FIN 125 Exam 2: Chapter 7 Problems

The Lo Sun Corporation offers a 5.0 percent bond with a current market price of $879.50. The yield to maturity is 6.14 percent. The face value is $1,000. Interest is paid semiannually. How many years until this bond matures?

*Finding maturity of SEMI-ANNUAL* i/YR = (6.14% / 2) = 3.07% PV = -879.50 PMT = (5.0% * 1,000) / 2 = +$25 FV = +1,000 N = 34.62 / 2 = 17.31 years

You purchase a bond with an invoice price of $1,053. The bond has a coupon rate of 5.72 percent, it makes semiannual payments, and there are 4 months to the next coupon payment. The par value is $1,000. What is the clean price of the bond?

*Clean vs. Dirty Price* Invoice means the Dirty Price so we need to subtract the accrued interest to find the answer. Coupon Payment = (5.72% * 1,053) = 28.60 Accrued Interest = 28.60 * (4/6) = 9.53 Clean Price = Invoice Price - Accrued Interest = 1,053 - 9.53 = 1,043.47

Workman Software has 6.4 percent coupon bonds on the market with 18 years to maturity. The bonds make semiannual payments and currently sell for 94.31 percent of par. What is the YTM?

*Find the YTM of SEMI-ANNUAL* N = 36 PV = -(94.31% x 1,000) = -943.10 PMT = (6.40% x 1,000) / 2 = $32 FV = 1,000 i/YR = 6.96%

A bond has a par value of $1,000, a current yield of 6.45 percent, and semiannual coupon payments. The bond is quoted at 95.32. What is the amount of each coupon payment?

*Finding Coupon From Current Yield* Current Yield = *ANNUAL Coupon* / Purchase price [6.45% = annual coupon / (95.32% * $1000)] / 2 = $30.74

A bond that pays interest semiannually has a price of $975.11 and a semiannual coupon payment of $28.25. If the par value is $1,000, what is the current yield?

*Finding Current Yield* Coupon payment = $28.25 * 2 PV = 975.11 Current Yield = ($28.25 * 2/975.11) = 5.79%

There is a zero coupon bond that sells for $4,664.38 and has a par value of $10,000. If the bond has 14 years to maturity, what is the yield to maturity? Assume semiannual compounding

*Finding Interest for Semi-annual Zero Coupon Bond* N = 28 PV = -$4,664.38 FV = $10,000 i/YR = ? -> 2.76% * 2 = 5.52%

Wine and Roses, Inc., offers a bond with a coupon of 5.0 percent with semiannual payments and a yield to maturity of 5.90 percent. The bonds mature in 10 years. What is the market price of a $1,000 face value bond?

*Finding PV of SEMI-ANNUAL*: N = 10 x 2 i/YR = (5.90% / 2) FV = +1,000 PMT = (5.0% x 1,000) / 2 PV = ?

Whatever, Inc., has a bond outstanding with a coupon rate of 5.78 percent and semiannual payments. The yield to maturity is 6.5 percent and the bond matures in 22 years. What is the market price if the bond has a par value of $1,000?

*Finding PV of SEMI-ANNUAL, eyes of the borrower*: N = 44 i/YR = 6.5% / 2 FV = *-1,000* PMT = *-(5.78% * 1,000) / 2 = -28.90* PV = ?

Footsteps Co. has a bond outstanding with a coupon rate of 5.9 percent and annual payments. The bond currently sells for $984.29, matures in 23 years, and has a par value of $1,000. What is the YTM of the bond?

*Finding YTM with ANNUAL, eyes of creditor for this*: N = 23 PV = -984.29 PMT = (0.059 * 1,000) = 59 FV = 1,000 i/YR = 6.03%

An investment had a nominal return of 10.0 percent last year. If the real return on the investment was only 7.6 percent, what was the inflation rate for the year?

*Fisher Effect*: [(1 + 0.100) / (1 + 0.076)] - 1 = 0.0223 or 2.23%

An investment had a nominal return of 10.9 percent last year. The inflation rate was 2.8 percent. What was the real return on the investment?

*Fisher Effect*: [(1 + 0.109) / (1 + 0.028)] - 1 = 0.0788 or 7.88%

You purchase a zero coupon bond with 21 years to maturity and a yield to maturity of 5.53 percent. The bond has a par value of $1,000. What is the implicit interest for the first year? Assume semiannual compounding.

*Implicit Interest* Solving PV for one period and then solving PV for the other and subtracting the values: 1. N = 42 i/YR = (5.53% / 2) FV = 1,000 PV = 318.05 2. N = 40 (2 less periods for a year) i/YR = (5.53% / 2) FV = 1,000 PV = 335.89 Implicit Interest = 335.89 - 318.05 = $17.83

There are zero coupon bonds outstanding that have a YTM of 5.19 percent and mature in 16 years. The bonds have a par value of $10,000. If we assume semiannual compounding, what is the price of the bonds?

*PV of a zero-coupon bond semi-annually* Simply a normal PV problem N = 32 i/YR = (5.19% / 2) FV = 10,000 PV = $4,405.16

Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 7.4 percent, has a YTM of 6.8 percent, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 6.8 percent, has a YTM of 7.4 percent, and also has 13 years to maturity. Assume a par value of $1,000. What is the price of Bond X in 13 Years?

*Semi-annual Present Value* *N = 0* i/YR = 3.40% PMT = (7.40% x 1,000) / 2 = 37 FV = 1,000 PV = $1,000

Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 7.4 percent, has a YTM of 6.8 percent, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 6.8 percent, has a YTM of 7.4 percent, and also has 13 years to maturity. Assume a par value of $1,000. What is the price of Bond X in 12 Years?

*Semi-annual Present Value* *N = 2* i/YR = 3.40% PMT = (7.40% x 1,000) / 2 = 37 FV = 1,000 PV = $1,005.71

Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 7.4 percent, has a YTM of 6.8 percent, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 6.8 percent, has a YTM of 7.4 percent, and also has 13 years to maturity. Assume a par value of $1,000. What is the price of Bond X in 8 Years?

*Semi-annual Present Value* *N = 20* i/YR = 3.40% PMT = (7.40% x 1,000) / 2 = 37 FV = 1,000 PV = $1,025.08

Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 7.4 percent, has a YTM of 6.8 percent, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 6.8 percent, has a YTM of 7.4 percent, and also has 13 years to maturity. Assume a par value of $1,000. What is the price of Bond X in 3 Years?

*Semi-annual Present Value* *N = 20* i/YR = 3.40% PMT = (7.40% x 1,000) / 2 = 37 FV = 1,000 PV = $1,043.03

Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 7.4 percent, has a YTM of 6.8 percent, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 6.8 percent, has a YTM of 7.4 percent, and also has 13 years to maturity. Assume a par value of $1,000. What is the price of Bond X in 1 Year?

*Semi-annual Present Value* *N = 24* i/YR = 3.40% PMT = (7.40% x 1,000) / 2 = 37 FV = 1,000 PV = $,1048.69

Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 7.4 percent, has a YTM of 6.8 percent, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 6.8 percent, has a YTM of 7.4 percent, and also has 13 years to maturity. Assume a par value of $1,000. What is the price of Bond X today?

*Semi-annual Present Value* *N = 26* i/YR = 3.40% PMT = (7.40% x 1,000) / 2 = 37 FV = 1,000 PV = $,1051.24

Crossfade Corp. has a bond with a par value of $2,000 that sells for $1,902.14. The bond has a coupon rate of 6.48 percent and matures in 12 years. If the bond makes semiannual coupon payments, what is the YTM of the bond?

*YTM with SEMI-ANNUAL, eyes of creditor*: N = 24 PV = -1902.14 PMT = +(6.48% x 2,000) / 2 = +64.80 FV = +2,000 i/YR = 3.55% * 2 = 7.09%

A bond has a par value of $1,000, a current yield of 7.31 percent, and semiannual coupon payments. The bond is quoted at 98.05. What is the coupon rate of the bond?

[7.31% = *Annual Coupon* / (98.05% * 1,000)] / 2 = $35.84