Question

IDENTIFY FORMULAS AND SHOW WORK.

Miller Corporation has a premium bond making semiannual payments. The bond pays an 8 percent coupon, has a YTM of 6 percent, and has a 13 years to maturity. The Modigliani Company has a discount bond making semiannual payments. The bond pays a 6 percent coupon, and has a YTM of 8 percent, and also has a 13 years maturity.

Assume a face value of $1,000 for both bonds. (a) If interest rates remain unchanged, what do you expect the price of these bonds to be 1 year from now? One day before maturity?

(b) Suppose the YTM increases 1 percent for each of the bonds (7 percent and 9 percent respectively). Calculate the Holding Period Yield of the one-year investment for each of the bonds (from today to one year from today).

Note: Holding Period Yield is the total effective annual return for the investor that buys the bond today and sells the bond in one year given the change in interest rates. The return can be decomposed in he income component (current yield) and the capital gain component (capital gain yield).

Answer 1

a]

1 year from now

Miller bond

Price of bond 1 year from now is calculated using PV function in Excel :

rate = 6% / 2 (converting annual YTM into semiannual YTM)

nper = 12 * 2 (12 years left to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 8% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value of bond receivable on maturity)

PV is calculated to be $1,169.36

Modigliani bond

Price of bond 1 year from now is calculated using PV function in Excel :

rate = 8% / 2 (converting annual YTM into semiannual YTM)

nper = 12 * 2 (12 years left to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 6% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value of bond receivable on maturity)

PV is calculated to be $847.53

1 day before maturity

1 day before maturity, the price of bond = face value + 1 semiannual coupon payment

Miller bond = $1000 + ($1000 * 8% / 2) = $1,040

Modigliani bond =   $1000 + ($1000 * 6% / 2) = $1,030

b]

Miller bond

Price of bond today is calculated using PV function in Excel :

rate = 6% / 2 (converting annual YTM into semiannual YTM)

nper = 13 * 2 (13 years left to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 8% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value of bond receivable on maturity)

PV is calculated to be $1,178.77

Price of bond 1 year from now is calculated using PV function in Excel :

rate = 7% / 2 (converting annual YTM into semiannual YTM)

nper = 12 * 2 (12 years left to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 8% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value of bond receivable on maturity)

PV is calculated to be $1,080.29

Holding period yield = (price after 1 year - current price + two semiannual coupon payments) / current price

Holding period yield = (1080.29 - 1178.77 + 40 + 40) / 1178.77 = -1.57%

Modigliani bond

Price of bond today is calculated using PV function in Excel :

rate = 8% / 2 (converting annual YTM into semiannual YTM)

nper = 13 * 2 (13 years left to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 6% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value of bond receivable on maturity)

PV is calculated to be $840.17

Price of bond 1 year from now is calculated using PV function in Excel :

rate = 9% / 2 (converting annual YTM into semiannual YTM)

nper = 12 * 2 (12 years left to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 6% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value of bond receivable on maturity)

PV is calculated to be $782.57

Holding period yield = (price after 1 year - current price + two semiannual coupon payments) / current price

Holding period yield = (782.57 - 840.17 + 30 + 30) / 840.17 = 0.29%