth)
=1000*2.5%*PVIFA(4%,14) + 1000*PVIF(4%,14th year)
=25*10.5631 + 1000*0.5775
=264.08 + 577.5
=841.58
B) Price of bond after one year
=25*PVIFA(3.5%,12) + 1000* PVIF(3.5%,12)
=25*9.6633 + 1000*0.6618
=241.58 + 661.8
=903.38$
Holding period gain = (903.38-841.58) + 25 /841.58
61.8+25/841.58
=86.8/841.58
=10.31%
2) Total price paid = 800*15 = 12000
Borrowed money = 4000 hence margin = 8000$
A) one will receive margin call = when
=(800P-4000)/800P = 0.4
800P-4000 = 320P
480P = 4000
P =8.33$
if price falls below 8.33$ one will require margin call
b) Amount left in equity account after repayment of loan
= (800*20) - 4000 - (4000*6%)
=16000-4000-240
=11760
Return = (11760-8000)/8000
3760/8000
=47%
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