Consider the Leverage Unlimited, Inc., zero coupon bonds of 2016. The bonds were

Question

Consider the Leverage Unlimited, Inc., zero coupon bonds of 2016. The bonds were issued in 1998 for $100. Determine the yield to maturity (to the nearest 1/10 of 1 percent) if the bonds are purchased at th

a. Issue price in 1998. (Note: To avoid a fractional year holding perilod, assume that the issue and maturity dates are at the midpoint - July 1 - of the respective years.)

b. Market price as of July, 1 2012, of $750.

c. Explain why the returns calculated in Parts a and b are different.

Please show how to input the numbers into the formulas needed so I can show my work, please and thank you.

Explanation / Answer

Hi,

Please find the answer as follows:

Part A: With the Use of Formula

Present Value of Bond = Present Value of All Interest Payments + Present Value of Maturity Amount

Present Value of Bond = 100

Present Value of All Interest Payments = 0

Present Value of Maturity Amount = 1000/(1+r)^18

r = Yield to Maturity

100 = 0 (No Interest Payments, since it is a zero coupon bond) + 1000/(1+r)^18

On Solving the above equation we get:

(1+r)^18 = 1000/100

You will have to use logrithms to get r,

18In(1+r) = In(10)

In(1+r) = .1279

r = exp^(.1279) - 1

r = 1.136 - 1 = .136 or 13.6%

Yield to Maturity = 13.6%

Part A: With the Use of Financial Calculator/Excel:

PV = 100 (indicates the issue price of the bond)

FV = 1000 (indicates the future/maturity value of the bond)

Nper = 2016 - 1998 = 18 Years (indicates the period of the bond)

PMT = 0 (no interest payment, since it is a zero value bond)

Yield to Maturity = Rate(Nper,PMT,PV,FV) = Rate(18,0,-100,1000) = 13.6%

Part B: With the Use of Formula:

Present Value of Bond (2012) = Present Value of All Interest Payments + Present Value of Maturity Amount

Present Value of Bond = 750

Present Value of All Interest Payments = 0

Present Value of Maturity Amount = 1000/(1+r)^4

r = Yield to Maturity

750 = 0 (No Interest Payments, since it is a zero coupon bond) + 1000/(1+r)^4

On Solving the above equation we get:

(1+r)^4 = 1000/750

You will have to use logrithms to get r,

4In(1+r) = In(1.33)

In(1+r) = .0719

r = exp^(.0719) - 1

r = 1.0745 - 1 = .0745 or 7.5%

Yield to Maturity = 7.5%

Part B: With the Use of Financial Calculator/Excel:

PV as in 2012 = 750

FV = 1000 (indicates the future/maturity value of the bond)

Nper = 2016 - 2012 = 4 Years (indicates the period of the bond)

PMT = 0 (no interest payment, since it is a zero value bond)

Yield to Maturity = Rate(Nper,PMT,PV,FV) = Rate(4,0,-750,1000) = 7.5%

Part C:

The difference in answers is on account of purchase of bonds at different points of time. A bond with a longer duration will carry a higher risk and therefore, will be expected to yield a higher rate of return (as is evident when bonds are purchased in 1998). On the contrary, bond with lower maturity period will carry a lower risk and according is expected to produce a lower yield to maturity ( as is evident when bonds are purchased in 2012 at the issue price of 750).

Thanks.

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