Lance Whittingham IV specializes in buying deep discount bonds. These represent
ID: 2469378 • Letter: L
Question
Lance Whittingham IV specializes in buying deep discount bonds. These represent bonds that are trading at well below par value. He has his eye on a bond issued by the Leisure Time Corporation. The $1,000 par value bond with semiannual payments has 4 percent annual interest and has 18 years remaining to maturity. The current yield to maturity on similar bonds is 8 percent.
What is the current price of the bonds?
By what percent will the price of the bonds increase between now and maturity?
What is the annual compound rate of growth in the value of the bonds? (An approximate answer is acceptable.)
a.
What is the current price of the bonds?
Explanation / Answer
Face value = $1000
Annual Coupon Payment = 4% (Though, coupon payment is done on semiannual basis)
Time = 18 years or 36 semiannual period (n)
YTM = R = 8%
a.
Current price of the bond = present value of the coupon payments + present value of the face value the bond
Current price of the bond = 20*(1-1/(1+R/2)^n)/(R/2) + 1000/(1+R/2)^n
Current price of the bond = 20*(1-1/(1+4%)^36)/.04 + 1000/(1+4%)^36
Current price of the bond = $621.834
b.
Increase in price = Maturity value - Current price =1000 - 621.834 = $378.166
Percentage increase in price = 378.166 / 621.834 =60.81%
c.
Let, annual compounding growth = r
1000 = 621.834*(1+r)^18
1.6081 = (1+r)^18
1.0267^18 = (1+r)^18
r = 2.67%
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